A Multi-Criteria Intuitionistic Fuzzy Group Decision Making Method for Supplier Selection with VIKOR Method

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain, and is typically a multi-criteria group decision problem. In many practical situations, there usually exists incomplete and uncertain information, and the decision makers cannot easily express their judgments on the candidates with exact and crisp values. Therefore, in this paper an extended VIKOR method for group decision making with intuitionistic fuzzy numbers is proposed to solve the supplier selection problem under incomplete and uncertain information environment. In other researches in this area, the weights of each decision makers and in many of them the weights of criteria are pre-determined, but these weights have been calculated in this paper by using the decision matrix of each decision maker. Also, normalized Hamming distance is proposed to calculate the distance between intuitionistic fuzzy numbers. Finally, a numerical example for supplier selection is given to clarify the main results developed in this paper. DOI: 10.4018/ijfsa.2012010101 2 International Journal of Fuzzy System Applications, 2(1), 1-17, January-March 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. INTRODUCTION Supplier selection is a fundamental issue of supply chain area which heavily contributes to the overall supply chain performance. Particularly for companies who spend a high percentage of their sales revenue on parts and material supplies, and whose material costs represent a larger portion of total costs, savings from supplies are of particular importance These, strongly urge for a more systematic and transparent approach to purchasing decision making, especially regarding the area of supplier selection. Selecting the suppliers significantly reduces the purchasing cost and improves corporate competitiveness, and that is why many experts believe that the supplier selection is the most important activity of a purchasing department. Supplier selection is the process by which suppliers are reviewed, evaluated, and chosen to become part of the company’s supply chain. The major aims of supply chain management are to reduce supply chain risk, reduce production costs, maximize revenue, improve customer service, optimize inventory levels, business processes, and cycle times, and resulting in increased competitiveness, customer satisfaction and profitability (Chou & Chang, 2008; Ha & Krishnan, 2008; Heizer & Render, 2004; Monczka et al., 2001; Simchi-Levi et al., 2003; Stevenson, 2005). Indeed supplier selection is a multiple criteria decisionmaking (MCDM) problem affected by several conflicting factors such as price, quality and delivery. Several factors affect a supplier’s performance. Dickson (1996), Ellram (1990), Roa and Kiser (1980), and Stamm and Golhar (1993) identified, respectively 60, 18, 13 and 23 criteria for supplier selection. One of the well-known studies on supplier selection belongs to Dickson (1966) who identified 23 important evaluation criteria for supplier selection. Weber et al. (1992) reviewed and classified 74 articles addressed the supplier selection problem. Over the years, several techniques have been developed to solve the problem efficiently. Supply Chain Management has received recently considerable attention in both academia and industry. de Boer et al. (2001) identified four stages for supplier selection including definition of the problem, formulation of criteria, qualification, and final selection, respectively. They reviewed and classified MCDM approaches for supplier selection. Several methodologies have been proposed for the supplier selection problem. The systematic analysis for supplier selection includes categorical method, weighted point method (Timmerman, 1986; Zenz, 1981), matrix approach (Gregory, 1986), vendor performance matrix approach (Soukup, 1987) vendor profile analysis (Thompson, 1990), analytic hierarchy process (AHP) (Barbarosoglu & Yazgac, 1997; Narasimhan, 1983), analytic network process (ANP) (Sarkis & Talluri, 2000), mathematical programming (Chaudhry et al., 2991; Pan, 1989; Rosenthal et al., 1995; Sadrian & Yoon, 1994) and multiple objective programming (MOP) (Buffa & Jackson, 1983; Feng et al., 2001; Ghoudsypour & O’Brien, 1998; Sharma et al., 1989; Weber & Ellram, 1992). In essential, the supplier selection problem in supply chain system is a group decision making combination of several and different criteria with different forms of uncertainty (Chena et al., 2006). Hence this problem is a kind of MCDM problem which requires MCDM methods for an effective problem-solving. The supplier selection process is often in influenced by uncertainty in practice (de Boer et al., 1998; Min, 1994). Several influence factors are often not taken into account in the decision-making process, such as incomplete information, additional qualitative criteria and imprecision preferences (Chen et al., 2006; Zhang et al., 2009). Therefore, fuzzy set theory has been applied to supplier selection recently. Li et al. (1997) and Holt (1998) discussed the application of fuzzy set theory in supplier