13071 FACTA UNIVERSITATIS Series: Mechanical Engineering Vol. 23, No 3, 2025, pp. 407 - 432 https://doi.org/10.22190/FUME241001052M © 2025 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper INTUITIONISTIC FUZZY MACONT METHOD FOR LOGISTICS 4.0 BASED CIRCULAR ECONOMY INTERESTED REGIONS ASSESSMENT IN THE AGRI-FOOD SECTOR Arunodaya Raj Mishra1, Pratibha Rani2, Dragan Pamucar3,4,5, Ahmad M. Alshamrani6, Adel Fahad Alrasheedi6 1Department of Mathematics, Government College Raigaon, Madhya Pradesh, India 2Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai, Tamil Nadu, India 3Department of Applied Mathematical Science, College of Science and Technology, Korea University, Sejong, Republic of Korea 4Dogus University, Istanbul, Türkiye 5Department of Industrial Eng. & Management, Yuan Ze University, Taoyuan City, Taiwan 6Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh, Saudi Arabia ORCID iDs: Arunodaya Raj Mishra https://orcid.org/0000-0001-9949-5813 Pratibha Rani https://orcid.org/0000-0002-9186-4167 Dragan Pamucar https://orcid.org/0000-0001-8522-1942 Ahmad M. Alshamrani https://orcid.org/0000-0001-7103-8872 Adel Fahad Alrasheedi https://orcid.org/0000-0003-4492-1082 Abstract. This study aims to evaluate and prioritize the key interested regions of Circular Economy (CE) in terms of implementing the industry 4.0 technologies for the performance of logistics activities in the agri-food sector. For this purpose, we introduce a hybrid ranking framework based on Relative Closeness Coefficient (RCC)-based objective weighting model, the RANking COMparison (RANCOM) subjective weighting procedure and the Mixed Aggregation by Comprehensive Normalization Technique (MACONT) with Intuitionistic Fuzzy Information (IFI). In this framework, new IF-score function and an improved distance measure are proposed in the context of IFI to evade the limitations of existing ones. A hybrid IF-RCC-RANCOM-MACONT framework is introduced to prioritize the options over defined criteria. To prove the applicability of introduced approach, it is employed on a case study of circular economy interested regions assessment in the agri-food sector, consisting of five alternatives and nine criteria under the dimensions of sustainability. Sensitivity analysis is shown to highlight the impact of used parameters on the final outcomes. At last, a comparison with extant approaches is made to demonstrate the robustness of obtained results. Received: October 01, 2024 / Accepted December 30, 2024 Corresponding author: Pratibha Rani, Dragan Pamucar Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai- 602105, Tamil Nadu, India Dept. of Applied Mathem. Science, College of Science and Technology, Korea University, Republic of Korea E-mail: pratibha138@gmail.com, dpamucar@gmail.com https://orcid.org/0000-0001-9949-5813 https://orcid.org/0000-0002-9186-4167 https://orcid.org/0000-0001-8522-1942 https://orcid.org/0000-0001-7103-8872 https://orcid.org/0000-0003-4492-1082 mailto:pratibha138@gmail.com 408 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI Key words: Logistics 4.0, Circular economy, Agri-food sector, Intuitionistic fuzzy sets, Distance measure, Score function, MACONT, Multi-criteria decision-making 1. INTRODUCTION Logistics management is the governance of supply chain management (SCM) functions that integrates the activities such as planning, packaging, material handling, warehousing, management of forward and reverse flow of goods, transportation, services and associated information between the point of origin and point of consumption to meet customers’ supplies [1-3]. “Forward logistics (FL)” consisting of a procedure of moving goods from the point of production to end customer. As a counter-part of FL, “reverse Logistics (RL)” refers to the procedure which reverses common flow of raw materials or finished goods along supply chain (SC) [4-8]. The purpose of efficient logistics management is to ensure customer satisfaction, achieve maximum competitiveness and profitability for the business along with the well-planned network of SC, including the end consumer [9, 10]. Both the logistics processes are covered by the term “closed-loop supply chain (CLSC)”, where goods lifecycle management is incorporated with its logistics solutions [11, 12]. In the past decade, the need for a transition towards a circular economy (CE) has been studied by several user groups and industries. The CE concept is defined as an economic system that aims to minimize the environmental and material footprint together with industrial transformation at different levels [13]. Moving towards a CE system offers a chance to bring business profits including advanced competitiveness, resource security, flexible and diverse business models to enable value formation [14, 15]. In the current age of growing resource scarcity, different researchers, policymakers, and business managers have made empirical assessments on the impact of adopting the CE principle, which does not only cover the reverse flow but also manage the forward flow of the SC involving operations of newer materials [16]. As a revolutionary digitalization, logistics 4.0 refers to the implementation of different digital technologies into logistics operations to optimize and streamline the SCM [17-19]. The paradigms of CE and logistics 4.0 offers several opportunities to create more sustainable and effective SC procedure. Food insecurity can lead to significant productivity losses, lesser cognitive facility and reduced work performance. Although, the agri-food sector cannot allow itself to missed the possibilities initiated by the convergence of logistics 4.0 and the CE. In this work, we consider the potentials of employing industry 4.0 (I4.0) for executing the logistics processes in the CE interest regions under the context of agri- food sector. This selection process may also include several DEs, whose opinions may differ and ambiguous. Considering the hesitation levels, knowledge and expertise of DEs, fuzzy set theory (FST) and its generalizations are preferred to handle the incomplete and imprecise information of such type of problems [20-23]. As one of the extensions of FST, the notion of intuitionistic fuzzy set (IFS) [24] has received much attention to deal with ambiguous and vague data. In IFSs, every object is described by the membership grade (MG) and non-membership grade (NG) with their sum is restricted to one. Çelik et al. [25] ensured socio-economic sustainability indicators of medical waste management (MWM). In this regard, they presented a unified approach with the weighting and ranking models and applied for MWM in six hospitals, where the data is given in terms of intuitionistic fuzzy numbers. Asif et al. [26] gave various form Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 409 Hamacher operators to deal with different decision-making problems. Bajaj & Kumar [27] studied a new correlation measure on IFSs and implemented to the pattern recognition, medical diagnosis and clustering problems. Further, an integrated decision support tool has been presented to evaluate the alternatives on IFSs. Majumder et al. [28] gave an IF- multiple criteria decision-making (MCDM) approach for deriving the significance values of criteria. Moreover, they used a unique decision support system to assume a feasibility assessment of solar power plant. Wan et al. [29] integrated IF-best worst method (BWM) with additive consistency. Based on this method, they gave a non-linear programming procedure for solving MCDM problems. Hussain and Ullah [30] presented a model using Sugeno-Weber aggregation operators on to solve real-life MCDM problem. Şahin et al. [31] used two methods, geographic information measure and IFSs-based method to evaluate and rank the locations for solar-wind power plant establishment in Netherlands. Considering the multiple criteria/factors and decision experts (DEs), choosing and prioritizing an appropriate CE interested regions in agri-food sector can be defined as a multiple criteria group decision-making (MCGDM) problem [32, 33]. To handle the MCDM problems, Wen et al. [34] initiated novel idea of Mixed Aggregation by COmprehensive Normalization Technique (MACONT) approach to execute and make three normalized assessment degrees into a single normalized degree to estimate the deviations of original data. The process of classical MACONT approach includes (i) different normalization techniques for finding the normalized performance values of options with respect to considered evaluation criteria; (ii) aggregating three normalized performance values; (iii) determining the virtual reference option; (iv) using two arithmetic and geometric operators to determine distances between each option and reference option and finding the subordinate comprehensive scores of options; (v) deriving final comprehensive degrees of options and accordingly prioritize the options. Truong & Li [35] proposed an integrated MACONT approach based on the Dempster-Shafer doctrine and e-STEP procedure for multiple attribute tradeoff assessment in transportation budget sharing. With the integration of different strategies, Nguyen et al. [36] developed an improved MACONT method and compared with existing normalization-based techniques. Apart from these studies, several other applications of MACONT method have been established in the literature [37-39]. Further, RANking COMparison (RANCOM) is a pairwise comparison structure using a three-value measure [40]. The RANCOM is considered for less experienced DEs, is categorized by strength to conflicts in criterion associations, is intuitive, time-efficient for dealing complex MCGDM problems, and handles with imprecisions in evaluations of DEs while certifying high repeatability of outcomes. The RANCOM comprises finding criterion preferences, constructing a matrix of ranking comparison (MAC) with pairwise assessments, computing summed criteria weights (SCW), and estimating overall weights of different criteria. As per authors’ knowledge, there is no work which introduces IF-modified RCC- RANCOM-MACONT method integrating an IF-score function-based DEs’ weighting procedure, the IF-modified relative closeness coefficient (RCC)-based objective weighting model, the IF-RANCOM subjective weighting procedure and the MACONT framework on IFI. The main contributions and novelties of the work are given as ▪ New IF-score function is developed to evade the drawbacks of existent IF-score functions (Xu [41] Xu et al. [42], Zeng et al. [43], Feng et al. [44]). ▪ New IF-distance measure is introduced to conquer the advantages of prior developed IF-distances (Shen et al. [45], Tripathi et al. [46], Wu et al. [47], Ejegwa & Agbetayo [48], Li et al. [49]). 410 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI ▪ A hybrid ranking approach is proposed by integrating the IF-score function-based experts’ weighting model, an objective-subjective criteria weight-determining model and the MACONT method with IFI ▪ To exemplify the feasibility and efficacy of introduced ranking framework, it is implemented to a case study of prioritizing the CE interested regions areas in agri- food sector. Rest part of this paper is organized in the following way. Section 2 confers the background of the work. Section 3 first develops new IF-score function and its effectiveness over the existent IF-score functions. Further, this section proposes a distance measure for IFSs and discusses its properties. Comparative study is performed to verify the consistency and rationality of introduced measure. Section 4 introduces a hybrid multi-criteria evaluation method, namely IF- modified RCC-RANCOM-MACONT. Section 5 implements the proposed method for prioritizing CE interested regions in the agri-food sector. Moreover, this section conducts sensitivity and comparative investigations to validate the determined outcomes. Finally, Section 6 confers the conclusions of the paper. 2. NEW SCORE FUNCTION AND DISTANCE MEASURE FOR IFSS This part of the study first presents the concepts of IFSs. To show comparison diverse IFNs, new IF-score function is introduced to reveal the effectiveness over the existing IF- score functions. Next, a modified IF-distance measure is introduced to describe dissimilarity on IFSs and further compared with previously introduced measures. 2.1 Preliminaries Here, we present the fundamental definitions used in this work. Definition 2.1 [24]. Let V = {v1, v2, …, vt} be the fixed universe of discourse. In 1986, Atanassov [24] presented the mathematical definition of IFS B on V = {v1, v2, …, vt}, given by Eq. (1) as ( )( ) , ( ), ( ) , = l B l B l lB v v v v V (1) where μB: V → [0, 1] and vB: V → [0, 1] symbolize MG and NG of a member vl ∈ V to B, respectively, satisfying 0 ≤ μB(vl) + vB(vl) ≤ 1. The hesitancy degree is defined as πB (vl)= 1- μB(vl) - vB(vl), for each vl ∈ V. The term “(μB(vl), νB(vl))” is termed as intuitionistic fuzzy number (IFN) and indicated in this study as ψ = (μ, ν), where μ, ν ∈ [0, 1] and 0 ≤ μ + v ≤ 1. Definition 2.2 [41]. For any two IFNs ψ1 = (μ1, ν1) and ψ2 = (μ2, ν2), some basic operations are discussed as a) ( )1 1 1, ,  =c b) ( ) ( )( )1 2 1 2 1 2, ,     =   c) ( ) ( )( )1 2 1 2 1 2, ,     =   d) ( )1 2 1 2 1 2 1 2, ,        = + − e) ( )1 2 1 2 1 2 1 2, ,        = + − f) ( ) ( )( )1 1 11 1 , , 0,       = − −  g) ( ) ( )( )1 1 1,1 1 , 0.     = − −  Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 411 Definition 2.3 [41]. For an IFN ψ = (μ, ν), IF-score function and IF-accuracy function are defined via Eq. (2) and Eq. (3), respectively. ( ) ( ), = −XS where ( )  1,1 ,  −XS ( ) ,  = +A where ( )  0,1 . A Xu et al. [42] gave the normalized version of IF-score function and defined as follows: ( ) ( ) 1 1 , 2  = −+XWS where ( )  0,1 . XWS Further, Feng et al. [44] presented the generalized version of IF-score function and defined as follows: For p > 1, ( ) 1 (1 ) , 2     + − =     p p p FZS where ( )  0,1 . FZS In recent times, Zeng et al. [43] developed the logarithmic function-based IF-score function and defined as follows: 2log (2 ) ( ) (1 ) , 100 ZCS        − − = − − − −  where ( )  0,1 . ZCS Definition 2.4 [41]. To aggregate the IFNs, Xu [41] introduced an “IF-weighted average (IFWA)” operator and an “IF-weighted geometric (IFWG)” operator on IFNs ψl = (μl, νl), l = 1, 2, …, t, and given as ( ) ( ) ( )1 2 1 1 , ,..., 1 1 , ,     = =   = − −      l l t t w w t l l l l IFWA (2) ( ) ( ) ( )1 2 1 1 , ,..., ,1 1 ,     = =   = − −      l l t t w w t l l l l IFWG (3) where, the set {w1, w2, …, wt} denotes the weights of IFNs ψl = (μl, νl), l = 1, 2, …, t, and wl lies between 0 and 1, and w1+w2+…+wt =1. Definition 2.5 [50]. Let A, B, H IFSs(V). A real-valued function d: IFSs(V)×IFSs(V) → [0,1] is said to be a distance measure for IFSs if it holds the following requirements: (i). 