IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 271 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 MULTI-ATTRIBUTE WAREHOUSE LOCATION SELECTION IN HUMANITARIAN LOGISTICS USING HESITANT FUZZY AHP Eda Boltürk Sezi Çevik Onar Başar Öztayşi Cengiz Kahraman Industrial Engineering Department, Istanbul Technical University, 34367, Istanbul, Turkey kahramanc@itu.edu.tr, cevikse@itu.edu.tr, oztaysib@itu.edu.tr, bolturk@itu.edu.tr, Kerim Göztepe Institute of Natural Sciences, Industrial Engineering Sakarya University, Turkey kerimgoztepe@gmail.com ABSTRACT Deploying warehouses at strategic locations becomes an important issue for humanitarian relief organizations in order to improve their relief aid capability and rescue plan. The delivery of sufficient technical equipment and provision of shelter and reinforcement to victims is a significant event during relief operations. Warehouse location selection in humanitarian logistics (HL) is a challenging process because choosing a non-optimal location may cause additional problems during rescue activities. The conventional decision making tools used for a warehouse location selection problem tend to be less effective in dealing with the imprecise or vague nature of the linguistic assessment. In many situations, the values of the qualitative attributes are often incompletely determined by the decision-makers. The fuzzy set theory can capture this type of uncertainty. In this paper, a recent extension of ordinary fuzzy sets, namely hesitant fuzzy sets, is used for considering the decision makers hesitancy in the evaluation. To solve the HL warehouse location selection problem, we propose a new hesitant fuzzy Analytic Hierarchy Process (AHP) method. We also present a HL warehouse location selection case study for a Turkish humanitarian relief organization by using hesitant fuzzy preference information. Keywords: Warehouse location selection; Multi-attribute decision-making (MADM); fuzzy logic; humanitarian logistics; Hesitant Fuzzy Sets 1. Introduction For the purpose of alleviating the suffering of vulnerable people, the activities of planning, implementing and controlling the efficient, cost-effective flow of and storage of goods and materials from production to consumption are called humanitarian logistics (Thomas & Kopczak, 2005). Another definition for humanitarian logistics is given in this way: the processes and systems involved in mobilizing people, resources, skills and knowledge to help vulnerable people affected by disaster (Van Wassenhove, 2006). https://scholar.google.com.tr/citations?view_op=view_org&hl=tr&org=11256784414184154164 IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 272 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Natural disasters, both rapid-onset events (such as earthquakes and floods) and slow- onset events (such as hunger, poverty and drought) or man-made crises (such as war and civil unrest), increase vulnerability of nations or regions and seriously affect local and national economies (Roh et al., 2015). In this paper, we focus on rapid-onset natural disasters which appear suddenly with no warning. Hence, disaster management, a vital issue to deal with natural and man-made disasters, needs a systematic approach (Ahmadi et al., 2015). Disaster management has four main phases which are mitigation, preparation, response and recovery (Ivgin, 2013). Long- term efforts should be made to keep the occurrence of disasters in the mitigation phase (Chou et al., 2015). The preparation phase is also another important part of disaster management. Government or social organizations should make a plan which includes the preparation phase before the occurrence of a disaster. The warehouse location in humanitarian logistics has high importance since it determines the success of the disaster response after an event. There are few studies on the warehouse location problem regarding humanitarian relief logistics in the literature. Warehouse location selection in humanitarian logistics has also drawn a lot of attention from humanitarian relief organizations in recent years. The world’s biggest humanitarian relief organizations, such as World Food Programme (WFP), International Federation of Red Cross and Red Crescent Societies (IFRC), and Action Against Hunger (AAH), have begun to deploy strategic pre-positioned warehouses around the world. Different researchers have studied the importance of the preparedness phase and the need for pre-positioned warehouses in humanitarian relief operations, but only a small number of papers are related to the warehouse location selection problem in humanitarian logistics (Dekle et al., 2005; Balcik and Beamon, 2008; Huang et al., 2015; Rath & Gutjahr, 2014; Florez et al., 2015). The evaluation process for the warehouse location decision usually includes different and possibly conflicting tangible and intangible attributes, which requires an evaluation to be performed with vague and incomplete information (Onut & Soner, 2007; Demirel & Kahraman, 2010). This reality generally forces decision makers to model the problem by applying a fuzzy multi-attribute decision-making (MADM) approach. The fuzzy set theory has a history starting with the introduction of ordinary fuzzy sets by L. A. Zadeh (1965) and continuing with the extensions of these sets as illustrated in Figure 1 (Kahraman et al., 2016). IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 273 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Figure 1. History of the fuzzy set theory Ordinary fuzzy sets and their new extensions have been extensively used in the solution of industrial problems: outsourcing (Bottani & Rizzi, 2006; Kahraman et al., 2010), transportation (Chana & Kuchta, 1996; Kaya et al., 2012), energy (Heo et al., 2010; Cevik Onar et al., 