Plane Thermoelastic Waves in Infinite Half-Space Caused Decision Making: Applications in Management and Engineering Vol. 1, Number 1, 2018, pp. 82-96 ISSN: 2560-6018 DOI: https://doi.org/10.31181/dmame180182v * Corresponding author. E-mail addresses: zeljkostevic88@yahoo.com (Ž. Stević) ** An earlier version of this paper was presented at the 1st International Conference on Management, Engineering and Environment – “ICMNEE 2017” (Fazlollahtabar et al., 2017). A ROUGH MULTICRITERIA APPROACH FOR EVALUATION OF THE SUPPLIER CRITERIA IN AUTOMOTIVE INDUSTRY Marko Vasiljević1, Hamed Fazlollahtabar2, Željko Stević1*, Slavko Vesković3 1 University of East Sarajevo, Faculty of Transport and Traffic Engineering Doboj, Bosnia and Herzegovina 2 Department of Industrial Engineering, School of Engineering, Damghan Univeristy, Damghan , Iran 3 University of Belgrade, Faculty of Transport and Traffic Engineering, Serbia Received: 25 December 2018; Accepted: 29 January 2018; Published: 15 March 2018. Original scientific paper Abstract. Ensuring costs reduction and increasing competitiveness and satisfaction of end users are the goals of each participant in the supply chain. Taking into account these goals, the paper proposes methodology for defining the most important criteria for suppliers’ evaluation. From a set of twenty established criteria, i.e. four sets of criteria: finances, logistics, quality and communication and business including its sub-criteria, we have allocated the most important ones for supplier selection. Analytic Hierarchy Process (AHP) based on rough numbers is presented to determine the weight of each evaluation criterion. For the criteria evaluation we have used knowledge from the expert in this field. The efficacy of the proposed evaluation methodology is demonstrated through its application to the company producing metal washers for the automotive industry. Next a sensitivity analysis is carried out in order to show the stability of the model. For checking stability the AHP method in conventional form is used in combination with fuzzy logic. Key words: Rough AHP, Supplier Criteria, Fuzzy AHP, Logistics, Quality. 1. Introduction One of the most important strategic issues in logistics procurement according to Stević, (2017c) is a correct and optimal supplier selection, which enables an increase of market competitiveness. The importance of an adequate supplier selection was recognized at the beginning of the last decade of the 20th century when Davis (1993) emphasized that the failure of suppliers to fulfill the promises and expectations regarding delivery is one of the three main sources of uncertainty plaguing the mailto:veskolukovac@yahoo.com A rough multicriteria approach for evaluation of the supplier criteria in automotive industry 83 supply chain. Kagnicioglu (2016) considers that the supplier selection is a critical procurement activity in the supply chain management because of the crucial role that the supplier characteristics play regarding price, quality, delivery and service in achieving the objectives of the supply chain. Van Weele (2009) points out that a healthy relationship with the suppliers can improve the financial position in a short term and so can a competitive strategy over a long period