0 ≤ d (A, B) ≤ 1, (ii). d (A, B) if and only if A = B, (iii). d (A, B) = d (B, A), (iv). If ,A B H  then d (A, B) ≤ d (A, H) and d (B, H) ≤ d (A, H). 2.2. New Score Function for IFN To rank the IFNs, Xu [41] defined the concept of score and accuracy functions. Further, many improved score functions have been introduced in the context of IFNs, while some of the well-known IF-score functions, presented in Definition 2.3 (Xu [41], Xu et al. [42], 412 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI Zeng et al. [43], Feng et al. [44]) present unreasonable results during the comparison of different pairs of IFNs. To this aim, this paper proposes a new score function for an IFN. For an IFN ψ = (μ, ν), we present a new IF-score function, defined as ( ) ( ) ( ) ( ) 11 1 1 1 . 2( 1) 2          − + − = + − + + −  +   S e e e (4) Using Eq. (4), we discuss the given axioms: Property 2.1. The IF-score function S (ψ) given in Eq. (4), increases monotonically w. r. t. μ and decreases monotonically w. r. t. ν. Property 2.2. The developed IF-score function fulfils S((0, 1)) = 0 and S((1, 0)) = 1. Property 2.3. Let ψ1 = (μ1, ν1) and ψ2 = (μ2, ν2) be the IFNs. If μ1 > μ2 and ν1 < ν2, then S(ψ1) > S(ψ2). The following example shows the drawbacks of existent IF-score functions Example 2.1. Let us suppose a pair of IFNs, given as ψ1 = (0.5, 0.5) and ψ2 = (0.3, 0.3). To compare these IFNs, we apply the proposed and existing IF-score functions and obtain the results as follows. It is clear that existent IF-score functions by Xu [41], Xu et al. [42] and Feng et al. [44] are unable to discriminate these two different IFNs as SX(ψ1) = 0 = SX(ψ2), SXW(ψ1) = 0.5 = SXW(ψ2) and SFZ(ψ1) = 0.5 = SFZ(ψ2) (p = 1), while the proposed score function (4) obtains the result as S(ψ1) = 0.341 and S(ψ2) = 0.318. Thus, ψ1> ψ2. Example 2.2. Consider that ψ1 = (0.7, 0.3) and ψ2 = (0.6, 0.2) are two IFNs. The score functions by Xu [41], Xu et al. [42], Zeng et al. [43] and Feng et al. [44] are unable to make difference between given IFNs as SX(ψ1) = 0.4 = SX(ψ2), SXW(ψ1) = 0.7 = SXW(ψ2), SZC(ψ1) = 0.4 = SZC(ψ2) SZC(ψ1) = 0.4 = SZC(ψ2) and SFZ(ψ1) = 0.7 = SFZ(ψ2) (p > 1), while the proposed IF-score function gives a reasonable result, which as S(ψ1) = 0.484 and S(ψ2) = 0.505. Thus, ψ1 < ψ2. It demonstrates the usefulness of developed IF-score function over several extant functions [41-44]. 2.3. New Distance Measure for IFSs To quantify the dissimilarity between IFSs, the concept of distance measure has been proposed by Szmidt & Kacprzyk [51]. In the past decade, several IF-distance measures have been introduced with wider perspectives, while some of them (Shen et al. [45], Tripathi et al. [46], Wu et al. [47], Ejegwa & Agbetayo [48], Li et al. [49]) present counter- intuitive results in the measurement of dissimilarity between IFSs. For E, G IFSs(V), we develop a modified distance measure for describing the dissimilarity between IFSs A and B:      (   ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) min ( ), ( ) min ( ), ( ) max ( ), ( ) 1 ( , ) max ( ), ( ) mi7 A l B l A l B l A l B l A l B l B l A l A l B l B l A l A l B l B l A l A l B l B l A l A l B l B l A l v v v v v v v v v v v v v v v v v v v v v v v v d A B v vt                           − + − + − + − + − + − + − + = − +    (     )  (   )     ) 1 . n ( ), ( ) min ( ), ( ) max ( ), ( ) max ( ), ( ) min ( ), ( ) min ( ), ( ) max ( ), ( ) max ( ), ( ) t A l B l B l A li A l B l B l A l A l B l B l A l A l B l B l A l v v v v v v v v v v v v v v v v                 =             −    + − +     − + −    (5) Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 413 Theorem 2.1. The function d (A, B), presented by Eq. (5), is a valid distance measure for IFSs. Proof. To prove this theorem, we need to verify the properties (i)-(iv) of Definition 2.5. (i). For any two IFSs A and B, we know that 0 ≤ μA(vl), μB(vl) ≤ 1, 0 ≤ vA(vl), vB(vl) ≤ 1 and 0 ≤ πA(vl), πB(vl) ≤ 1, for each vl ∈ V. It implies that each term of Eq. (5) ranges between 0 and 1 and thus, 0 ≤ d (A, B) ≤ 1. (ii). Consider that d (A, B) = 0. As each term of Eq. (5) lies between 0 and 1, therefore, from our assumption, d (A, B) = 0 is only possible when every term of Eq. (5) should be equal to zero. It implies that μA(vl) = μB(vl), vA(vl) = vB(vl) and πA(vl) = πB(vl), for each vl ∈ V. Hence, A = B. Conversely, if A = B, then it is obvious from Eq. (5) that d (A, B) = 0. Hence, d (A, B) = 0 iff A = B. (iii). It is clear from the property of modulus and IFS, so we have omitted the proof. (iv). For any three IFSs A, B and H on a finite universe of discourse V = {v1, v2, …, vt}, if , A B H then 0 ≤ μA(vl) ≤ μB(vl) ≤ μH(vl) ≤1, 0 ≤ vH(vl) ≤ vB(vl) ≤ vA(vl) ≤1 and 0 ≤ πH(vl) ≤ πB(vl) ≤ πA(vl) ≤1. It implies that for each vl ∈V, we have ( ) ( ) ( ) ( ) ,   −  −A l B l A l H lv v v v ( ) ( ) ( ) ( ) ,   −  −A l B l A l H lv v v v ( ) ( ) ( ) ( ) ,   −  −A l B l A l H lv v v v     0 min ( ), ( ) min ( ), ( ) min ( ),      A l H l A l B l B lv v v v v   ( ) min ( ), ( ) 1,    A l H l A lv v v      0 min ( ), ( ) min ( ), ( ) min ( ), ( )       A l H l A l B l B l A lv v v v v v  min ( ), ( ) 1,  H l A lv v        0 min ( ), ( ) min ( ), ( ) min ( ), ( ) min ( ), ( ) 1,           A l H l A l B l B l A l H l A lv v v v v v v v        0 max ( ), ( ) max ( ), ( ) max ( ), ( ) max ( ), ( ) 1,           A l H l A l B l B l A l H l A lv v v v v v v v        0 max ( ), ( ) max ( ), ( ) max ( ), ( ) max ( ), ( ) 1,           A l H l A l B l B l A l H l A lv v v v v v v v        0 max ( ), ( ) max ( ), ( ) max ( ), ( ) max ( ), ( ) 1,           A l H l A l B l B l A l H l A lv v v v v v v v Also, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ,       −  −A l H l H l A l A l B l B l A lv v v v v v v v ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ,       −  −A l H l H l A l A l B l B l A lv v v v v v v v ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , .       −  −  A l H l H l A l A l B l B l A l lv v v v v v v v v V Hence, it shows that d (A, B) ≤ d (A, H). Similarly, we can prove that d (B, H) ≤ d (A, H). Example 2.3. Let us assume some pairs of IFSs, which are Case-1: {A= (0.7, 0.3), B = (0, 0)}, Case-2: {A = (0.4, 0.6), B = (0, 0)}, Case-3: {A = (0.5, 0.45), B = (0.55, 0.4)}, Case-4: {A = (0.45, 0.4), B = (0.45, 0.32)}, Case-5: {A = (0.3, 0.41), B = (0.5, 0.344)} and Case-6: {A = (0.41, 0.2), B = (0.22,0.28)}. To compare each pair of IFSs, the proposed and existent IF-distance measures are applied to the given six pairs of IFSs. Table 1 presents the required computational results. From Table 1, we can observe the unreasonable results of existent measures, while the proposed IF-distance measure successfully obtains the discrimination between all the given pairs of IFSs. 414 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI Table 1 Comparative results of developed and extant IF-distance measures (Highlighted texts denote counter-intuitive results) Measures Case-1 {(v1,0.7, 0.3)} {(v1,0,0)} Case-2 {(v1,0.4, 0.6)} {(v1,0,0)} Case-3 {(v1,0.5, 0.45)} {(v1,0.55, 0.4)} Case-4 {(v1,0.45, 0.4)} {(v1,0.45, 0.32)} Case-5 {(v1,0.3, 0.41)} {(v1,0.5, 0.344)} Case-6 {(v1,0.41, 0.2)} {(v1, 0.22, 0.28)} Shen et al. [45] 0.533 -0.033 0.05 0.026 0.152 0.155 Shen et al. [45] 0.539 0.51 0.052 0.052 0.159 0.192 Tripathi et al. [46] 0.582 0.684 0.001 0.005 0.013 0.013 Wu et al. [47] 0.351 0.306 0.05 0.046 0.139 0.139 Ejegwa & Agbetayo [48] 1.0 1.0 0.001 0.006 0.024 0.021 Li et al. [49] 1.0 1.0 0.036 0.081 0.156 0.146 Proposed measure 0.9143 0.8857 0.0504 0.0851 0.2051 0.1913 3. AN INTEGRATED IF-MODIFIED RCC-RANCOM-MACONT METHOD FOR MCGDM PROBLEMS In this section, we propose an improved version of MACONT approach that incorporates the DEs’ weight-determining procedure, the IFWA operator, and an integrated objective-subjective weighting model with IFI. This approach firstly computes the DEs’ weights through a collective IF-score function and rank reciprocal model and further calculates an aggregated IF-decision matrix (A-IFDM). Next, the weights of criteria are computed with the combination of objective and subjective weights via IF-modified RCC and IF-RANCOM models, respectively. Finally, the stepwise procedure of MACONT approach is presented to solve the MCDM problems with IFI. Fig. 1 presents the pictorial representation of the proposed framework. Fig. 1 Flow diagram of the IF-modified RCC-RANCOM-MACONT framework Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 415 This method involves subsequent procedural steps: Step 1: Construction of linguistic decision-matrix (LDM). For an IFI-based MCGDM problem, let F = {F1, F2, ..., Fm} be a defined set of options over considered criteria set R = {R1, R2, ..., Rn}. To make an optimal decision, a committee of ‘p’ DEs B = {B1, B2, ..., Bp} is invited to provide their opinion regarding the assessment of each option over defined criteria. Let X = (xij (k))m×n be an LDM, where xij (k) denotes the linguistic performance value of an option Fj over a criterion Rj presented by kth DE. Further, the LDM is converted into IF-decision matrix (IFDM) using Likert scale. Step 2: Computing the weights of DEs. For determining the DEs’ weights, let us consider a linguistic significance degree of each DE based on their skills, expertise and knowledge. Let Bk = (μk, νk) be an IF-significance degree of kth DE, then the weight of kth DE is estimated as follows, where k = 1, 2, 3, ..., p. Step 2.1: Using developed IF-score function, a normalized assessment rating of kth DE is calculated, where k = 1, 2, 3, ..., p. ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 2 1 1 1 2 .                 − − =  + − + − + + −       + − + − + + −      =  k k k k k k k k p k k k k k k k k k e e k e e a (6) Step 2.2: Estimate the rank of each DE using proposed IF-score rating and estimate the rank (rk) of each expert. Then, rank-based performance rating of each expert using the rank reciprocal weight of DE is estimated through Eq. (7) as 1 1 , 1,2,..., . (1/ ) r k k t k k r a k p r = = =  (7) Step 2.3: Based on the combination of Eq. (6) and Eq. (7) by means of a parameter ‘α’, we present the following formula to derive the overall weight of kth DE, given by Eq. (8). ( ) (1 )( ), 1,2,..., ,r k k ka a k p  = + − = (8) where α [0,1] denotes the expert weighting strategy coefficient for assigning significance degree to each DE. Moreover, λk denotes the weight vector of DEs’ set B = {B1, B1, …, Bp} with λk belongs to [0,1] and λ1 + λ2 +…+ λp = 1. Step 3: Determine the A-IFDM. In this step, all individual opinions of DEs are collected through to obtain the combined performance degree of each option over defined criteria. To this aim, we use IFWA (or IFWG) operator to create an A-IFDM ( ) ( , ),ij m n ij ijX x  = = where (1) (2) ( ) (1) (2) ( )( , ) , ,..., or , ,..., .( ) ( ) k k p p ij ij ij ij ij ij ij ij ijx xF x x x xI WA IFW xG  = = (9) Step 4: Determination of criteria weights by IF-modified RCC-RANCOM model During the procedure of MCDM, weight of criterion is an important aspect for the experts. In the present work, we propose new weighting model with the combination of objective weight using IF-modified RCC tool and subjective weight by IF-RANCOM tool 416 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI with IFI. We discuss an integrated procedure based on the combination of IF-modified RCC and IF-RANCOM models. Case I: Objective weighting through the IF-modified RCC model. This approach involves subsequent steps: Step 4a: Determine the positive distance matrix (PDM) ( , )ijd x + on an aggregated IFN ijx and IF-positive ideal rating (IF-PIR) ρ+ through Eq. (10). ( )                     1 , min , min , max , max , 7 min , min , max , max , min , min ,                                                           + + + + + + + + + + + + + + + + + + + + − + − + − + − + − + −  = + − + −     + − + −    + −  ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij d x     , max , max ,      + +                          + −    ij ij (10) where ( , )ij ij ijx  = and ( , ) (1,0).     + + + = = Compute the negative distance matrix (NDM) ( , )ijd x − on an aggregated IFN ijx and IF-negative ideal rating (IF-NIR) ρ- via Eq. (11). ( )                     1 , min , min , max , max , 7 min , min , max , max , min , min ,                                                           − − − − − − − − − − − − − − − − − − − − − + − + − + − + − + −  = + − + −     + − + −    + −  ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij ij d x     , max , max ,      − −                          + −    ij ij (11) wherein ( , )ij ij ijx  = and ( , ) (0,1).     − − − = = Step 4b: Using Eq. (10)-Eq. (11), we make a relative closeness-decision matrix (RC- DM) ψ = (βj)1×n, wherein ( , ) , ( , ) ( , ) ij j ij ij D x D x D x     − − + = + (12) and ( 1 1 ( , ) ( , )ij jD x d x m  − −= 2 3( , ) ( , )j jd x d x − −+ + )... ( , ) ,mjd x −+ ( 1 1 ( , ) ( , )ij jD x d x m  + += 2 3( , ) ( , )j jd x d x + ++ + )... ( , ) ,mjd x ++ j = 1, 2, …, n. Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 417 Step 4c: Finding the objective weight (wj o) from Eq. (13) as 1 ,   = =  jo j n jj w j = 1, 2, …, n. (13) Case II: Subjective weight of criteria by IF-RANCOM approach. This approach includes subsequent procedure as Step 4d: Linguistic values of criteria for expert panels are defined and changed into IFNs. We create an aggregated matrix to evaluate the performance of each criterion using Eq. (2). Step 4e: With the use of proposed IF-score function, we find an IF-score value of each aggregated IFN for each criterion and form a column matrix Ω = (ηj)1×n, j = 1, 2, …, n, where ( ) ( ) ( ) 1 11 1 1 , 2( 1) 2          − + −  = + − + + −  +   j j j j j j j j je e e (14) Step 4f: Considering the IF-score ratings, we estimate the preference order of defined criteria. Step 4g: Based on the pairwise assessment of criteria, create a ranking comparison matrix (RCM) C = (θlj)n×n, j = 1, 2, …, n, as 1 2 1 11 11 1 2 21 22 2 1 2 ,                =       n n n lj n n n nn R R R R R R where ( ) ( ) ( ) ( ) ( ) ( ) 1, , 0.5, , 0, .      = =   j l lj j l j l if S R S R if S R S R if S R S R (15) Here, the comparison result is presented by δij. Step 4h: Determination of summed criteria weight (SCW) of criteria as 1 , = = n j lj t Q j = 1, 2, …, n. (16) Step 4i: Finding the subjective weight of criteria as 1 , = =  js j n jj Q w Q j = 1, 2, …, n. (17) Case III: Calculation of combined weight of criteria by IF-modified RCC-RANCOM model. In this process, we integrate objective and subjective weights obtained through IF- modified RCC and IF-RANCOM models, respectively. Thus, the combined weighting formula is defined as (1 ) ,o s j j jw w w = + − j = 1, 2, …, n. (18) wherein γ [0,1] is weighting precision coefficient. 