2015), urban transformation (Olazabal & Pascual, 2016; Oztaysi et al., 2016), engineering economics (Shahriari, 2011; Kahraman et al., 2015). In the literature, the most used MADM method is the Analytic Hierarchy Process (AHP) developed by Saaty (1980). It has been used in the solution of various MADM problems: outsourcing (Atkinson et al., 2015), capability development (Dangol et al, 2015) and personnel management (Kashi, 2016), etc. In our proposed MADM method, we utilize hesitant fuzzy sets (HFSs), which are the latest extension of ordinary fuzzy sets. HFSs are a novel extension of fuzzy sets aiming at modeling the uncertainty caused by the hesitation arising in the assignment of membership degrees of the elements to a fuzzy set. A HFS is defined in terms of a function that returns a set of membership values for each element in the domain (Rodriguez et al., 2014). In this paper, we used hesitant fuzzy linguistic term sets (HFLTS) which was introduced by Rodríguez et al. (2012). Through the usage of HFLTS, different linguistic evaluations of different actors can be aggregated without loss of information. HFLTS enable expressing the hesitance existing in linguistic evaluation as clearly as possible. A multi-attribute warehouse location selection problem in humanitarian logistics employs linguistic evaluations which mostly include hesitance of multiple experts. The proposed hesitant fuzzy MADM method evaluates warehouse location alternatives in humanitarian logistics using a number of tangible and intangible Ordinary fuzzy sets, Zadeh (1965) Type-2 fuzzy sets, Zadeh (1975 Interval-valued fuzzy sets, Zadeh (1975), Grattan- Guiness (1975), Jahn (1975), Sambuc (1975) Intuitionis tic fuzzy sets, Atanassov (1986) Fuzzy multisets, Yager (1986) Nonstationa ry fuzzy sets, Garibaldi and Ozen (2007) Hesitant fuzzy sets, Torra (2010) IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 274 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 attributes. The proposed MADM method is based on a new hesitant fuzzy AHP method for the evaluation of alternative warehouse locations. The novelty of the developed fuzzy HFLTS based AHP method is its capability to overcome the hesitancy involved in multi criteria warehouse selection problem with linguistic assessments of multiple experts. Our paper is structured as follows.: in Section 2, a literature review on Humanitarian Logistics (HL) and related definitions is presented. Warehouse location selection attributes in HL are given in Section 3. Section 4 focuses on the methodological background of the hesitant fuzzy sets and hesitant fuzzy AHP. A case study and a sensitivity analysis are given in Section 5. Finally, conclusions and future directions are presented in Section 6. 2. Humanitarian Logistics (HL) The creation of an effective disaster supply chain to deliver necessary goods to disaster relief organizations is an essential function of disaster management. This function is also called humanitarian logistics. Humanitarian logistics is a broad term that covers the operations concerning supply chain strategies, processes, and technologies that will maintain the flow of goods and materials needed for the humanitarian effort. The management of the supply chain in disaster relief operations is considered an essential element in the resolution of a crisis since the tsunami in South East Asia (December, 26th 2004) and Hurricane Katrina (August, 2005). Security is a very important requirement in humanitarian logistics. In the aftermath of a disaster, many goods (e.g., medicine, foods), which are usually available in normal conditions, became extremely valuable and a potential target of thieves. Supply chain management for business applications had a long evolution and many companies have well established supply chains around the world, but the strategic goal of commercial supply chains and disaster supply chains is different. Commercial supply chains are focused on quality and profitability whereas humanitarian supply chains must be focused on minimizing loss of life and suffering. The works on HL can be classified into conceptual and strategic works and operation research (OR) based works. Some recent papers on conceptual and strategic HL are as follows. Vaillancourt (2016) developed a theoretical framework to better understand incentives and obstacles to consolidation of materials in humanitarian logistics. L'Hermitte et al. (2016) explored the underlying strategic mechanisms of agility in a humanitarian logistics context. Based on the research conducted in business disciplines, the paper empirically examines a set of four strategic dimensions (being purposeful, being action-focused, being collaborative, and being learning- oriented) and identifies an emergent relationship between these capabilities and agile humanitarian logistics operations. Vega and Roussat (2015) investigated the role of logistics service providers in humanitarian relief. Leiras et al. (2014) presented a literature review of HL that aims to identify trends and suggest some directions for future research. Some recent papers on operation research (OR) based HL are as follows. Tofighi et al. (2016) addressed a two-echelon humanitarian logistics network design problem involving multiple central warehouses and local distribution centers and developed a novel two-stage scenario-based possibilistic-stochastic programming approach. Ransikarbum and Mason (2016) presented a multiple objective, integrated network optimization model for making strategic decisions in the supply distribution and https://www.scopus.com/authid/detail.uri?authorId=57188550272&eid=2-s2.0-84961621937 https://www.scopus.com/authid/detail.uri?authorId=56416407700&eid=2-s2.0-84954372836 https://www.scopus.com/authid/detail.uri?authorId=7202152323&eid=2-s2.0-84954372836 IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 275 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 network restoration phases of humanitarian logistics operations. Their model provides an equity-based solution for constrained capacity, budget and resource problems in post-disaster logistics management. Gralla et al. (2015) provided a basis for the design and improvement of simulated emergency training exercises, which are common in the humanitarian practice community. Özdamar and Ertem (2015) presented a survey that focused on the response and recovery planning phases of the disaster lifecycle. The related mathematical models developed in this research area were classified in terms of vehicle/network representation structures and their functionality. Díaz-Delgado and Gaytán Iniestra (2014) dealt with the relationship between a flood risk assessment and the humanitarian logistics process design related to emergency events caused by flooding. The magnitude and timing of the flooding is estimated using a forecasting model that requires a hydrologic component to convert rainfall into runoff as well as a hydraulic component to route the flow through the stream network predicting time and severity of the flood wave. Figure 2 illustrates the frequencies of publications on HL with respect to publication years. This figure was obtained by entering “humanitarian logistics” as an “article title, abstract or keywords” to the Scopus database considering the publications up to August 2016. As seen in Figure 2, researchers have been focused on HL especially after the year 2005 since disasters such as the tsunami in South East Asia in 2004 and Hurricane Katrina in 2005 which caused the deaths of many people. Figure 2. Frequencies of publications on HL with respect to publication years Figure 3 presents the journals publishing HL papers. The Journal of Humanitarian Logistics and Supply Chain Management is the leading journal publishing HL papers. The journals that publish the second most HL papers are Procedia Engineering and Socio Economic Planning Sciences. 0 10 20 30 40 50 60 70 80 90 2004 2006 2008 2010 2012 2014 2016 https://www.scopus.com/authid/detail.uri?authorId=6506956166&eid=2-s2.0-84919779039 https://www.scopus.com/authid/detail.uri?authorId=56460374900&eid=2-s2.0-84919779039 IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 276 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Figure 3. Journals publishing HL works Figure 4 shows the document types of the publications on HL. Articles and conference papers are by far the first two most popular ways of publication media for HL works. Figure 4. Document types of the publications on HL Figure 5 illustrates the subject areas of the publications on HL. Business, management and accounting, decision sciences, engineering, computer science, and social sciences are the leading subject areas used in HL. 0 10 20 30 40 50 60 70 0 50 100 150 200 250 IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 277 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Figure 5. Subject areas of the publications on HL 3. Warehouse location selection in HL Warehousing is essentially an act of storing goods between the time they are assembled and the time they are handed to the customer. Warehousing commonly depends on human resources and required facilities and equipment costs (Stock & Lambert, 2001). Besides, warehouse performance directly affects the whole supply chain performance of a firm or organization (Tuzkaya & Önüt, 2009). Ineffective warehouse location selection, design or management will threaten the achievement of a humanitarian relief organization and result in unnecessarily high costs (Pazour & Carlo, 2015). Logistic researchers commonly agree that warehouse location is a problem of strategic level network design (Powers, 1989; Özcan et al., 2011; Ashrafzadeh et al., 2012). This kind of decision is long-term and the influence of the warehouse location selection affects the profitability of the company. A warehouse system not only reduces cost and simplifies operations, but also allows companies to focus on their main targets (Choi et al., 2001). We know that items are transformed into final products by being processed sequentially at multiple locations in supply chain networks. Hence, a warehouse is a vital part of a typical supply chain management. In recent years, the demand for strategic stock-holding for humanitarian purposes has become increasingly vital. Human relief organizations or governments notice that a large number of high-impact natural and man-made disasters influence the stability of states (Guha-Sapir et al., 2013; Roh et al., 2015). For instance, the 2004 earthquake and resulting tsunami in South Asia caused approximately 230,000 deaths and displaced 1.7 million people in many urban areas. More than 40 countries and 700 nongovernmental organizations (NGOs) provided humanitarian materials (Russell, 2005; Cozzolino, 2012). 