of time. Today the company must strive to enlarge the quality of product itself so that the end user is satisfied with provided services, which would make him a loyal user. Due to the above mentioned, it is necessary, during the first phase of logistics, i.e. purchasing logistics, to commit good evaluation and choice of the supplier, which can largely influence the forming of the product’s final price; thus, it can, in this way, accomplish a significant effect in the complete supply chain. It is possible to accomplish the above mentioned if the evaluation is done on the basis of a multi- criteria decision-making that includes a large number of criteria as well as an expert’s estimation of their relative significance (Stević et al. 2016). This paper is structured as follows. Section 2 shows the fundamentals of a rough set theory, operations with rough numbers and rough Analytic Hierarchy Process. Section 3 makes up the body of the paper: it gives a practical example besides showing results of the proposed model. Section 4 presents a sensitivity analysis. This section also gives discussion and model stability. Section 5 presents conclusions before the paper ends with a list of references. 2. Methods 2.1. A rough set theory Due to the complexity and uncertainty of numerous real indicators in the process of multi-criteria decision-making, as well as the occurrence of the ambiguity of human thinking, there are difficulties in presenting information about the attributes of decisions through accurate (precise) numerical values. These uncertainties and ambiguities are commonly exploited through application of rough numbers (Song et al., 2014; Zhu et al., 2015). In addition to the fuzzy theory, a very suitable tool for the treatment of uncertainty without any impact of subjectivism is a rough set theory, which was first introduced in (Pawlak, 1982). From the beginning until today, the theory of rough sets has evolved through solving many problems by using rough sets (Khoo & Chai, 2001; Chai & Liu, 2014; Nauman et al. 2016; Liang et al. 2017; Pamučar et al. 2017a) and through the use of rough numbers as in (Tiwari et al., 2016; Shidpour et al., 2016; Stević et al., 2017b; 2017d; 2017e). In the theory of rough sets only the internal knowledge is used, i.e. operational data, and there is no need to rely on the models of assumptions. In other words, in the application of rough sets, instead of various additional/external parameters, we use exclusively the structure of the data provided (Duntsch et al., 1997). In rough sets the measurement of uncertainty is based on the uncertainty that is already contained in the data (Khoo & Chai, 2001). This leads to objective indicators that are contained in the data. In addition, the theory of rough sets is suitable for application in the sets that are characterized by a small number of data, and for which statistical methods are not suitable (Pawlak, 1991). Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96 84 2.2. Operations with rough numbers In the rough set theory, any vague concept can be represented as a pair of precise concepts based on the lower and upper approximations (Pawlak, 1991) as shown in Figure 1. Figure 1. Basic notions of the rough set theory (Stević et al., 2017a) Let’s U be a universe containing all objects and X be a random object from U . Then we assume that there exists set build with k classes representing DMs preferences, ( ) q Apr J 1 2 ( , ,..., ) k R J J J with condition 1 2 ,..., k J J J   . Then, , , 1 q X U J R q k     lower approximation , upper approximation ( ) q Apr J and boundary interval ( ) q Bnd J are determined, respectively, as follows:  ( ) / ( )q qApr J X U R X J   (1)  ( ) / ( )q qApr J X U R X J   (2)      ( ) / ( ) / ( ) / ( )q q q qBnd J X U R X J X U R X J X U R X J        (3) The object can be presented with rough number (RN) defined with lower limit ( ) q Lim J and upper limit ( ) q Lim J , respectively: 1 ( ) ( ) ( ) q q L Lim J R X X Apr J M   (4) 1 ( ) ( ) ( ) q q U Lim J R X X Apr J M   (5) where L M and U M represent the sum of objects contained in the lower and upper object approximation of q J , respectively. Obviously, the lower limit and upper limit denote the mean value of elements included in the lower approximation and upper approximation, respectively. Their difference is defined as rough boundary interval (𝐼𝑅𝐵𝑛𝑑(𝐺𝑞)): 𝐼𝑅𝐵𝑛𝑑(𝐺𝑞) = 𝐿𝑖𝑚(𝐺𝑞) − 𝐿𝑖𝑚(𝐺𝑞) (7) Operation for two rough numbers 𝑅𝑁(𝛼) = [𝐿𝑖𝑚(𝛼), 𝐿𝑖𝑚(𝛼)] and 𝑅𝑁(𝛽) = [𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛽)] according to (Zhai et al., 2009) are: A rough multicriteria approach for evaluation of the supplier criteria in automotive industry 85 Addition (+) of two rough numbers (𝛼) and (𝛽) 𝑅𝑁(𝛼) + 𝑅𝑁(𝛽) = [𝐿𝑖𝑚(𝛼) + 𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛼) + 𝐿𝑖𝑚(𝛽)] (8) Subtraction (-) of two rough numbers (𝛼) and (𝛽) 𝑅𝑁(𝛼) − 𝑅𝑁(𝛽) = [𝐿𝑖𝑚(𝛼) − 𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛼) − 𝐿𝑖𝑚(𝛽)] (9) Multiplication (×) of two rough numbers (𝛼) and (𝛽) 𝑅𝑁(𝛼) × 𝑅𝑁(𝛽) = [𝐿𝑖𝑚(𝛼) × 𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛼) × 𝐿𝑖𝑚(𝛽)] (10) Division (÷) of two rough numbers 𝑅𝑁(𝑎) and 𝑅𝑁(𝑏) 𝑅𝑁(𝛼) ÷ 𝑅𝑁(𝛽) = [𝐿𝑖𝑚(𝛼) ÷ 𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛼) ÷ 𝐿𝑖𝑚(𝛽)] (11) Scalar multiplication of rough number 𝑅𝑁(𝛼), where 𝜇 is a nonzero constant 𝜇 × 𝑅𝑁(𝛼) = [𝜇 × 𝐿𝑖𝑚(𝛼), 𝜇 × 𝐿𝑖𝑚(𝛼)] (12) 2.3. Rough Analytic Hierarchy Process The procedure of the rough AHP is described as follows (Zhu et al., 2015): Step 1: Identify the evaluation objective, criteria and alternatives. Construct a hierarchical structure with the evaluation objective at the top layer, criteria in the middle and alternatives at the bottom. Step 2: Conduct AHP survey and construct a group of pair-wise comparison matrices. The pair-wise comparison matrix of the eth expert is described as: 𝐵𝑒 = [ 1 𝑥21 𝑒 ⋮ 𝑥𝑚1 𝑒 𝑥12 𝑒 1 ⋮ 𝑥𝑚2 𝑒 ⋯ ⋯ ⋱ ⋯ 𝑥1𝑚 𝑒 𝑥2𝑚 𝑒 ⋮ 1 ] (13) where 𝑥𝑔ℎ 𝑒 (1 ≤ 𝑔 ≤ 𝑚, 1 ≤ ℎ ≤ 𝑚, 1 ≤ 𝑒 ≤ 𝑠)is the relative importance of criterion g on criterion h given by expert e, m is the number of criteria, s is the number of experts. Calculate maximum eigenvalue 𝜆𝑚𝑎𝑥 𝑒 of Be, then compute consistency index 𝐶𝐼 = (𝜆𝑚𝑎𝑥 𝑒 − 𝑛)/(𝑛 − 1). Determine random consistency index (RI) in Table 1 according to n. Compute consistency ratio CR=CI/RI. Table 1. Value of random index depending on the rank of matrix (Saaty & Vargas, 2012) n 1 2 3 4 5 6 7 8 9 10 RI 0.00 0.00 0.52 0.89 1.11 1.25 1.35 1.40 1.45 1.49 Conduct consistency test. If CR<0.1, the comparison matrix is