418 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI Step 5: Normalize an A-IFDM. In this step, the normalized A-IFDM (NA-IFDM) U = (ԑij)m×n from IF-score value of A- IFDM ( ) nij mZ x  = is calculated by the normalization techniques, given as follows: Step 5.1. This process abolishes the dimensions of criteria with linear sum-based procedure. Thus, the linear NA-IFDM U(1) = (ԑij (1))m×n is created by Eq. (19), where ( ) ( ) ( ) 11 1 ( ) ( ) , , 1 ( ) 1 ( ) , , m ij ij j b i ij m ij ij j n i x x R R x x R R  = =    =       (19) where Rb and Rn symbolize benefit and cost-type of criteria, respectively. Step 5.2. This process uses the max operator and finds the normalized extended assessment matrix, i.e., NA-IFDM U(2) = (ԑij (2))m×n using Eq. (20), where ( ) ( ) ( ) ( )( ) 2 ( ) max ( ) , , 1 ( ) max 1 ( ) , , ij i F ij j b ij ij i F ij j n x x R R x x R R       =   (20) where F denotes the set of alternatives. Step 5.3. This process utilizes the max-mix operator and gets the normalized extended assessment matrix, i.e., NA-IFDM U(3) = (ԑij (3))m×n via Eq. (21), where ( )3 ( ) min ( ) , , max ( ) min ( ) max ( ) ( ) , . max ( ) min ( ) ij i F ij j b i F ij i F ij ij i F ij ij j n i F ij i F ij x x R R x x x x R R x x        −  − =  −   − (21) Step 5.4. Computation of overall normalized assessment matrix. Combining the aforesaid normalized values by means of two parameters α and β, the averaged NA-IFDM U = (ԑij)m×n is computed, where ԑij is an IF-score value obtained using the following expression: ( ) ( ) ( )1 2 3 (1 ) ,ij ij ij ij     = + + − − (22) where ԑij denotes the averaged NA-PF-DM. where α ∈ [0, 1], β ∈ [0, 1] and these two balanced coefficients are estimated by DEs. In this work, we consider α = β = 1/3. Step 6: Evaluation of reference/average solution matrix (ASM). The reference/average solution matrix is calculated, where the reference value ςj is given by Eq. (23) as 1 1 ( ), m j ij i m   = =  j = 1, 2, …, n. (23) Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 419 Step 7: Calculate the subordinate scores for each alternative. This step computes the subordinate scores (pi (1) and pi (2)) of ith alternative by means of the distance between each option and the reference value, where i = 1, 2, …, m. Here, we combine the arithmetic and geometric weighted operators for combining distances on each alternative and ASM in relation to all criteria. ( )(1) 1 1 1 ( ) ( ) 1 , ( ) j j n w n j ijt i j ij j n w j ij js p w         = = =  −   = − + −   −       (24) From Eq. (24), it is combined best and worst performance of options over defined criteria. Here, t (t = 1, 2, . . ., n) represents the part of criteria that holds ԑij < ςj, and s (s = 1, 2, . . ., n) represents the part of criteria that holds ԑij > ςj. In addition, ϑ (0 ≤ ϑ ≤ 1) denotes the preference parameter. If expert considers comprehensive performance of options, then higher rating of ϑ is taken, whereas expert considers individual performance of options, then smaller rating of ϑ is taken. ( ) ( )(2) max ( ) (1 )min ( ) ,i j ij j j ij j jj p w w     = − + − − (25) where i = 1, 2, …, m and j = 1, 2, …, n. ϕ (0 ≤ ϕ ≤ 1) is preference parameter. If the DEs consider the best performance of options, then higher rating of ϕ is taken, whereas DEs consider worst performance of options, then smaller rating of ϕ is taken. Step 8: Computation of final comprehensive score (FCS) for each option. In accordance with subordinate scores (pi (1) and pi (2)) of ith alternative, the FCS of ith alternative is calculated by Eq. (26), where i = 1, 2, …, m. (1) (2) (1) 2 (2) 2 1 1 1 . 2 ( ) ( ) i i i m m i ii i p p p p p = =    = +        (26) For the precision and consistency of outcomes, we need to utilize normalization procedure to certify that proportions of subordinate scores pi (1) and pi (2) are identical. Since values of pi (1) and pi (2) may be negative, therefore, we implement vector normalization procedure, given in Eq. (26). Step 9: On the basis of decreasing values of FCS (pi), i = 1, 2, …, m, prioritize the options. Higher the FCS (pi) determines the best option. 4. EXPERIMENTAL RESULTS This section first implements the proposed IF-modified RCC-RANCOM-MACONT method on a case study of CE interest areas evaluation problem in the agri-food sector. Further, sensitivity and comparative discussions are provided to test the validity of obtained results. 420 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI 4.1. Case Study: Assessment of CE Interested Regions in the Agri-food Sector Here, we present a case study related to CE interested regions assessment in the agri- food sector. By utilizing the proposed framework, we recognize CE interested regions that contribute to the sustainability perspectives of CE scheme in the agri-food sector. For this purpose, some CE areas of interest are taken for evaluation, which are Resource efficiency (F1), Digital transformation (F2), Circular business model (F3), Supply chain management (F4), Product life cycle management (F5). To collect the data, we have conducted online and offline meetings with the DEs. Next, a committee is formed consisting of four DEs, who are having expertise in the agricultural sustainability, I4.0, CE and logistics management. Based on the discussion with experts’ committee and analysis of the relevant literature, nine criteria are taken to evaluate the CE areas of interest in agri-food sector and specified in Table 2. Table 2 Different types of sustainability criteria (Krstic et al. [15], Verdouw et al. [19]) for assessing CE interested regions in agri-food sector Dimensions Criteria Description Economic Implementation costs (R1) It comprises all the costs associated with learning how to use the technology and adapting it for specific purposes, purchasing equipment, software development, training of employees, etc. Operational costs (R2) It refers to the costs related to logistics activities including ordering, packing, supply, collection, storage, shipping, etc. Material value preservation (R3) It refers to the degree of preservation of the value of materials to minimize its value degradation and maximize its residual value, and consequently increase its utilization, life cycle, and the overall value. Social Health (R4) It refers the degree of impact of logistics activities on the health of people. Safety (R5) It refers to improve safety culture throughout the logistics network. Labor market (R6) It considers the positive impact of CE interest area on the labor market. Environmental Waste reduction (R7) It considers the role of the CE area of interest to waste reduction. Emissions reduction (R8) It considers the role of the CE interest area to the reduction of emissions. Energy resource preservation (R9) It refers the degree of preservation of non-renewable and renewable energy resources. The implementation of IF-modified RCC-RANCOM-MACONT is discussed as follows. Step 1: To assess the CE interested regions concerning the taken evaluation criteria, we adopt Table 3 from Tripathi et al. [52], which represents LVs and their corresponding IFNs. The DEs are asked to present the importance rating of alternatives using Table 3. Next, different opinions of four DEs are collected regarding the performance of each alternative area and created a LDM with regard to each criterion, and presented in Table 5. Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 421 Table 3 LVs and corresponding IFNs for assessing CE interested regions in agri-food sector LVs IFNs Extremely high (EH) (0.95, 0.05) Very very high (VVH) (0.85, 0.1) Very high (VH) (0.8, 0.15) High (H) (0.7, 0.2) Moderate high (MH) (0.6, 0.3) Medium (M) (0.5, 0.4) Moderate low (ML) (0.4, 0.5) Low (L) (0.3,0.6) Very low (VL) (0.2, 0.7) Very very low (VVL) (0.1, 0.8) Extremely low (EL) (0.05, 0.95) Table 4 Linguistic decision opinions for assessing CE interested regions in agri-food sector F1 F2 F3 F4 F5 R1 (VVL,ML,L,M) (VL,L,ML,ML) (EL,VL,L,L) (M,L,L,VL) (ML,EL,L,VL) R2 (L,VL,ML,L) (VL,ML,VL,M) (VL,VL,VL,ML) (VVL,ML,L,ML) (L,ML,VL,VL) R3 (MH,L,ML,H) (ML,ML,H,H) (L,VVH,M,M) (M,H,MH,VVH) (L,VVH,ML,H) R4 (VH,M,H,ML) (MH,H,VH,ML) (M,VH,M,ML) (ML,VVH,M,H) (VH,L,MH,M) R5 (ML,M,H,MH) (H,L,MH,MH) (VL,H,MH,M) (H,VVH,H,M) (M,MH,VH,VH) R6 (M,ML,VVH,H) (H,M,ML,VVH) (ML,ML,H,VH) (MH,M,M,H) (MH,H,MH,M) R7 (M,MH,ML,MH) (MH,MH,H,VH) (ML,M,EH,H) (M,MH,ML,H) (H,M,H,MH) R8 (H,ML,VVH,ML) (VH,M,ML,MH) (L,ML,MH,MH) (M,H,M,VH) (M,H,MH,VH) R9 (M,H,MH,M) (L,MH,MH,M) (H,MH,M,VVH) (VVH,H,M,H) (MH,VH,VH,M) Step 2: With the utilization of Table 2 and Table 3, the linguistic significance ratings of DEs are assigned as per their skills, expertise and knowledge and given in Table 4. From Eq. (6)-Eq. (8), weight of expert is calculated and mentioned in Table 5. Table 5 Weight of DEs for assessing CE interested regions in agri-food sector DEs B1 B2 B3 B4 LVs VH VVH VH EH ak 0.228 0.252 0.228 0.291 ak r 0.138 0.241 0.138 0.483 λk 0.183 0.247 0.183 0.387 Step 3: To obtain the group decision opinion regarding the performance of each CE interested regions, we use Eq. (9) to create an A-IFDM in Table 6. Step 4: For determining an objective weight of indicators using IF-modified RCC model, the first step is to measure PDM and NDM. Based on Eq. (10), we find PDM ( , )ijd x + between an aggregated element ijx and IF-IS ρ+ = (1, 0), given as 0.674, 0.658, 0.341, 0.371, 0.357, 0.331, 0.334, 0.356 and 0.332. Next, we calculate the NDM ( , )ijd x − between an aggregated element ijx and IF-AIS ρ- = (0, 1) through Eq. (11), and presented as 0.366, 0.386, 0.699, 0.668, 422 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI 0.684, 0.709, 0.704, 0.682 and 0.706. The RC-DM is derived via Eq. (12) and given as β1 = 0.352, β2 = 0.37, β3 = 0.672, β4 = 0.643, β5 = 0.657, β6 = 0.682, β7 = 0.678, β8 = 0.657 and β9 = 0.68. From Eq. (13), an objective weight of criteria is estimated as wj o = (0.0653, 0.0686, 0.1246, 0.1193, 0.1219, 0.1265, 0.1258, 0.1219, 0.1261). To find subjective weight of each criterion, an IF-RANCOM tool is used. In the following, each expert presents his/her views concerning assessment of each considered criterion and changed into an aggregated IFN using Eq. (2). Next, the score values of criterion are determined via Eq. (14) and accordingly ranked them. Table 7 presents an IF- score value and preference of each criterion, respectively. Table 6 Aggregated IFDM to identify the most potential CE interest areas in the agri-food sector Criteria F1 F2 F3 F4 F5 R1 (0.381, 0.517) (0.343, 0.556) (0.235, 0.678) (0.307, 0.591) (0.227, 0.69) R2 (0.297, 0.603) (0.379, 0.519) (0.284, 0.615) (0.335, 0.563) (0.273, 0.626) R3 (0.557, 0.334) (0.596, 0.297) (0.605, 0.306) (0.734, 0.187) (0.665, 0.244) R4 (0.587, 0.321) (0.616, 0.291) (0.572, 0.342) (0.685, 0.226) (0.559, 0.35) R5 (0.568, 0.328) (0.564, 0.33) (0.539, 0.354) (0.692, 0.22) (0.719, 0.213) R6 (0.656, 0.251) (0.705, 0.215) (0.655, 0.265) (0.606, 0.29) (0.594, 0.303) R7 (0.551, 0.347) (0.710, 0.213) (0.722, 0.218) (0.598, 0.297) (0.620, 0.278) R8 (0.59, 0.315) (0.599, 0.311) (0.51, 0.386) (0.691, 0.231) (0.703, 0.219) R9 (0.577, 0.32) (0.517, 0.381) (0.73, 0.192) (0.71, 0.2) (0.676, 0.249) Table 7 An aggregated IFN and preferences of criteria for assessing CE interested regions in agri-food sector Criteria B1 B2 B3 B4 Aggregated IFN Crisp value Rank R1 VVH M ML L (0.528, 0.378) 0.391 9 R2 VH H M ML (0.6, 0.307) 0.452 8 R3 VH M H M (0.615, 0.294) 0.464 7 R4 MH ML VH VH (0.702, 0.229) 0.535 3 R5 L M H VVH (0.696, 0.222) 0.536 1.5 R6 H MH M VH (0.698, 0.225) 0.536 1.5 R7 L VH ML H (0.64, 0.269) 0.487 6 R8 M H VVH MH (0.676, 0.234) 0.521 5 R9 MH VH M H (0.686, 0.228) 0.529 4 Next, an RCM is constructed using Eq. (15). In accordance with an RCM, the SCWs are computed using Eq. (16). Lastly, we obtain subjective weight of criteria with Eq. (17). Table 8 presents the required computational steps of the IF-RANCOM model. By utilizing Eq. (18), the combined weight of criteria is computed as a sum of γ multiplied by objective weight of and the complement of γ i.e., (1 − γ) multiplied by the subjective weight of criteria. For γ = 0.5 combined weight of criteria is estimated and presented as wj = (0.0388, 0.0528, 0.0932, 0.1399, 0.1597, 0.162, 0.1061, 0.1165, 0.131). Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 423 Table 8 Results of IF-RANCOM model for assessing CE interested regions in the agri- food sector Criteria RCM Qj wj s R1 R2 R3 R4 R5 R6 R7 R8 R9 R1 0.5 0 0 0 0 0 0 0 0 0.5 0.0123 R2 1 0.5 0 0 0 0 0 0 0 1.5 0.037 R3 1 1 0.5 0 0 0 0 0 0 2.5 0.0617 R4 1 1 1 0.5 0 0 1 1 1 6.5 0.1605 R5 1 1 1 1 0.5 0.5 1 1 1 8 0.1975 R6 1 1 1 1 0.5 0.5 1 1 1 8 0.1975 R7 1 1 1 0 0 0 0.5 0 0 3.5 0.0864 R8 1 1 1 0 0 0 1 0.5 0 4.5 0.1111 R9 1 1 1 0 0 0 1 1 0.5 5.5 0.1358 Next, Fig. 2 exhibits the significance values of considered criteria for assessing CE interested regions in the agri-food sector. Labor market (R6) (0.162) is the most significant criterion, safety (R5) (0.1597) is the second most significant criterion, health (R4) (0.1399) is third, energy resource preservation (R9) (0.131) is fourth and emissions reduction (R8) (0.1165) is fifth most vital criteria for assessing CE interested regions in the agri-food sector. Fig. 2 Weights of considered criteria for CE interested regions in agri-food sector Step 5: From Eq. (19)-Eq. (22) and Table 6, we determine the first, second, third and averaged normalized A-IFDM, and presented in Tables 9 and 10. For averaged NA-IFDM, we took α = β = 1/3. Step 6: Based on Table 10 and Eq. (23), we calculate reference/average solution matrix F0 = (ςj)1×9 and rating ςj, (j = 1, 2, …, 9) of options over each criterion as follows: ς1 = 0.5131, ς2 = 0.5709, ς3 = 0.4809, ς4 = 0.4691, ς5 = 0.4956, ς6 = 0.511, ς7 = 0.5436, ς8 = 0.5383 and ς9 = 0.5474. 424 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI Table 9 First and second normalized A-IFDM for assessing CE interested regions in agri- food sector First Normalization Second Normalization F1 F2 F3 F4 F5 F1 F2 F3 F4 F5 R1 0.154 0.1698 0.2404 0.188 0.2483 0.619 0.684 0.968 0.7558 1.0 R2 0.208 0.1659 0.2159 0.186 0.2239 0.929 0.741 0.964 0.8316 1.0 R3 0.175 0.1881 0.1881 0.238 0.2114 0.733 0.791 0.791 1.0 0.888 R4 0.193 0.2047 0.1867 0.233 0.1827 0.832 0.881 0.803 1.0 0.786 R5 0.183 0.1814 0.1726 0.228 0.2353 0.776 0.771 0.734 0.9695 1.0 R6 0.205 0.2218 0.2018 0.188 0.1835 0.924 1.0 0.91 0.8480 0.827 R7 0.169 0.2245 0.2256 0.187 0.194 0.751 0.995 1.0 0.8268 0.86 R8 0.189 0.1916 0.1623 0.226 0.231 0.82 0.83 0.703 0.9776 1.0 R9 0.177 0.1568 0.2315 0.226 0.2087 0.765 0.677 1.0 0.9754 0.902 Table 10 Third and combined normalized A-IFDM for assessing CE interested regions in agri-food sector Third Normalization Combined Normalization F1 F2 F3 F4 F5 F1 F2 F3 F4 F5 R1 0.0 0.248 0.946 0.475 1.0 0.258 0.367 0.718 0.473 0.749 R2 0.782 0.0 0.894 0.42 1.0 0.64 0.302 0.692 0.479 0.741 R3 0.0 0.215 0.215 1.0 0.582 0.303 0.398 0.398 