0 20 40 60 80 100 120 140 160 180 200 IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 278 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Warehouse location selection is a multi-attribute decision making problem including both tangible and intangible attributes. Table 1 summarizes the attributes used in warehouse location selection problems in the literature. Table l Literature on warehouse location selection attributes Researchers Research Areas Main Evaluation attributes for Warehouse (or Logistics Center) Selection Korpela, J., Tuominen, M., (1996). A decision aid in warehouse site selection. Reliability Compliance; Flexibility Special, Strategic compatibility Alberto, P., (2000). The logistics of industrial location decisions. Environmental aspects, Cost, Quality of living, Local incentives, Time reliability provided to customers, Response flexibility to customer's demand, Integration with customers Sarkis, J., Sundarraj, R.P., (2002). Hub location selection for Digital Equipment Corporation Cost, Accessibility, Time, Regulatory, Risk, Labour, Strategy Demirel, T., Demirel, N. Ç., & Kahraman, C. (2010). Warehouse location selection using Choquet integral. Costs, Labor characteristics, Infrastructure, Markets, Macro environment Kayikci, Y., (2010) Logistics center location using conceptual model. Economical scale, National stability, Intermodal operation and management, International market location, and Environmental effect Li, Y., Liu, X., Chen, Y. (2011). Selection of logistics centre Weather and landform condition, Water supply, Power supply, Solid cast-off disposal, Communication, Traffic, Candidate land area, Candidate land shape, Candidate land circumjacent main line, Candidate land land-value, Freight transport, and Fundamental construction investment. Özcan, T., Çelebi, N., & Esnaf, Ş. (2011). Warehouse location selection problem using multi-attributes decision making methodologies. Unit price ($/m2), Stock holding capacity (unit), Average distance to shops (kilometer), Average distance to main suppliers (kilometer), Movement, Flexibility, Roh, S. Y., Jang, H. M., & Han, C. H. (2013). Warehouse location decision factors in humanitarian relief logistics. Location, Logistics, National stability, Cost, Cooperation. Roh, S., Pettit, S., Harris, I., & Beresford, A. (2015). The pre-positioning of warehouses at regional and local levels. Location, National Stability, Cost, Cooperation, Logistics Based on the above literature review, warehouse location selection attributes have been determined as follows:  Geographical location (Roh, 2015): Geographic location refers to a position on the Earth. Absolute geographic location of a point is defined by two coordinates, longitude and latitude. This attribute is crucial in order to provide a cost-effective flow and storage of goods. It has four sub-attributes determined as “proximity to disaster areas”, “logistics experts” availability”, “warehouse security”, “proximity to urban facilities”, and “closeness to other warehouses”.  Transport connectivity (Vitoriano et al., 2011; Barbarosoglu and Arda, 2004): Transportation is a critical issue in humanitarian relief operations to deliver IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 279 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 aid at the right time and to the right place. We know that the deliveries must be fast, fair and safe. Decision makers must consider the actual fuel availability, available vehicles, climate, road conditions and airports and port’s capacity after the disaster during planning process of transportation operations (Wassenhove & Martinez, 2012). This attribute includes the sub- attributes “availability of seaport and airport”, “near to (potential) beneficiaries”, “adequate warehouse facilities”, “adequate warehouse infrastructure”, and “warehouse accessibility”.  Cost (Roh et al., 2013; Kahraman et al., 2007; Sari et al., 2013): Cost effective flow and storage of goods and materials is one of the main issues in humanitarian logistics together with the planning, implementing and controlling processes (Tomasini &Wassenhove, 2009). When developing a warehouse location selection plan for a new organization, decision makers must assign cost estimates in order to assess whether an organization’s budget will cover costs. Costs are usually underestimated; it should be analyzed during the execution of humanitarian relief operations. Although there are different types of cost in management (Blocher et al., 2008), we have classified the sub-attributes as “storage cost”, “cost relate to logistics”, “land cost”, “labor price”, and “replenishment cost”.  Stable government (Roh et al., 2015; Seaman, 1999): A stable political situation is important for the operation of the pre-positioned warehouse. If the political, economic, and social state of a country is very fragile and unstable, it will be difficult for a humanitarian organization to operate their supply chain in a risky and dangerous environment. The stable government attribute has four sub-attributes “cooperation with logistics agents”, “political and economic stability”, “existence of other agents (NGOs)”, and “IT/Communication”.  Labor availability (Roh et al., 2013; Demirel et al., 2010): Today’s warehouses include large amounts of materials, machines, and people and have complex infrastructures. Thus, the availability of qualified labor is another issue for our proposed model. This is one of the main requirements of warehouse management in order to perform a better humanitarian relief operation. We assume that the qualified labor does not have the same standards at each location. The sub-attributes of availability of labor are “trained and qualified personnel”, “flexible customs regulations”, “population density”, and “climate”. Based on the determined main-attributes and sub-attributes, the hierarchy of the proposed model is given in Figure 6. There are 5 main attributes and 4 sub-attributes under each main attribute, and 5 HL warehouse location alternatives (HLW). IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 280 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 HLW1 HLW2 HLW3 HLW4 HLW5 Alternatives Figure 6. Hierarchy of the problem 4. Preliminaries: Hesitant Fuzzy Sets Torra (2010) introduced Hesitant Fuzzy Sets (HFSs) since determining the membership degree of an element to a fuzzy set is not an easy work. The difficulty comes from possible values that cause hesitation about which one would be the right one. Definition 1: Let X be a fixed set, a hesitant fuzzy set (HFS) on X is in terms of a function that when applied to X returns