acceptable. Otherwise, experts’ judgments should be adjusted until CR < 0.1 Then, integrated comparison matrix �̃� is built as: �̃� = [ 1 �̃�21 𝑒 ⋮ �̃�𝑚1 𝑒 �̃�12 𝑒 1 ⋮ �̃�𝑚2 𝑒 ⋯ ⋯ ⋱ ⋯ �̃�1𝑚 𝑒 �̃�2𝑚 𝑒 ⋮ 1 ] (14) Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96 86 where �̃�𝑔ℎ{𝑥𝑔ℎ 1 , 𝑥𝑔ℎ 2 , … . , 𝑥𝑔ℎ 𝑠 }, �̃�𝑔ℎ is the sequence of relative importance of criterion g on criterion h. Step 3: Construct a rough comparison matrix. Translate element 𝑥𝑔ℎ 𝑒 in �̃� into rough number 𝑅𝑁(𝑥𝑔ℎ 𝑒 ) using Eqs. (1) - (6): 𝑅𝑁(𝑥𝑔ℎ 𝑒 ) = [𝑥𝑔ℎ 𝑒𝐿 , 𝑥𝑔ℎ 𝑒𝑈] (15) where 𝑥𝑔ℎ 𝑒𝐿 is the lower limit of 𝑅𝑁(𝑥𝑔ℎ 𝑒 ) while 𝑥𝑔ℎ 𝑒𝑈 is the upper limit. Then rough sequence 𝑅𝑁(�̃�𝑔ℎ) is represented as: 𝑅𝑁(�̃�𝑔ℎ) = {[𝑥𝑔ℎ 1𝐿, 𝑥𝑔ℎ 1𝑈], [𝑥𝑔ℎ 2𝐿, 𝑥𝑔ℎ 2𝑈], … , [𝑥𝑔ℎ 𝑠𝐿 , 𝑥𝑔ℎ 𝑠𝑈]} (16) It is further translated into an average rough number 𝑅𝑁(𝑥𝑔ℎ) by rough arithmetic Eqs. (8) - (12): 𝑅𝑁(𝑥𝑔ℎ) = [𝑥𝑔ℎ 𝐿 , 𝑥𝑔ℎ 𝑈 ] (17) 𝑥𝑔ℎ 𝐿 = 𝑥𝑔ℎ 1𝐿 +𝑥𝑔ℎ 2𝐿 +⋯+𝑥𝑔ℎ 𝑠𝐿 𝑆 (18) 𝑥𝑔ℎ 𝑈 = 𝑥𝑔ℎ 1𝑈 +𝑥𝑔ℎ 2𝑈 +⋯+𝑥𝑔ℎ 𝑠𝑈 𝑆 (19) where 𝑥𝑔ℎ 𝐿 is the lower limit of 𝑅𝑁(𝑥𝑔ℎ) and 𝑥𝑔ℎ 𝑈 is the upper limit. Then rough comparison matrix M is formed as: 𝑀 = [ [1,1] [𝑥21 𝐿 , 𝑥21 𝑈 ] ⋮ [𝑥𝑚1 𝐿 , 𝑥𝑚1 𝑈 ] [𝑥12 𝐿 , 𝑥12 𝑈 ] [1,1] ⋮ [𝑥𝑚2 𝐿 , 𝑥𝑚2 𝑈 ] ⋯ ⋯ ⋱ ⋯ [𝑥1𝑚 𝐿 , 𝑥1𝑚 𝑈 ] [𝑥2𝑚 𝐿 , 𝑥2𝑚 𝑈 ] ⋮ [1,1] ] (20) Step 4: Calculate rough weight wg of each criterion: 𝑤𝑔 = [ √∏ 𝑥𝑔ℎ 𝐿 ,𝑚ℎ=1 𝑚 √∏ 𝑥𝑔ℎ 𝑈 ,𝑚ℎ=1 𝑚 ] (21) 𝑤𝑔 ′ = 𝑤𝑔/max (𝑤𝑔 𝑈) (22) where 𝑤𝑔 ′ is the normalization form. Finally, the criteria weights are obtained. 3. Numerical example The main activity of the company which is the subject of research is the production of metal washers for the automotive industry. Its product range covers up over 3000 types of metal washers, and the largest part of it is used for mechanical transmissions in heavy machinery, cranes, trucks, and the like. The company is focused on the production and sale of flat and elastic washers. The ability of production is over 3500 tons of finished products. The aim of this paper is to determine the most important criteria for suppliers’ evaluation in the mentioned company. Figure 2 presents criteria finance, logistics, quality and communications and business, and each of these criteria contains five subcriteria which are also shown in the figure below each criterion. A review of the given criteria for suppliers’ evaluation through literature is presented in the paper (Stević, 2017c). A rough multicriteria approach for evaluation of the supplier criteria in automotive industry 87 Figure 2. Criteria for supplier selection (Stević, 2017b) Collect individual judgments and construct a group of pairwise comparison matrices. Take the consistency examination until all the comparison matrices can pass through. Integrate individual comparison matrices to generate an integrated comparison matrix. The individual pair-wise comparison matrices are as follows: 𝐵1 = [ 1 1/4 1/3 4 1 3 3 1/3 1 1/3 1/5 1/4 3 5 4 1 ] , 𝐶𝑅 = 0,068 < 0,10 𝐵2 = [ 1/ 1 4 1 4 1 1/4 1 4 1 1/3 3 1/3 3 1/3 4 1 ] , 𝐶𝑅 = 0,047 < 0,10 𝐵3 = [ 1 4 1/4 1 1 4 1/4 3 1 4 1/4 1/3 1 5 1/5 1 ] , 𝐶𝑅 = 0,049 < 0,10 Obviously CRe < 0.1 (e= 1, 2, 3), all the comparison matrices are acceptable. Then integrated comparison matrix �̃� is generated by combining with the above three individual comparison matrices. �̃� = [ 1,1,1 1/4,4,4 4,1/4, 1/4 1,1,1 1/3,1,1 3,3,4 3,1/4,1/4 5,1/3,3 3,1,1 1/3,4,4 1/3,1/4,1/4 1/5,3,1/3 1,1,1 4,4,5 1/4,1/3,1/5 1,1,1 ] Translate the elements in �̃� into rough numbers and correspondingly original integrated comparison matrix �̃� is converted into a rough comparison matrix. Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96 88 Take as an example x̃24 = {5,1/3,3} 𝐿𝑖𝑚 ( 1 3 ) = 1 3 , 𝐿𝑖𝑚 ( 1 3 ) = 1 3 (5 + 1 3 + 3) = 2,78 𝐿𝑖𝑚(3) = 1 2 ( 1 3 + 3) = 1,67, 𝐿𝑖𝑚(3) = 1 2 (3 + 5) = 4 𝐿𝑖𝑚(5) = 1 3 (5 + 1 3 + 3) = 2,78, 𝐿𝑖𝑚(5) = 5 Thus, 𝑥24 𝑒 can be expressed in rough number: 𝑅𝑁(𝑥24 1 ) = 𝑅𝑁(5) = [2,78; 5] 𝑅𝑁(𝑥24 2 ) = 𝑅𝑁 ( 1 3 ) = [0,33; 2,78] 𝑅𝑁(𝑥24 3 ) = 𝑅𝑁(3) = [1,67; 4] According to Eqs. (17) - (19) 𝑥24 𝐿 = 𝑥24 1 + 𝑥24 2 + 𝑥24 𝑠 𝑆 = 2,78 + 0,33 + 1,67 3 = 1,59 𝑥24 𝑈 = 𝑥24 1 + 𝑥24 2 + 𝑥24 𝑠 𝑆 = 5 + 2,78 + 4 3 = 3,93 Thus rough sequence �̃�24 in �̃� is transformed into rough number 𝑅𝑁(𝑥24) = [1,59; 3,93]. The transformation of other elements in �̃� is implemented in the same way. Then, the rough comparison matrix is obtained: 𝑀 = [ [1; 1] [0,67; 2,33] [1,22; 2,11] [0,28; 0,32] [1,92; 3,58] [1; 1] [1,96; 3,59] [0,57; 1,95] [0,63; 0,93] [0,56; 1,78] [1; 1] [0,22; 0,24] [3,11; 3,55] [1,59; 3,93] [4,11; 4,55] [1; 1] ] Calculate rough weights of the criteria using Eqs. (21) and (22). 𝑤 = {[1,39; 1,85]; [0,88; 2,01]; [1,77; 2,42]; [0,43; 0,62]} 𝑤′ = {[0,57; 0,76]; [0,36; 0,83]; [0,73; 1]; [0,18; 0,26]} According to the obtained results, the third criterion quality is the most important in the target company. Observing the obtained values of the upper and lower limits of the rough number in all, except for the second criterion, shows that they have relatively approximate values. The cause of a large difference between the lower and the upper limit of logistics criteria are the different attitudes of decision-makers when this criterion is concerned. That is why the decision-makers gave different assessments of their preferences, for example, 1/3 and 5, etc. A rough multicriteria approach for evaluation of the supplier criteria in automotive industry 89 Figure 3. Comparison of rough numbers (Zhai et al., 2008) Figure 3 shows a comparison of rough numbers on the basis of which the criteria or alternatives are ranked. A comparison of the two rough numbers is clearly defined, depending on the lower and upper limits. After obtaining the values that mark the weight of the criteria in the same way it is necessary to make calculation for sub-criterion; so, the following is an example of the calculation for the subcriteria that belong to the logistics. The individual pair-wise comparison matrices are as follows: 𝐵1 = [ 1 1/4 1/4 4 4 4 1 1/3 5 5 4 3 1 5 5 1/4 1/5 1/5 1 1 1/4 1/5 1/5 1 1 ] , 𝐶𝑅 = 0,088 < 0,10 𝐵2 = [ 1 1/4 3 1 3 4 1 5 4 5 1/3 1/5 1 1/3 1 1 1/4 3 1 3 1/3 1/5 1 1/3 1 ] , 𝐶𝑅 = 0,028 < 0,10 𝐵3 = [ 1 3 1/4 1/5 1/7 1/3 1 1/5 1/7 1/9 4 5 1 1/3 1/4 5 7 3 1 1/3 7 9 4 3 1 ] , 𝐶𝑅 = 0,062 < 0,10 Obviously CRe < 0.1 (e= 1, 2, 3), all the comparison matrices are acceptable. Then integrated comparison matrix �̃� is generated by combining with the above three individual comparison matrices. �̃� = [ 1,1,1 4,4,1/3 1/4,1/4, 3 1,1,1 4,1/3,4 1/4,1,5 1/4,1/3,7 3,1/5,5 1/5,1/4,7 1/5,1/5, 9 1/4,3,1/4 1/3,5,1/5 4,1,1/5 5,4,1/7 4,3,1/7 5,5,1/9 1,1,1 1/5,3,3 1/5,1,4, 5,1/3,1/3 