0.746 0.561 R4 0.214 0.442 0.079 1.0 0.0 0.413 0.509 0.356 0.744 0.323 R5 0.158 0.141 0.0 0.886 1.0 0.372 0.365 0.302 0.694 0.745 R6 0.558 1.0 0.477 0.121 0.0 0.562 0.741 0.529 0.386 0.337 R7 0.0 0.979 1.0 0.305 0.438 0.307 0.733 0.742 0.44 0.497 R8 0.393 0.427 0.0 0.925 1.0 0.467 0.483 0.288 0.709 0.744 R9 0.273 0.0 1.0 0.924 0.695 0.405 0.278 0.744 0.708 0.602 Step 7: From Eq. (24)-Eq. (25) and Table 10, we compute two subordinate scores pi (1) and pi (2), i = 1, 2, 3, 4, 5, of each option (for ϑ = 0.5 and ϕ = 0.5) as p1 (1) = 0.1288, p2 (1) = 0.3409, p3 (1) = 0.6275, p4 (1) = 0.5826, p5 (1) = 0.6728, p1 (2) = -0.0084, p2 (2) = 0.001, p3 (2) = -0.0026, p4 (2) = 0.0091 and p5 (2) = 0.0058. Step 8: Based on Eq. (26), the final comprehensive score (FCS) pi, i = 1, 2, 3, 4, 5, of each CE interest area is computed as p1 = -0.2451, p2 = 0.1835, p3 = 0.1814, p4 = 0.5909 and p5 = 0.5026. Step 9: Rank the alternatives based on obtained FCSs p1 = -0.2451, p2 = 0.1835, p3 = 0.1814, p4 = 0.5909 and p5 = 0.5026. Thus, “Supply chain management (F4) is the most potential CE interested regions contribute to the sustainability development of CE structure in agri-food sector and the prioritization ordering of CE interested regions is F4 F5 F2 F3 F1. 4.2. Sensitivity Investigation This section analyses the impacts of criteria weighting parameter on the final results. To this aim, we present the following cases Case I (Objective weight shuffling): Considering the IF-modified RCC model in place of integrated IF-modified RCC-RANCOM, i.e., we are taking γ = 1.0 in Eq. (18) to assess the CE interested regions in the agri-food sector. Using an IF-modified RCC tool, the FCSs Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 425 of CE interest areas are calculated and presented as p1 = -0.3258, p2 = 0.0425, p3 = 0.1808, p4 = 0.5079 and p5 = 0.4703. Corresponding to decreasing ratings of FCSs, the ranking order of CE interested regions as F4 F5 F2 F3 F1, and the “supply chain management (F4)” is the most potential area among a set of CE regions of interest with respect to nine criteria. Case II (Subjective weight shuffling): This case obtains the FCSs of CE interested regions in agri-food sector by taking subjective weight instead of combined objective- subjective weight of indicators, i.e., we are putting γ = 0.0 in Eq. (18). Using the subjective weighting IF-RANCOM method, the FCSs of CE interested regions in agri-food sector are computed and given as p1 = -0.163, p2 = 0.3142, p3 = 0.0898, p4 = 0.6017 and p5 = 0.4847. Thus, the prioritization order of considered CE interested regions in the agri-food sector is F4 F5 F2 F3 F1, and the “supply chain management (F4)” is the most suitable choice in relation to given evaluation criteria. Case III (Integrated weight shuffling): Considering the combined IF-modified RCC- RANCOM approach, i.e., γ = 0.5 in Eq. (18), the FCSs of CE interested regions in agri- food sector are calculated as p1 = -0.2451, p2 = 0.1835, p3 = 0.1814, p4 = 0.5909 and p5 = 0.5026. By means of decreasing values of FCSs, the prioritization order of CE interested regions in agri-food sector is F4 F5 F2 F3 F1 and hence, “supply chain management (F4)” is the most optimal choice for the given data set. Fig. 3 present required outcomes in relation to the weighting factor (γ). Fig. 3 Variation of FCSs of CE interested regions w.r.t. different values of factor (γ) 4.3. Comparative Study This subsection performs comparative study to analyze rationality of proposed ranking approach in comparison with existing IF-MCDM models, given by Mardani et al.’s IF- COPRAS [53], Komal’s WASPAS method [54], Qin et al.’s IF-TOPSIS model [55] and 426 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI Tripathi et al.’s IF-CoCoSo [52]. To this aim, we have applied these extant methods on aforesaid case study of SEP sites selection problem. 4.3.1. IF-COPRAS Method Using the IF-COPRAS [53] on abovementioned case study of CE interested regions assessment, we first compute the maximization and minimization indices, which are denoted as si and ti, respectively. The computed values are s1 = (0.554, 0.347), s2 = (0.586, 0.320), s3 = (0.590, 0.323), s4 = (0.639, 0.268), s5 = (0.616, 0.297), t1 = (0.554, 0.347), t2 = (0.068, 0.911), t3 = (0.090, 0.885), t4 = (0.075, 0.902) and t5 = (0.093, 0.882). With the use of score function (Xu et al. [42]), the score values of maximization and minimization indices are computed as SXW (s1) = 0.604, SXW (s2) = 0.633, SXW (s3) = 0.633, SXW (s4) = 0.686, SXW (s1) = 0.659, SXW (t1) = 0.085, SXW (t2) = 0.078, SXW (t3) = 0.103, SXW (t4) = 0.087 and SXW (t5) = 0.106. Further, relative degree (RD) of each interested region is obtained as 0.3505, 0.3695, 0.3571, 0.3906 and 0.369, and finally, a UD of alternative is estimated as 89.75%, 94.6%, 91.43%, 100.00% and 94.48%. Corresponding to the decreasing ratings of UDs, prioritization of CE interested regions in the agri-food sector is 4 2 5 3 1F F F F F and thus, “supply chain management (F4)” is the best region of interest among the set of five CE interested regions in agri-food sector. 4.3.2. IF-WASPAS Method By applying IF-WASPAS method [54] on the aforesaid case study, the additive importance (ci (1)) using weighting sum model is computed as c1 (1) = (0.587, 0.313), c2 (1) = (0.614, 0.292), c3 (1) = (0.627, 0.286), c4 (1) = (0.666, 0.242) and c5 (1) = (0.652, 0.262). Next, the multiplicative importance (ci (2)) using weighted product model is determined as c1 (2) = (0.585, 0.316), c2 (2) = (0.604, 0.300), c3 (2) = (0.614, 0.296), c4 (2) = (0.66, 0.247) and c5 (2) = (0.645, 0.267). Using Xu et al.’s score function (Xu et al. [42]) the score values of additive and multiplicative importance values are calculated and shown as SXW (c1 (1)) 0.637, SXW (c2 (1)) = 0.661, SXW (c3 (1)) = 0.67, SXW (c4 (1)) = 0.712, SXW (c5 (1)) = 0.695, SXW (c1 (2)) = 0.635, SXW (c2 (2)) = 0.652, SXW (c3 (2)) = 0.659, SXW (c4 (2)) = 0.707 and SXW (c5 (2)) = 0.689. Lastly, total significance of each CE interest area is estimated as the arithmetic mean of additive and multiplicative significance values and given as 0.6358, 0.6564, 0.6647, 0.7096 and 0.6919. Thus, the ranking order of CE interested regions in agri-food sector is 4 5 3 2 1F F F F F and the “supply chain management (F4)” is the best choice for considered data set. 4.3.3. IF-TOPSIS Method By applying IF-TOPSIS method [55] on abovementioned case study of CE interested regions assessment in agri-food sector, we compute the best and worst values from A- IFDM and obtains as ϕj + = {(0.227, 0.690), (0.273, 0.626), (0.734, 0.187), (0.685, 0.226), (0.719, 0.213), (0.705, 0.215), (0.722, 0.218), (0.703, 0.219), (0.730, 0.192)} and ϕj + = {(0.381, 0.517), (0.379, 0.519), (0.557, 0.334), (0.559, 0.350), (0.539, 0.354), (0.594, 0.303), (0.551, 0.347), (0.510, 0.386), (0.517, 0.381)}. Using the similarity measure, relative closeness rating (RCR) of each CE interested region is estimated as 0.2504, 0.3849, 0.4524, 0.7242 and 0.6278, respectively. Hence, the preference order of CE interested Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 427 regions in agri-food sector is 4 5 3 2 1F F F F F and “supply chain management (F4)” is the best choice among a set of five CE interested regions in agri-food sector. Fig. 4 presents the acquired ranking results by the proposed and extant IF-MCDM methods. As per the obtained results, we found that