Advances in Fuzzy Preference Relations and Decision-Making Methods with Applications

Dear Colleagues,

Preference relations are matrix structures constructed by a two-by-two comparison of alternatives, where each element represents the degree of preference of one alternative over another. Considering the advantage of fuzzy set theory in expressing the uncertainty of preference information, preference relations are extended into fuzzy environments. Fuzzy preference relations (FPR), interval-valued fuzzy preference relations (IVFPR), intuitionistic fuzzy preference relations (IFPR), Pythagorean fuzzy preference relations (PFPR), q-rung orthopair fuzzy preference relations (q-ROFPR), hesitant fuzzy preference relations (HFPR) and hesitant fuzzy linguistic preference relations (HFLPR) have emerged in recent years. Compared with the traditional preference relation, the FPR and its extensions express and provide feedback on the expert's preference in a more reasonable way. In some decision-making processes, due to subjective factors such as knowledge structure and the judgement level of experts, experts often provide some fuzzy membership values and their extensions when constructing judgement matrices. The FPR and its extensions provide more reasonable feedback on the decision maker's cognitive outcome, describing the uncertainty of the decision maker's preference. The core of the decision-making problem in preference-based relationship environments includes to the ways in which we can define the consistency of preference relationships and how to obtain the weight vector of preference relations.

We hope that this Special Issue will stimulate both theoretical and applied research on fuzzy reference relations and decision-making methods. It is certainly impossible in this short editorial to provide a more comprehensive description of all the potential articles in this Special Issue. However, we sincerely hope that our effort in compiling these articles will enrich our readers and inspire researchers with regard to the seemingly common but indeed important issue of fuzzy preference relations and decision-making methods.

Dr. Zhenyu Zhang
Dr. Vladimir Simic
Dr. Jing Li
Guest Editors

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