Abstract
The concept of dual hesitant fuzzy sets (DHFSs), which was first introduced as a new extension of fuzzy sets and hesitant fuzzy sets in 2012, is a useful tool to deal with the vagueness and ambiguity in many practical problems under hesitant fuzzy environment. Normally, we use the definition of distance to describe the relationship of two DHFSs. However, considering that the existing distance measures of DHFSs still have some major shortcomings, so in this paper, we firstly introduce a new concept –hesitance degree of each dual hesitant fuzzy element (DHFE) to these existing distance measures and then develop several novel distance measures in which both the values and the numbers of values of DHFE are taken into account. The properties of these new distance measures are discussed. Finally, we apply our proposed distance measures of DHFSs in pattern recognition making to illustrate their validity and applicability.
Highlights
The concept of fuzzy set was introduced by Zadeh in 1965 as an extension of the classical notion of sets
In the process of practical application, we found that these existing distance measures of dual hesitant fuzzy sets (DHFSs) still have some notable short comings, the most obvious is that they can only cover the divergence of the values but fail to consider the numbers of value of two given DHFSs
It’s very necessary to take into account both the difference of the values and that of the numbers when we study the difference between the DHFSs
Summary
The concept of fuzzy set was introduced by Zadeh in 1965 as an extension of the classical notion of sets (see [1, 2]). On the basis of HFSs, Zhu and Xu [3] introduced the definition of DHFSs which uses the membership hesitancy function and the non-membership hesitancy function to support a more exemplary and flexible access to assign values for each element in the domain, it is a very useful tool to deal with vagueness and ambiguity in the pattern recognition problems under hesitant fuzzy environment. It’s very necessary to take into account both the difference of the values and that of the numbers when we study the difference between the DHFSs. In this paper, we referred to [4, 5], we propose some new distance measures for DHFSs in this paper by taking into account the hesitance of the hesitant fuzzy sets and investigate their application in practical pattern recognition.
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