a subset of [0, 1] (Torra, 2010). Mathematical expression for HFS is as follows: 𝐸 = {< 𝑥,ℎ𝐸(𝑥) > | 𝑥𝜖 𝑋 }, (1) where ℎ𝐸(𝑥) is a set of some values in [0, 1], denoting the possible membership degrees of the element 𝑥𝜖 𝑋 to the set E. Xia and Xu (2011) give some basic definition about h as follows. Definition 2: The upper and lower bound is defined as in Eq. 2 and Eq. 3. ℎ−(𝑥) = minℎ(𝑥); (2) ℎ+(𝑥) = maxℎ(𝑥); (3) Definition 3: The compliment of h is given in Eq. 4. ℎ𝑐 = ∪𝛾∈ℎ {1 − 𝛾}; (4) Warehouse location selection in Humanitarian Logistics Geographical location Proximity to urban facilities Proximity to disaster areas Closeness to other warehouses Warehouse security Cost Storage cost Investment cost Labor price Replenishment cost Transport connectivity Availability of seaport and airport Near to (potential) beneficiaries Adequate warehouse facilities Adequate warehouse infrastructure Labor availability Trained and qualified personnel Flexible customs regulations Population density Climate Stable government Cooperation with logistics agents Political and economical stability Existence of other agents (NGOs) IT/Communication IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 281 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Definition 4: The envelope of h, Aenv(h), is an intuitionistic fuzzy set which is defined as 𝐴𝑒𝑛𝑣(ℎ) = {𝑥,𝜇(𝑥),𝑣(𝑥)} (5) where 𝜇(𝑥) = ℎ−(𝑥) (6) 𝑣(𝑥) = 1 − ℎ+(𝑥) (7) The basic operations on HFSs can be found in Zhang and Wei (2013). Rodríguez et al. (2012) have introduced hesitant fuzzy linguistic term sets (HFLTS) to improve the elicitation of linguistic information in decision making when experts hesitate among several linguistic terms to express their assessments. These sets provide greater flexibility to elicit comparative linguistic expressions by using context-free grammar that formalizes the generation of flexible linguistic expressions. Hence, we prefer the use HFLTS in this paper. Definition 5. The envelope of an hesitant fuzzy linguistic term sets (HFLTS), env(HS), is a linguistic interval whose limits are obtained by means of its upper bound and lower bound: 𝑒𝑛𝑣(𝐻𝑆) = [𝐻𝑆−,𝐻𝑆+], 𝐻𝑆− ≤ 𝐻𝑆+, (8) where the upper bound and lower bound are defined as 𝐻𝑆+ = 𝑚𝑎𝑥{𝑆𝑖} = 𝑆𝑗,𝑆𝑖 ≤ 𝑆𝑗 𝑎𝑛𝑑 𝑆𝑖 ∈ 𝐻𝑆,∀𝑖, (9) 𝐻𝑆− = 𝑚𝑖𝑛{𝑆𝑖} = 𝑆𝑗,𝑆𝑖 ≥ 𝑆𝑗 𝑎𝑛𝑑 𝑆𝑖 ∈ 𝐻𝑆,∀𝑖, (10) Definition 6. An OWA operator of dimension n is a mapping OWA: 𝑅𝑛 → 𝑅, so that 𝑂𝑊𝐴(𝑎1,𝑎2,…,𝑎𝑛) = ∑ 𝑤𝑗𝑏𝑗 𝑛 𝑗=1 (11) where 𝑏𝑗 is the jth largest of the aggregated arguments 𝑎1,𝑎2,…,𝑎𝑛, and 𝑊 = (𝑤1,𝑤2,…,𝑤𝑛) 𝑇 is the associated weighting vector satisfying wi ∈ [0,1], i = 1,2,…,n and ∑ wi = 1 n i=1 . Definition 7. A triangular fuzzy membership function �̃�=(a, b, c) is used as the representation of the comparative linguistic expressions based on HFLTS, the definition domain of �̃� should be the same as the linguistic terms {si, . . . , sj} ∈ HS. The min and the max operators are used to compute a and c. 𝑎 = 𝑚𝑖𝑛{𝑎𝐿 𝑖 ,𝑎𝑀 𝑖 ,𝑎𝑀 𝑖+1,…,𝑎𝑀 𝑗 ,𝑎𝑅 𝑗 } = 𝑎𝐿 𝑖 (12) 𝑐 = 𝑚𝑎𝑥{𝑎𝐿 𝑖 ,𝑎𝑀 𝑖 ,𝑎𝑀 𝑖+1,…,𝑎𝑀 𝑗 ,𝑎𝑅 𝑗 } = 𝑎𝑅 𝑖 (13) The remaining elements 𝑎𝑀 𝑖 ,𝑎𝑀 𝑖+1,…,𝑎𝑀 𝑗 ∈ 𝑇 should contribute to the computation of the parameter b. The aggregation operator OWA will be used to aggregate them: 𝑏 = 𝑂𝑊𝐴𝑊𝑆(𝑎𝑀 𝑖 ,𝑎𝑀 𝑖+1,…,𝑎𝑀 𝑗 ) (14) IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 282 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 5. Hesitant Fuzzy AHP model In the proposed hesitant fuzzy AHP method, we first determine the main and sub- attributes and the hierarchy for the warehouse location selection problem, then make a multi-attributes evaluation of the warehouse location alternatives to illustrate how the proposed model is used to solve it. The steps of the Hesitant Fuzzy AHP extended based on Buckley (1985)’s AHP method are given: Step 1. Pairwise comparison matrices for attributes, sub-attributes and alternatives are constructed and expert’s evaluations using linguistic terms are collected. Step 2. Using the scale given in Table 1, the linguistic terms are transformed into triangular fuzzy numbers (Tan et al., 2014) and trapezoidal fuzzy numbers. Table 2 Linguistic scale for Hesitant Fuzzy AHP Linguistic Term Abb. Triangular Fuzzy Number Trapezoidal Fuzzy Number Absolutely High Importance (AHI) (7,9,9) (7,9,9,9) Very High Importance (VHI) (5,7,9) (5,7,7,9) Essentially High Importance (ESHI) (3,5,7) (3,5,5,7) Weakly High Importance (WHI) (1,3,5) (1,3,3,5) Equally High Importance (EHI) (1,1,3) (1,1,1,3) Exactly Equal (EE) (1,1,1) (1,1,1,1) Equally Low Importance (ELI) (0.33,1,1) (0.33,1,1,1) Weakly Low Importance (WLI) (0.2,0.33,1) (0.2,0.33,0.33,1) Essentially Low Importance (ESLI) (0.14,0.2,0.33) (0.14,0.2,0.2, 0.33) Very Low Importance (VLI) (0.11,0.14,0.2) (0.11,0.14,0.14,0.2) Absolutely Low Importance (ALI) (0.11,0.11,0.14) (0.11,0.11,0.11,0.14) Each element (�̃�𝑖𝑗 𝑘 ) of the pairwise comparison matrix �̃�𝑘 is a fuzzy number corresponding to its linguistic term. The pairwise comparison matrix is given by; �̃�𝑘 = | 1 �̃�21 𝑘 ⋮ �̃�𝑛1 𝑘 �̃�12 𝑘 1 ⋮ �̃�𝑛2 𝑘 … … ⋮⋮⋮ … �̃�1𝑛 𝑘 �̃�2𝑛 𝑘 ⋮ 1 | (15) where (�̃�𝑖𝑗 𝑘 ) represents the kth expert’s evaluation on comparison of ith element to jth element. Step 3. The consistency of each fuzzy pairwise comparison matrix is examined. In order to check the consistency of the fuzzy pairwise comparison matrices, pairwise comparison values are defuzzified by the graded mean integration approach (Hsieh & Chen, 1999). Assume  ijaA ~ ~  is a fuzzy positive reciprocal matrix and  ijaA  is its defuzzified positive reciprocal matrix. If the result of the comparisons of  ijaA  is consistent, then it can imply that the result of the comparisons of  ijaA ~ ~  is also consistent (Buckley, 1985). According to the graded mean integration approach, a triangular fuzzy number ),,( ~ umlA  can be transformed into a crisp number by employing the below equation: IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 283 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 𝐴 = 𝑙+4𝑚+𝑢 6 (16) If the pairwise comparisons are not consistent, experts must reevaluate the pairwise comparisons. Step 4: Identification of conflicts and renewing the evaluations. The evaluations of the experts are checked for their closeness to each other. If the evaluations are not close then experts are informed of the need to discuss the situation and renew their evaluations. Step 5: Fuzzy envelope approach, proposed by Liu and Rodriguez (2014), is used to combine expert evaluations. The scale given in Table 1 is sorted from the lowest (𝑠0) to the highest (𝑠𝑔). Assume the expert evaluations vary between two terms i.e. 