Ranking Method of Intuitionistic Fuzzy Numbers and Multiple Attribute Decision Making Based on the Probabilistic Dominance Relationship

Abstract

The uncertainty of intuitionistic fuzzy numbers (IFNs) is further enhanced by the existence of the degree of hesitation (DH). The shortcomings of existing researches are mainly reflected in the following situations: when comparing IFNs, the comparison rules of IFNs are difficult to apply to the comparison of any two IFNs, or the relevant methods do not fully consider the uncertainty expressed by DH. Thus, the rationality of the decision results needs to be improved. On the other hand, multi-attribute decision making (DADM) based on IFNs is often not objective due to the need to determine the attribute weight. Moreover, the strict condition of attribute aggregation of classical dominance relation makes it a method that fails considering the practical application. Aiming at the comparison problem of IFNs, this paper takes probability conversion as the starting point and proposes an IFN comparison method based on the area method, which can better deal with the comparison problem of “either superior or inferior” IFNs. In addition, aiming at the MADM problem of an intuitionistic fuzzy information system, we propose an intuitionistic fuzzy probabilistic dominance relation model and construct the MADM method under the probabilistic dominance relation. The series properties of IFNs and probabilistic dominance relation were summarized and proved, which theoretically ensured the scientificity and rigor of the method. The results show that the comparison and ranking method of IFNs proposed in this paper can be applied to the comparison of any two IFNs, and the dominance degree of IFNs is presented in the form of probability, which is more flexible and practical than the classical method. The probabilistic dominance relation method based on IFNs avoids the problem of determining attribute weights subjectively or objectively, and the decision maker can reflect decision preference by adjusting decision parameters to better match the actual problem. The application of this model to a campus express site evaluation further verifies the feasibility of the proposed method and the rationality of the results. In addition, various extension problems of the model and method proposed in this paper are discussed, which pave the way for future related research. This paper constructs a complete decision-making framework through theoretical analysis and application from practical problems, which provides a reference for enriching and improving uncertain decision-making theory and the MADM method.

New Ranking Approach of Intuitionistic Fuzzy Sets and its Application in Cognitive Transportation Problem

“…Garai [51] constructed a novel ranking method for GIFSs, by utilizing the concept of possibility measure. Huang [52] works on the ranking of IFSs based on the area method and multiple attribute decision-making based on the probabilistic dominance relationship. Recently, Robust's ranking index of the MF and the NMF of TrIFSs have been utilized by Popa [53] to build a new ranking function.…”

Multiple-Attribute Decision Making Based on the Probabilistic Dominance Relationship with Fuzzy Algebras

“…Fuzzy algebra-based ranking methods have shown promising results in terms of consistency, accuracy, and applicability. For instance, Huang et al [4] proposed a new ranking method for IFSs based on the probabilistic dominance relationship and fuzzy algebras. The proposed method transformed IFSs into fuzzy sets using the degree of membership and non-membership functions and compared the fuzzy sets using the concept of fuzzy algebras.…”

“…However, there is still a need to develop more effective ranking methods for IFSs that can handle incomplete and uncertain information. For example, Huang et al [4] proposed a new method based on hesitant intuitionistic fuzzy sets, which can handle incomplete and uncertain information in MADM.…”

“…Baklouti et al [26,27] give relevant examples of the application of optimization techniques in solar photovoltaic systems and the consideration of energetic types and maintenance costs in the decision-making process of selling or leasing used vehicles, respectively. The reader can find some other interesting references in [4].…”

Probabilistic Interval Ordering Prioritized Averaging Operator and Its Application in Bank Investment Decision Making

“…Verma et al [47] subsequently introduced the generalized Pythagorean fuzzy probabilistic ordered weighted cosine similarity (GPFPOWCS) operator. Huang et al [48] initiated an IFN comparison method with probability conversion as the foundation.…”