Analysis on the Hesitation and its Application to Decision Making

Youpeng Yang; Sanghyuk Lee; Kyeong Soo Kim; Haolan  Zhang; Xiaowei Huang; Witold Pedrycz

doi:10.31181/dmame722024978

Authors

Youpeng Yang School of Advanced Technology, Xi’an Jiaotong-Liverpool University, Suzhou Jiangsu, China https://orcid.org/0000-0003-2248-8679
Sanghyuk Lee School of computing, New Uzbekistan University, Tashkent, Uzbekistan https://orcid.org/0000-0003-0253-6936
Kyeong Soo Kim School of Advanced Technology, Xi’an Jiaotong-Liverpool University, Suzhou Jiangsu, China https://orcid.org/0000-0002-4123-2647
Haolan Zhang SCDM Centre, Zhejiang University, Ningbo, China https://orcid.org/0000-0002-5033-1866
Xiaowei Huang Department of Computer Science, University of Liverpool, Liverpool, United Kingdom https://orcid.org/0000-0001-6267-0366
Witold Pedrycz Department of Electrical & Computer Engineering, University of Alberta, Edmonton, Canada https://orcid.org/0000-0002-9335-9930

DOI:

https://doi.org/10.31181/dmame722024978

Keywords:

Intuitionistic fuzzy sets, Poincaré metric, Score function, Decision-making strategy

Abstract

A novel score function based on the Poincaré metric is proposed and applied to a decision-making problem. Decision-making on Fuzzy Sets (FSs) has been considered due to the flexibility of the data, and it is applied to the decision-making. However, decisions with FSs are sometimes nondecisive even for different membership degrees. Hence, Intuitionistic Fuzzy Sets (IFSs) data is applied to design a score function for the decision-making with the Poincaré metric. This function is supported by the profound information of IFSs; IFSs include hesitation degree together with membership and non-membership degree. Hence, IFS membership and non-membership degree are expressed as two-dimensional vectors satisfying the Poincaré metric for simplification. At the same time, the proposed approach addresses the hesitation information in the IFS data. Next, a score function is proposed, constructed and provided. The proposed score function has a strict monotonic property and addresses the preference without resorting to the accuracy function. The strict monotonic property guarantees the preference of all attributes. Additionally, the existing problem of score function design in IFSs is addressed: they return zero scores even with different meanings for the same membership and non-membership degree. The advantages of the proposed score function over existing ones are demonstrated through illustrative examples. From the calculation results, the proposed decision score function discriminates between all candidates. Hence, the proposed research provides a solid foundation for the hesitation analysis on the decision-making problem.

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