An information-based score function of interval-valued intuitionistic fuzzy sets and its application in multiattribute d
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METHODOLOGIES AND APPLICATION
An information-based score function of interval-valued intuitionistic fuzzy sets and its application in multiattribute decision making An-Peng Wei1 • Deng-Feng Li2
•
Ping-Ping Lin1 • Bin-Qian Jiang1
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The score functions are often used to rank the interval-valued intuitionistic fuzzy sets (IVIFSs) in multiattribute decision making (MADM). The purpose of this paper is to develop an information-based score function of the IVIFS and apply it to MADM. Considering the information amount, the reliability, the certainty information, and the relative closeness degree, we propose an information-based score function of the IVIFS. Comparing the information-based score function with existing ranking methods, we find that the information-based score function can overcome the drawbacks of the existing ranking methods and can rank the IVIFSs well. Three illustrative examples of MADM with linear programming are examined to demonstrate the applicability and feasibility of the information-based score function. It is shown that the information-based score function is well defined and can be applied to MADM. Keywords Score function Ranking method Interval-valued intuitionistic fuzzy set Multiattribute decision making
1 Introduction Multiattribute decision making (MADM) is an important part of the decision-making theory, and it has been widely used in many areas such as engineering, scientific research, and artificial intelligence (Wan and Li 2013; Li and Ren 2015; Liang 2018; Yu et al. 2019). How to evaluate the alternatives under attributes accurately and then select the most desirable alternative from the alternative sets is the key problem of the MADM. Due to the lack of knowledge and uncertainty of information, it is difficult for the decision maker to evaluate alternatives under attributes accurately. Instead, people use the method of uncertainty and vagueness to evaluate alternatives under attributes. How to deal with the uncertainty and vagueness is an interesting and important
Communicated by V. Loia. & Deng-Feng Li [email protected] 1
School of Economics and Management, Fuzhou University, Fuzhou 350108, China
2
School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 611731, China
subject. Fuzzy sets (FSs) (Zadeh 1965) seem to be suitable for dealing with the uncertainty and vagueness, and they are often used to evaluate the alternatives under attributes in the MADM. As the extension of the FSs, the intuitionistic fuzzy sets (IFSs) (Bustine and Burillo 1996) are often used to evaluate the alternatives through the membership and non-membership degrees. Regarding as the generalization of the IFSs, the membership and nonmembership degrees of the interval-valued intuitionistic fuzzy sets (IVIFSs) (Atanassov 1994; Atanassov and Gargov 1989) are intervals instead of crisp numbers. Thus, the IVIFS is more flexible to simulat
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