Management Science and Research December 2015, Volume 4, Issue 4, PP.50-55
A Note about Multi-criteria Fuzzy Decision Making Method Based on a Novel Accuracy Function Defined on Two Opposite Aspects Xinshang You†, Tong Chen College of Management and Economics, Tianjin University, Tianjin 300072, China †
Email: xinshangyou@163.com
Abstract This article proposes a method on multi-criteria decision making problem depending on a novel accuracy function under the interval-valued intuitionistic fuzzy (IVIF) environment. The novel accuracy function is denoted in two opposite aspects, leading to the decision making problem considered more reasonably. In this paper, the IVIF weighted arithmetic operator and the IVIF weighted geometric average operator are both utilized. Based on the developed method, we rank the alternatives and choose the desirable one. Finally, an illustrative example is given to demonstrate the developed approach. Keywords: Interval-valued Intuitionistic Fuzzy Set; Aggregation Operator; Multi-criteria Fuzzy Decision Making; Accuracy Function
1 INTRODUCTION Fuzzy set theory system has been developed successfully, which is attracting the attentions of scholars from different fields. Half of a century ago, Zadeh (1965) proposed the theory of fuzzy set (FS) firstly, which describes the membership degree by an exact number belonging to the interval [0, 1]. In 1975, Zadeh introduced the concept of interval-valued fuzzy set (IVFS), whose membership degree is given by a subinterval of [0, 1]. Atanassov (1986) developed the fuzzy set theory by defining intuitionistic fuzzy set (IFS) which is characterized by a membership degree and a non-membership degree whose values are both numbers between [0, 1]. Later, Atanassov and Gargov (1989) extended IFS to the interval-valued intuitionistic fuzzy set (IVIFS), which is denoted also by a membership degree and a non-membership degree, but the values are subintervals of [0, 1] rather than the real numbers of IFS. Depending on these extensions of above researchers, significant theoretical developments (Z. Xu, 2010; Z. Xu, R. Yager, 2006; Z. Xu, 2007; Y. Jiang, Z. Xu, X. Yu, 2015) and various applications (S. De, R. Biswas, A.Roy, 2001; F. Ye, 2010; M. Medineckene, E. Zavadskas, F. Bjork, Z. Turskis, 2015; J.Wu, Chiclana, 2014) have been published in numerical influential journals. Multi-criteria fuzzy decision making problem (Z. Xu, M. Xia, 2012; N. Chen, Z. Xu, M. Xia, 2013) is an important branch of applications derived from fuzzy sets theory. And this paper mainly discusses this kind of problem. In our daily life, people always need to deal with decision-making problems with respect to choosing the optimal alternative according to the objective criteria. Xu (2007) proposed the score function and accuracy function for IVIFS to rank the elements named interval-valued intuitionistic fuzzy numbers (IVIFNs) of it. However, his definitions loose valid in some cases. To overcome this drawback, Z. Wang et al. (2009) studied the comparisons between any interval-valued intuitionistic fuzzy numbers (IVIFNs) in much more full aspects, considering the uncertainty degree. J. Ye (2009) and V. Lakshmana (2011) proposed two different novel accuracy functions, respectively. However, as known well, the magic charm of fuzzy set theory is that, it describes objective things with the consideration of uncertainty, leading it closer to the realities. The researchers mentioned above, ranked the IVIFSs by combining the membership degree and non-membership degree together, obtaining an exact value for comparison. In this paper, we discuss the ranking problems of IVIFSs in two points of view: the positive aspect and - 50 www.ivypub.org/msr