𝑠𝑖 and 𝑠𝑗. Then 𝑠0 ≤ 𝑠𝑖 < 𝑠𝑗 ≤ 𝑠0. The parameters a and d of the trapezoidal fuzzy membership function �̃� = (a, b, c, d) are computed as 𝑎 = min{𝑎𝐿 𝑖 ,𝑎𝑀 𝑖 ,𝑎𝑀 𝑖+1,…. .𝑎𝑀 𝑗 ,𝑎𝑅 𝑗 } = 𝑎𝐿 𝑖 (17) 𝑑 = min{𝑎𝐿 𝑖 ,𝑎𝑀 𝑖 ,𝑎𝑀 𝑖+1,… . .𝑎𝑀 𝑗 ,𝑎𝑅 𝑗 } = 𝑎𝑅 𝑗 (18) 𝑏 = { 𝑎𝑚 𝑖 , 𝑖𝑓 𝑖 + 1 = 𝑗 𝑂𝑊𝐴𝑤2 (𝑎𝑚 𝑖 ,…. .𝑎𝑚 𝑖+𝑗 2 ), 𝑖𝑓 𝑖 + 𝑗 𝑖𝑠 𝑒𝑣𝑒𝑛 𝑂𝑊𝐴𝑤2 (𝑎𝑚 𝑖 ,…. .𝑎𝑚 𝑖+𝑗−1 2 ), 𝑖𝑓 𝑖 + 𝑗 𝑖𝑠 𝑜𝑑𝑑 (19) 𝑐 = { 𝑎𝑚 𝑖+1 , 𝑖𝑓 𝑖 + 1 = 𝑗 𝑂𝑊𝐴𝑤1 (𝑎𝑚 𝑗 ,𝑎𝑚 𝑗−1 …..𝑎𝑚 𝑖+𝑗 2 ), 𝑖𝑓 𝑖 + 𝑗 𝑖𝑠 𝑒𝑣𝑒𝑛 𝑐 = 𝑂𝑊𝐴𝑤1 (𝑎𝑚 𝑗 ,𝑎𝑚 𝑗−1 ,…. .𝑎𝑚 𝑖+𝑗+1 2 ), 𝑖𝑓 𝑖 + 𝑗 𝑖𝑠 𝑜𝑑𝑑 (20) OWA operation given in Definition 6 requires a weight vector. Filev and Yager (1998) define the first and second type of weights using α parameter which belong to the unit interval [0,1]. The first kind of weights 𝑊1 = (𝑤1 1,𝑤2 1 …𝑤𝑛 1) is defined as: 𝑤1 1 = 𝛼2,𝑤2 1 = 𝛼2(1 − 𝛼2),…….𝑤𝑛 1 = 𝛼2(1 − 𝛼2) 𝑛−2 The second kind of weights 𝑊2 = (𝑤1 2,𝑤2 2 …𝑤𝑛 2) is defined as: 𝑤1 2 = 𝛼1 𝑛−1,𝑤2 2 = (1 − 𝛼1)𝛼1 𝑛−2,…….𝑤𝑛 2 = 1 − 𝛼1, where 𝛼1 = 𝑔−(𝑗−𝑖) 𝑔−1 and 𝛼2 = (𝑗−𝑖)−1 𝑔−1 where g is the number of terms in the evaluation scale, j is the rank of highest evaluation and i is the rank of lowest evaluation value of the given interval. Step 6: Collaborative pairwise comparison matrix (�̃�) is formed. IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 284 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 �̃� = | 1 �̃�21 ⋮ �̃�𝑛1 �̃�12 1 ⋮ �̃�𝑛2 … … ⋮⋮⋮ … �̃�1𝑛 �̃�2𝑛 ⋮ 1 | (21) where �̃�𝑖𝑗 = (𝑐𝑖𝑗𝑙 ,𝑐𝑖𝑗𝑚1 ,𝑐𝑖𝑗𝑚2 ,𝑐𝑖𝑗𝑢 ) Since the fuzzy envelopes, obtained in the previous step are trapezoidal fuzzy numbers, reciprocal values are calculated as follows: �̃�𝑗𝑖 = ( 1 𝑐𝑖𝑗𝑢 , 1 𝑐𝑖𝑗𝑚2 , 1 𝑐𝑖𝑗𝑚1 , 1 𝑐𝑖𝑗𝑙 ) (22) Step 7: Fuzzy geometric mean for each row (�̃�𝑖) of the collaborative pairwise matrix is computed using Eq. 23. �̃�𝑖 = (�̃�𝑖1 ⨂�̃�𝑖2 …⨂�̃�𝑖𝑛) 1/𝑛 (23) Step 8: The fuzzy weight (�̃�𝑖) of each attribute (or alternative) is calculated using (�̃�𝑖) values as follows: �̃�𝑖 = �̃�𝑖 ⨂(�̃�1 ⊕ �̃�2 …⊕ �̃�𝑛) −1 (24) In this study, r̃1 ⊕ r̃2 …⊕ r̃n value is accepted as the maximum parameter of the Absolutely High Importance in Table 1 in order to decrease the deviation in the weights. Step 9: The next step is to calculate the fuzzy performance scores of each alternative. To this end, steps 1 – 7 are repeated for each pairwise comparison matrix formed according to the predetermined decision model. The final fuzzy score of each alternative is calculated by Eq 25. �̃�𝑖 = ∑ �̃�𝑗�̃�𝑗,∀𝑖. 𝑛 𝑗=1 (25) where �̃�𝑖 is the fuzzy performance score of alternative i; �̃�𝑗 is the weight of the attribute j, and �̃�𝑗 is the performance score of alternative i with respect to attribute j. Step 10: Trapezoidal fuzzy numbers are defuzzified in order to determine the importance ranking of the alternatives. Defuzzification of the trapezoidal fuzzy numbers is made using Eq. 26 (Sahoo et al., 2016). 𝐷 = 𝑐𝑙+ 2𝑐𝑚1 + 2𝑐𝑚2+ 𝑐𝑢 6 (26) Step 11: The alternatives are ranked according to the defuzzified values and the alternative with the best score is selected. 6. A case study The presented multi-attribute HL warehouse location selection model was applied for an earthquake prone area in the northwest of Turkey. This area contains eight districts and has 23 million inhabitants. Approximately 67,000 km² and 8.5% of Turkey's revenue comes from this region. It is Turkey's main industrial region and includes the city İstanbul, the center of Turkish economy. However, in this region there is a giant IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 285 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 earthquake risk, and the expected damage of an earthquake here is very large anticipating a high number of deaths and physical destruction. The level of damage occurred by the Izmit earthquake in 1999 was so high that it killed around 17,000 people and left almost half a million people homeless. The prioritization of five feasible HL warehouse location alternatives is required in Marmara region. The possible alternatives are Lüleburgaz, Çorlu, Kocaeli, Bursa, and Gönen. The main and sub-attributes given in Fig. 6 are used in the multi-attribute evaluation. The five alternative locations for a warehouse are shown in Fig. 7. Figure 7. Alternative locations for warehouse selection A team of three experts discussed the importance of the main attributes and came to a compromise. Table 3 presents the compromised pairwise comparisons of main attributes using HFLTS. Table 3 Pairwise comparison of main attributes using HFLTS Comparison of Main Attributes w.r.t. Goal Geographical location Cost Transport connectivity Labor availability Stable government Geographical location EE Between WLI and EE Between ELI and EHI Between EHI and ESHI Between WLI and ELI Cost EE Between EHI and ESHI Between EHI and ESHI Between ELI and EHI Transport connectivity EE Between EHI and WHI Between ESLI and ELI Labor availability EE Between EHI and WHI Stable government EE Using the OWA operations defined in Eqs. 17-20, HFLTSs are aggregated into trapezoidal fuzzy sets as in Table 4. IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 286 