Abstract
This paper investigates an approach for multiple attribute decision making (MADM) problems with interval-valued intuitionistic fuzzy numbers (IVIFNs). To do that, the nonlinear score, accuracy and hesitation functions of IVIFNs are developed based on the normal distribution. The novelty of these nonlinear functions is that they have an additional variance value, which can have more information to rank IVIFNs than Xu and Chen’s score function and Ye’s accuracy function. Based on these nonlinear functions, a ranking method for IVIFNs is proposed. Furthermore, a nonlinearly optimized model is proposed to obtain attribute weights by integrating these nonlinear functions. Then, we develop an approach for interval-valued intuitionistic fuzzy MADM programs in which two cases are considered: the attribute weight information is known and particularly known. In the end, we apply the proposed approach to select green supplier.
Highlights
The theory of fuzzy sets (FSs) proposed by Zadeh (1965) is a powerful tool to deal with vagueness, whose basic component is only a membership function. Atanassov (1986) introduced the concept of intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, which is an extension of Zadeh’s fuzzy sets
This article aims to develop the nonlinear score, accuracy and hesitation functions of interval-valued intuitionistic fuzzy numbers (IVIFNs) based on the normal distribution, and investigate a novel ranking approach
Based on these three types of values for IVIFNs: the score function S, the accuracy function H and hesitation function π, we shall present a method for the comparison between any two IVIFNs as follows: Definition 10 (Order relation of IVIFNs)
Summary
The theory of fuzzy sets (FSs) proposed by Zadeh (1965) is a powerful tool to deal with vagueness, whose basic component is only a membership function. Atanassov (1986) introduced the concept of intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, which is an extension of Zadeh’s fuzzy sets. IVIFNs are more complicate than IFNs because that their membership and non-membership functions are interval numbers, which are nonlinear functions and can not be compared directly They are not rich enough to capture all the information contained in IVIFNs. they are not rich enough to capture all the information contained in IVIFNs To resolve these problems, we firstly build some judgment criterions to study the rationality of score and accuracy functions.
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