selection. Haq and Kannan (2006) presented a structured model for evaluating the supplier selection for the rubber industry using AHP and the model is verified with the fuzzy AHP. Bayrak et al. (2007) presented a fuzzy multi-criteria group decision-making approach to supplier selection based on fuzzy arithmetic operation. Chou and Chang (2008) International Journal of Fuzzy System Applications, 2(1), 1-17, January-March 2012 3 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. presented strategy-aligned fuzzy simple multiattribute rating technique (SMART) approach for solving the supplier selection problem from the perspective of strategic management of the supply chain. Chan et al. (2008) presented fuzzy AHP to efficiently tackle both quantitative and qualitative decision factors involved in the selection of global supplier. Also, in the TOPSIS method is extended for decision-making problems with fuzzy and interval data. This paper proposes an intuitionistic fuzzy multi-criteria group decision making with VOKOR method for supplier selection problem. VIKOR (VIsekriterijumsko KOmpromisno Rangiranje) is a multi-attribute decision making technique which has a simple computation procedure that allows simultaneous consideration of the closeness to ideal and anti-ideal alternatives. It determines the compromise ranking-list, the compromise solution, and the weight stability intervals for preference stability of the compromise solution obtained with the initial (given) weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. It introduces the multicriteria ranking index based on the particular measure of closeness to the ideal solution (Opricovic, 1998; Opercovic & Tzeng, 2002). In the process of VIKOR, the performance ratings and the weights of the criteria are given as exact values. In real-world situation, because of incomplete or non-obtainable information, the data (attributes) are often not so deterministic, there for they usually are fuzzy/ imprecise. Therefore, some researches try to use VIKOR method for fuzzy/imprecise data. For example, Sayadi et al. (2009) extended the VIKOR method for decision making problem with interval number. And also, Sanayei et al. (2010) developed a group decision making process for supplier selection with VIKOR under fuzzy environment. In fuzzy sets theory, the membership of an element to a fuzzy set is only a single value between zero and one (Wang & Xin, 2005). However, in reality, the degree of nonmembership of an element in a fuzzy set is not certainly equal to 1 minus the degree of membership. That is to say, there may be some hesitation degree. Therefore, Atanassov (1986) extended Zadeh’s fuzzy sets (Zadeh, 1965) to intuitionistic fuzzy sets, which is a generalization of the concept of fuzzy sets. The theory of intuitionistic fuzzy sets is characterized by a membership degree, a non-membership degree, and a hesitation degree. In Boran et al. (2009) TOPSIS method combined with intuitionistic fuzzy set is proposed to select appropriate supplier in group decision making environment. Group decision making involves weighted aggregation of all individual decisions to obtain a single collective decision. The weights of DMs play an important role in the processes of weighted aggregation. In this paper an extended VIKOR method for group decision making with intuitionistic fuzzy numbers is proposed to solve the supplier selection problem under incomplete and uncertain information environment. In other researches in this area, the weights of each decision makers and in many of them the weights of criteria are pre-determined, but these weights have been calculated in this paper in new method by using the decision matrix of each decision maker. In the presented method, first, we select the most important criteria by Delphi method, then we define a new similarity measure to obtain the weights of each decision maker and by use of these weights, we can determine the weights of criteria. Also, normalized Hamming distance is proposed to calculate the distance between intuitionistic fuzzy numbers. Rest of the paper is organized as follows. A brief description about the concept of intuitionistic fuzzy sets, operations on IF sets, comparison between two IF numbers and distance between intuitionistic fuzzy sets is given. We will focus on the proposed method. Then, a numerical example is demonstrated. Finally, some conclusions are drawn for the study. 4 International Journal of Fuzzy System Applications, 2(1), 1-17, January-March 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. BASIC CONCEPTS The Concept of Intuitionistic Fuzzy Sets Concept of fuzzy set defined by Zadeh (1965) is as follows. Definition 1. Let X be a classical set of objects, called the universe, whose generic elements are denoted by x . The membership in a crisp subset of X is often viewed as characteristic function μA from X to {0,1} such that: μA x if andonly if x A other ( ) = ∈ 1 0 , , , wise.     where {0,1} is called a valuation set. If the valuation set is allowed to be the real interval [0,1], A is called a fuzzy set and denoted by A and μ A x ( ) is the degree of membership of x