1,1,1 1,1/3,3 5,1,1/4 1,3,1/3 1,1,1 ] Translate the elements in �̃� into rough numbers and correspondingly original integrated comparison matrix �̃� is converted into a rough comparison matrix. Take as an example �̃�45 = {1,1/3,3} Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96 90 𝐿𝑖𝑚 ( 1 3 ) = 1 3 , 𝐿𝑖𝑚 ( 1 3 ) = 1 3 (1 + 1 3 + 3) = 1,44 𝐿𝑖𝑚(1) = 1 2 (1 + 1 3 ) = 0,66, 𝐿𝑖𝑚(1) = 1 2 (1 + 3) = 2 𝐿𝑖𝑚(3) = 1 3 (1 + 1 3 + 3) = 1,44, 𝐿𝑖𝑚(3) = 3 Thus, 𝑥45 𝑒 can be expressed in rough number: 𝑅𝑁(𝑥45 1 ) = 𝑅𝑁(1) = [0,66; 2] 𝑅𝑁(𝑥45 2 ) = 𝑅𝑁 ( 1 3 ) = [0,33; 1,44] 𝑅𝑁(𝑥45 3 ) = 𝑅𝑁(3) = [1,44; 3] According to Eqs. (17) - (19) 𝑥45 𝐿 = 𝑥45 1 + 𝑥45 2 + 𝑥45 𝑠 𝑆 = 0,66 + 0,33 + 1,44 3 = 0,81 𝑥45 𝑈 = 𝑥45 1 + 𝑥45 2 + 𝑥45 𝑠 𝑆 = 2 + 1,44 + 3 3 = 2,15 Thus rough sequence �̃�245 in �̃� is transformed into rough number 𝑅𝑁(𝑥45) = [0,81; 2,15]. The transformation of other elements in �̃� is implemented in the same way. Then, the rough comparison matrix is obtained: 𝑀 = [ [1; 1] [0,56; 1,78] [0,56; 1,78] [0,84; 2,74] [1,36; 3,29] [1,96; 3,59] [1; 1] [0,77; 3,17] [1,75; 4,18] [2,28; 4,46] [1,96; 3,59] [1,51; 3,91] [1; 1] [0,85; 2,93] [0,98; 3,36] [0,98; 3,36] [0,97; 4,37] [1,45; 2,69] [1; 1] [0,81; 2,15] [1,02; 4,40] [1,18; 5,09] [0,84; 2,74] [0,81; 2,15] [1; 1] ] Calculate rough weights of the criteria using Eqs. (21) and (22). 𝑤 = {[1,31; 2,86]; [0,99; 2,74]; [0,88; 2,11]; [1,00; 2,35]; [1,20; 2,54]} 𝑤′ = {[0,46; 1,00]; [0,35; 0,96]; [0,31; 0,74]; [0,35; 0,82]; [0,42; 0,89]} In order to obtain the final values of the subcriteria belonging to the logistics group, the following values are needed: 𝑤′ = {[0,46; 1,00]; [0,35; 0,96]; [0,31; 0,74]; [0,35; 0,82]; [0,42; 0,89]} Multiplying with the values of the main criterion-logistics [0,36; 0,83] gives the following values: 𝑤′′ = {[0,17; 0,83]; [0,13; 0,80]; [0,11; 0,61]; [0,13; 0,68]; [0,15; 0,74]} The most important logistics sub-criteria are delivery and reliability, which in the overall ranking occupy high positions, which can be seen in Table 2. Following the above described methodology, the values for all the twenty criteria are obtained and shown in Figure 4. A rough multicriteria approach for evaluation of the supplier criteria in automotive industry 91 Figure 4 Values of all criteria in rough numbers Figure 4 shows that the certification of products which is used in (Birgün Barla, 2003; Jamil et al., 2013; Ting & Cho, 2008; Uygun et al., 2013) and quality (Fallahpour et al., 2017; Kilic, 2013; Özbek, 2015; Stević et al., 2016; Wang et al., 2017) are of utmost importance in the company which is the subject of our research. These two criteria are very important because the company exports its products to the international market. The third place is taken by the criterion of volume discounts (Jamil et al., 2013; Wang, 2010) because the company is located on the territory of Bosnia and Herzegovina which is a very poor country; thus, additional discounts in business are very popular. The next most important criterion is that of delivery time (Chan & Kumar, 2007; Sawik, 2010; Yücenur et al., 2011; Rezaei et al., 2014) and reliability (Gencer & Gürpinar, 2007; Muralidharan et al., 2002; Büyüközkan & Göçer, 2017). 