the preference ranks of CE interest areas by the developed IF-modified RCC-RANCOM-MACONT approach is slightly different from the Mardani et al.’s IF-COPRAS [53], Komal’s WASPAS method [54], Qin et al.’s IF-TOPSIS model [55] and Tripathi et al.’s IF-CoCoSo [52], while the most suitable choice “Supply chain management (F4)” is the same by all the IF-MCDM models. From Fig. 5, the Spearman's rank correlation coefficient (SRCC) is higher than 0.9 for each existing approach with the developed ranking framework. Moreover, the WS-coefficient (Sałabun and Urbaniak [56]) is are higher than 0.85 for each existing approach with the developed ranking framework. The benefit of WS-coefficient describes the similarity degree of preference order of options, which illustrates the consistency of prioritization of CE interested regions in agri-food sector, is high (Mishra et al. [57], Biswas et al. [58], Jafar et al. [59], Ullah and Shah [60]). Accordingly, it can be observed that there is very robust association between prioritization outcomes. Also, the generalization and flexibility discussed by the developed IF-modified RCC-RANCOM-MACONT framework are lacking in the existing methods. Fig. 4 Ranking orders of CE interested regions in the agri-food sector by different IF- MCDM models 428 A. R. MISHRA, P. RANI, D. PAMUCAR, A. M. ALSHAMRANI, A. F. ALRASHEEDI Fig. 5 Variation of SRCC and WS-coefficient of the proposed method with different existing approaches 4.3.4. IF-CoCoSo Method This model first computes the additive and multiplicative importance of alternatives, which are similar as IF-WASPAS model [54]. Based on additive and multiplicative importance, the relative compromise ratings are determined as t1 (1) = 0.1893, t2 (1) = 0.1955, t3 (1) = 0.1979, t4 (1) = 0.2113, t5 (1) = 0.206, t1 (2) = 0.7773, t2 (2) = 0.8026, t3 (2) = 0.8127, t4 (2) = 0.8676, t5 (2) = 0.8459, t1 (3) = 0.8959, t2 (3) = 0.925, t3 (3) = 0.9367, t4 (3) =1.0 and t5 (3) = 0.975. Finally, the overall compromise ratings of five CE interested regions in agri-food sector are estimated and given as 0.5649, 0.5832, 0.5906, 0.6305 and 0.6147, respectively. Based on decreasing ratings of overall compromise ratings, Thus, the ranking order of CE interested regions in agri-food sector is 4 5 3 2 1F F F F F and “supply chain management (F4)” is the best interested region among a set of five CE interested regions in agri-food sector. Next, we present the advantages of developed IF-modified RCC-RANCOM-MACONT over the existing IF-MCDM models as follows: ▪ The developed IF-modified RCC-RANCOM-MACONT model utilizes new IF-score function, which avoids shortcomings of extant IF-score functions (Xu [41], Xu et al. [42], Zeng et al. [43], Feng et al. [44]). ▪ The proposed method uses new IF-distance measure, which overcomes drawbacks of extant IF-distance measures (Shen et al. [45], Tripathi et al. [46], Wu et al. [47], Ejegwa and Agbetayo [48], Li et al. [49]). The developed distance measure is implemented to compute distance matrix in criteria weighting procedure and further employed to determine the deviation from the normalized weighted evaluation values of alternatives to the reference point. ▪ The introduced model calculates the DEs’ weights through new score function and rank reciprocal-based weighting procedure, while Qin et al.’s IF-TOPSIS [55] and Komal’s IF-WASPAS [54] ignores the significance weight of DEs in the procedure of group decision-making. ▪ The proposed model computes weight of indicators through a collective objective- subjective weighting procedure combining the IF-modified RCC and the IF-RANCOM models for objective and subjective weights of indicators, which does not only estimate weight of indicators with given data but also involve the DEs’ opinions during the criteria weighting procedure. Intuitionistic Fuzzy MACONT Method for Logistics 4.0 based Circular Economy... 429 5. CONCLUSION This paper aimed to develop a ranking framework for identifying the CE interested regions which are most affected by implementing the I4.0 technologies during the assessment of logistics process in agri-food sector. To this aim, we have assessed the performance of five CE interest areas including Resource efficiency, Digital transformation, Circular business model, Supply chain management, Product life cycle management with respect to nine criteria under the three dimensions of sustainability. In this framework, we have derived the weights of involved DEs using an integrated score function and rank reciprocal-based procedure. In the following, new IF-score function has been developed on IFSs with its efficiency over existing ones. Next, the group decision opinions have been aggregated into a single opinion regarding the performance value of each CE interest area on the basis of given criteria. Further, the criteria weights have been computed with integrated IF-modified RCC- RANCOM approach in which objective weight has been derived from IF-modified RCC tool, while the subjective weights have determined via IF-RANCOM procedure. To do so, new IF-distance measure has been given for IFSs with its efficiency over existing distance measures. Finally, a stepwise procedure of IF-modified RCC-RANCOM-MACONT methodology has been presented to rank the five CE interested regions in agri-food sector, which proves its effectiveness and practicality. The acquired result shows that a region “supply chain management” has highest final comprehensive score among a set of five CE interested regions over economic, social and environmental aspects of sustainability. Sensitivity assessment has been conducted to see the effect of criteria weighting coefficient on the final result. Lastly, a comparison with extant approaches has been made to test the effectiveness and robustness of proposed ranking framework. This paper has some limitations, which are i) the developed IF-modified RCC- RANCOM-MACONT approach does not replicate the way to find the importance rating of DEs to determine the weight of DEs, and ii) One of key limitation of proposed method is its computational procedure, which is the outcomes of executing the modified RCC, RANCOM and MACONT approaches using the proposed IF-distance measure, IF-score function to estimate subordinate comprehensive scores of options. Further, deriving final comprehensive degrees of options and determine the prioritization the options. This complexity of IF-modified RCC-RANCOM-MACONT is a potentially protective characteristic for implementing by diverse DEs. In future studies, the IF-modified RCC- RANCOM-MACONT framework can be extended with several MCGDM models such as stochastic identification of weights (SITW), reference ideal method (RIM), characteristic object method (COMET), stable preference ordering towards ideal solution (SPOTIS), and so on. The developed IF-modified RCC-RANCOM-MACONT method can be extended with diverse uncertain environments, such as q-ROF-rough sets, linear Diphantine fuzzy, type-2 fuzzy sets, Pythagorean hypersoft sets and different types of linguistic term sets. In future, we can develop new methodologies to solve the interactive CE interested regions assessment in agri-food sector. FUNDING: This research was conducted under a project titled “Ongoing Research Funding program”, funded by King Saud University, Riyadh, Saudi Arabia under grant number (ORF-2025-533). 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