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Table 4 Aggregated HFLTS scores Comparison of Main Attributes w.r.t. Goal Geographical location Cost Transport connectivity Labor availability Stable government Geographical location (1,1,1,1) (0.2,0.926,1,1) (0.333,1,1,3) (1,2.778,3.222,7) (0.2,0.333,1,1) Cost (1,0.931,1.08,5) (1,1,1,1) (1,2.778,3.222,7) (1,2.778,3.222,7) (0.333,1,1,3) Transport connectivity (0.333,1,1,3) (0.143,0.31,0.36, 1) (1,1,1,1) (1,1,3,5) (0.143,0.319,0.348,1) Labor availability (0.143,0.31,0.36,1) (0.143,0.31,0.36, 1) (0.2,0.333,1,1) (1,1,1,1) (1,1,3,5) Stable government (1,1,3,5) (0.333,1,1,3) (1,2.872,3.14,7) (0.2,0.333,1,1) (1,1,1,1) Table 5 presents the defuzzified weights of the main attributes. Geometric means are calculated by using Eq. 23. Normalized weights are obtained based on Eq. 24. Defuzzified weights are calculated by using Eq. 26. Table 5 Calculation of defuzzified weights of the main attributes Geometric Means Normalized Weights Defuzzified Weights Geographical location (0.508,1.266,1.364,2.141) (0.041,0.193,0.263,0.782) 0.213 Cost (1,1.637,1.83,3.956) (0.082,0.249,0.361,1) 0.280 Transport connectivity (0.467,0.746,1.019,1.968) (0.038,0.114,0.201,0.719) 0.169 Labor availability (0.253,0.423,0.6,1) (0.021,0.064,0.119,0.365) 0.091 Stable government (0.508,0.989,1.752,3.201) (0.041,0.151,0.346,1) 0.247 Tables 6-10 present the pairwise comparison matrices of the sub-attributes with respect to the main attributes geographical location, cost, transport connectivity, labor availability, and stable government respectively. Table 6 Pairwise comparison of sub-attributes using HFLTS w.r.t. geographical location w.r.t. Geographical Location Proximity to urban facilities Proximity to disaster areas Closeness to other warehouses Warehouse security Proximity to urban facilities EE Betweeen ALI and VLI Betweeen EE and EHI Betweeen ESLI and WLI Proximity to disaster areas EE Betweeen VSHI and AHI Betweeen WHI and ESHI Closeness to other warehouses EE Betweeen ESLI and ELI Warehouse security EE From Table 6, the trapezoidal fuzzy weights of the sub attributes with respect to Geographical Location, are obtained as (0.039,0.056,0.086,0.253), (0.246,0.502,0.823,1), (0.03,0.063,0.087,0.192), and (0.068,0.165,0.278,0.761), respectively. IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 287 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Table 7 Pairwise comparison of sub-attributes using HFLTS w.r.t. cost w.r.t. Cost Storage cost Investment cost Labor price Replenishment cost Storage cost EE Betweeen WLI and ELI Betweeen EHI and ESHI WHI Investment cost EE Betweeen ESHI and VSHI Betweeen WHI and ESHI Labor price EE Betweeen WLI and ELI Replenishment cost EE From Table 7, the trapezoidal fuzzy weights of the sub attributes with respect to Cost, are obtained as (0.075,0.207,0.428,0.924), (0.148,0.315,0.778,1), (0.027,0.056,0.126,0.289), and (0.046,0.081,0.185,0.568), respectively. Table 8 Pairwise comparison of sub-attributes using HFLTS w.r.t. transport connectivity w.r.t. Transport Connectivity Availability of seaport and airport Near to (potential) beneficiaries Adequate warehouse facilities Adequate warehouse infrastructure Availability of seaport and airport EE EHI Betweeen EHI and WHI Betweeen EHI and ESHI Near to (potential) beneficiaries EE Betweeen EE and EHI Betweeen EHI and WHI Adequate warehouse facilities EE Betweeen EE and WHI Adequate warehouse infrastructure EE From Table 8, the trapezoidal fuzzy weights of the sub attributes with respect to Transport Connectivity, are obtained as (0.13,0.266,0.487,1),(0.099,0.206,0.364,0.774), (0.066,0.157,0.276,0.588), and (0.036,0.117,0.214,0.393), respectively. Table 9 Pairwise comparison of sub-attributes using HFLTS w.r.t. labor availability w.r.t. Labor Availability Trained and qualified personnel Flexible customs regulations Population density Climate Trained and qualified personnel EE Betweeen WHI and VSHI Betweeen EE and EHI Betweeen ESHI and VSHI Flexible customs regulations EE Betweeen ELI and EE Betweeen EHI and WHI Population density EE Betweeen WHI and ESHI Climate EE From Table 9, the trapezoidal fuzzy weights of the sub attributes with respect to Labor Availability, are obtained as (0.158,0.413,0.546,1), (0.053,0.124,0.198,0.543), (0.091,0.246,0.332,0.778), and (0.028,0.058,0.113,0.276), respectively. IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 288 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Table 10 Pairwise comparison of sub-attributes using HFLTS w.r.t. stable government w.r.t. Stable Government Cooperation with logistics agents Political and economical stability Existence of other agents (NGOs) IT/ Communication Cooperation with logistics agents EE Betweeen WLI and ELI Betweeen ELI and EHI ESHI Political and economical stability EE Betweeen WHI and ESHI ESHI Existence of other agents (NGOs) EE Betweeen EHI and WHI IT/Communication EE From Table 10, the trapezoidal fuzzy weights of the sub attributes with respect to Stable Government, are obtained as (0.077,0.193,0.364,0.791), (0.152,0.334,0.716,1), (0.054,0.114,0.243,0.728), and (0.029,0.058,0.109,0.213), respectively. The next step is to obtain the pairwise comparison matrices of alternatives with respect to each sub-attribute. In our case, there are 20 matrices of such comparisons. Due to the space constraints we only present one of them. Table 11 gives the pairwise comparison of alternatives using HFLTS with respect to proximity to urban facilities. Table 11 Pairwise comparison of alternatives using HFLTS w.r.t. proximity to urban facilities w.r.t. proximity to urban facilities HLW1 HLW2 HLW3 HLW4 HLW5 HLW1 EE Betweeen VLI and WLI Betweeen WHI and ESHI Betweeen ESLI and WLI Betweeen WHI and VSHI HLW2 EE Betweeen ESHI and VSHI Betweeen WLI and ELI Betweeen WHI and ESHI