Abstract
Based on comparative studies on correlation coefficient theory and utility theory, a series of rules that utility functions on dual hesitant fuzzy rough sets (DHFRSs) should satisfy, and a kind of novel utility function on DHFRSs are proposed. The characteristic of the introduced utility function is a parameter, which is determined by decision-makers according to their experiences. By using the proposed utility function on DHFRSs, a novel dual hesitant fuzzy rough pattern recognition method is also proposed. Furthermore, this study also points out that the classical dual tool is suitable to cope with dynamic data in exploratory data analysis situations, while the newly proposed one is suitable to cope with static data in confirmatory data analysis situations. Finally, a medical diagnosis and a traffic engineering example are introduced to reveal the effectiveness of the newly proposed utility functions on DHFRSs.
Highlights
Fifty years ago, Zadeh [1] introduced the famous concept “fuzzy set”
Motivated by the works mentioned above, this study explores the dual hesitant fuzzy rough sets (DHFRSs) from the viewpoint of utility
The correlation coefficient on DHFRSs is a kind of exploratory data which is studied from dynamic
Summary
Zadeh [1] introduced the famous concept “fuzzy set”. In fuzzy set theory, it is intermittently difficult for people to resolve the membership degree of an element of a set. By combining the dual hesitant fuzzy set (DHFS) and rough set theory, Zhang et al [19] developed a rough set model called dual hesitant fuzzy rough sets (DHFRSs) over two universes They built up a general shell frame of the decision making methods based upon the DHFRSs of two universes. By using the novel utility function on DHFRSs, a dual hesitant fuzzy rough pattern recognition method was introduced.
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