4. Comparison and discussion Once the results are obtained, a sensitivity analysis including comparison of the values of the criteria using three different forms of the AHP method is carried out. Figure 5 presents the values of the main criteria obtained using conventional AHP, Fuzzy AHP and Rough AHP, while in Table 2 presented are all the results of the sensitivity analysis including all the twenty criteria. The sensitivity analysis is very important for all types of research; a very studious example of the sensitivity analysis in the multicriteria decision-making can found in the paper (Pamučar et al., 2017b) in which the authors use different methods for ranking solution. Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96 92 Figure 5. Values of main criteria using AHP, FAHP and RAHP Certification of products is the most important criterion using AHP and rough AHP, while quality is the most important one using fuzzy AHP. Of equal rank by all the methods is volume discount which thus occupies the third position. The results show that the rough AHP has more similarity with the conventional AHP for this research. Table 2. Results of sensitivity analysis Criteria AHP FAHP RAHP Values Rank Values Rank Values Rank Price of material 0,084 4 0,068 4 (0,28;0,53) 7 Financial stability 0,047 5 0,052 6 (0,16;0,58) 8 Method of payment 0,025 14 0,039 13 (0,08;0,19) 14 Price of transport 0,025 14 0,026 18 (0,08;0,17) 15 Volume discounts 0,122 3 0,074 3 (0,42;0,76) 3 Delivery time 0,047 5 0,056 5 (0,17;0,83) 4 Reliability 0,033 10 0,043 11 (0,13;0,80) 5 Flexibility 0,034 9 0,042 12 (0,11;0,61) 9 Logistics capacity 0,039 7 0,050 7 (0,13;0,68) 10 The percentage of correct realization of delivery 0,043 6 0,047 10 (0,15;0,74) 6 Quality of material 0,149 2 0,114 1 (0,46;0,90) 2 Warranty period 0,032 11 0,037 14 (0,09;0,20) 13 Certification of products 0,164 1 0,102 2 (0,50;1,00) 1 Reputation 0,037 8 0,033 15 (0,10;0,21) 12 Awards and honors 0,017 16 0,021 19 (0,04;0,09) 18 Communication system 0,012 17 0,032 16 (0,04;0,10) 17 Speed of response to requirements 0,029 12 0,048 8 (0,10;0,26) 11 Reactions to reclamation 0,027 13 0,044 9 (0,08;0,24) 11 Information Technology 0,021 15 0,043 11 (0,08;0,24) 11 Clean of business 0,011 18 0,031 17 (0,04;0,14) 16 Ranking all criteria from the first to the twentieth place is also shown in Figure 6. A rough multicriteria approach for evaluation of the supplier criteria in automotive industry 93 Figure 6. Ranking criteria by the three forms of the AHP method The consequence of different results using different methods is reflected in different scales for evaluating criteria, which according to Mukhametzyanov & Pamučar (2017) is one of the five main reasons that influence the obtaining of results and their ranking. Rough AHP according to (Roy et al., 2016) enables us to measure consistency of preferences, manipulate multiple decision-makers and calculate relative importance for each criterion. The rough AHP according to (Song et al., 2013) combines the strength of rough sets in handling subjectivity and the advantage of AHP in hierarchy evaluation. 5. Conclusion This study proposes a rough group AHP approach to the evaluation supplier criteria in the company for producing metal washers for the automotive industry. 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