HLW3 EE Betweeen VLI and ESLI Betweeen ESLI and WLI HLW4 EE ESHI HLW5 EE Table 12 shows the trapezoidal fuzzy weights of the main and sub-attributes all together. IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 289 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Table 12 Trapezoidal fuzzy weights of main and sub-attributes Main Attribute Weight Sub-attribute Weight Geographical location (0.041,0.193,0.269,0.782) Proximity to urban facilities (0.002,0.011,0.023,0.198) Proximity to disaster areas (0.02,0.097,0.221,0.782) Closeness to other warehouses (0.001,0.012,0.023,0.15) Warehouse security (0.001,0.032,0.075,0.595) Cost (0.082,0.249,0.361,1) Storage cost (0.006,0.052,0.155,0.924) Investment cost (0.012,0.078,0.281,1) Labor price (0.002,0.014,0.045,0.289) Replenishment cost (0.004,0.02,0.067,0.568) Transport connectivity (0.038,0.114,0.201,0.719) Availability of seaport and airport (0.005,0.03,0.098,0.719) Near to (potential) beneficiaries (0.004,0.023,0.073,0.557) Adequate warehouse facilities (0.003,0.018,0.055,0.423) Adequate warehouse infrastructure (0.001,0.013,0.043,0.283) Labor availability (0.021,0.064,0.119,0.365) Trained and qualified personnel (0.003,0.026,0.065,0.365) Flexible customs regulations (0.001,0.008,0.024,0.198) Population density (0.002,0.016,0.04,0.284) Climate (0.001,0.004,0.013,0.101) Stable government (0.041,0.151,0.346,1) Cooperation with logistics agents (0.003,0.029,0.126,0.791) Political and economical stability (0.006,0.05,0.248,1) Existence of other agents (NGOs) (0.002,0.017,0.084,0.728) IT/Communication (0.001,0.009,0.038,0.213) Table 13 shows the final defuzzified weights of the alternatives with respect to subattributes. According to these results, the prioritization of the alternatives is Bursa (0.261) > Kocaeli (0.232) > Corlu (0.191) > Luleburgaz (0.171) > Gonen (0.146). Turkish humanitarian relief organization should establish the first two warehouses in Bursa and then Kocaeli. IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 290 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 Table 13 Weights of the alternatives Alternative Scores Sub-attribute Bursa Corlu Gonen Kocaeli Luleburgaz Proximity to urban facilities 0.02 0.038 0.007 0.039 0.015 Proximity to disaster areas 0.085 0.093 0.131 0.177 0.037 Closeness to other warehouses 0.027 0.016 0.008 0.031 0.005 Warehouse security 0.116 0.035 0.016 0.081 0.045 Storage cost 0.055 0.068 0.094 0.025 0.189 Investment cost 0.134 0.22 0.093 0.07 0.225 Labor price 0.028 0.036 0.026 0.022 0.06 Replenishment cost 0.108 0.043 0.062 0.092 0.032 Availability of seaport and airport 0.13 0.05 0.089 0.144 0.06 Near to (potential) beneficiaries 0.102 0.063 0.041 0.106 0.02 Adequate warehouse facilities 0.073 0.05 0.034 0.082 0.014 Adequate warehouse infrastructure 0.059 0.015 0.025 0.036 0.011 Trained and qualified personnel 0.08 0.043 0.028 0.061 0.014 Flexible customs regulations 0.013 0.021 0.033 0.006 0.04 Population density 0.049 0.032 0.015 0.059 0.008 Climate 0.004 0.011 0.019 0.007 0.018 Cooperation with logistics agents 0.158 0.093 0.06 0.136 0.034 Political and economical stability 0.226 0.171 0.076 0.118 0.174 Existence of other agents (NGOs) 0.136 0.091 0.052 0.136 0.052 IT/Communication 0.045 0.021 0.011 0.037 0.023 Normalized Total Score 0.261 0.191 0.146 0.232 0.171 7. Conclusion A large number of high-impact natural and man-made disasters, such as floods, earthquakes, storms, and civil disturbance or war have occurred in dissimilar parts of the world in recent years. This condition triggered the need for well-organized stock- holding for humanitarian purposes. Recent studies in MCDM show that Hesitant Fuzzy Set (HFS) exposes a new viewpoint on fuzzy decision making. Contrary to ordinary fuzzy sets, HFSs characterize fuzziness by setting out all the possible values while assigning the membership degree of the elements of a set. Based on these new arguments, we proposed a hesitant fuzzy multi-attribute method to solve HL warehouse location selection problems. Our model based on hesitant fuzzy AHP successfully evaluated alternative HL warehouse location alternatives. We extended Buckley’s ordinary fuzzy AHP method to its hesitant fuzzy version since the other fuzzy AHP have been seriously criticized in the literature methods (Chang, 1996; van Laarhoven and Pedrycz 1983; etc.). Hesitant linguistic term sets provided the flexibility to elicit comparative linguistic expressions by using context-free grammar. The fuzzy linguistic scale is based on the AHP’s classical 1-9 scale. Our hierarchy included 5 main attributes, 16 IJAHP Article: Boltürk, Onar, Öztayşi, Göztepe, Kahraman/ Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP International Journal of the Analytic Hierarchy Process 291 Vol. 8 Issue 2 2016 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v8i2.387 sub-attributes and 5 HL warehouse location alternatives. This research yielded several useful managerial insights. First, the proposed method allows one to deal with incomplete information due to the vagueness of the criteria such as “cooperation with logistics agents” and “political and economic stability”. Second, it provides a systematic approach for solving complex problems that involve many stakeholders. This systematic approach can be used to solve other decision making problems with the same characteristics. A limitation of the proposed method is the cumbersome calculations that are involved. However, this difficulty can be overcome by developing software for this purpose. For further research, other extensions of fuzzy sets such as intuitionistic fuzzy sets, type-2 fuzzy sets, multi fuzzy sets, etc. can be used in the proposed model above. The obtained results can be compared with our results. 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