Abstract
In this paper, the dual hesitant fuzzy rough set (DHFRS) is studied from the viewpoint of assessment deviations. Firstly, according to the relationship between intuitionistic fuzzy set and vague set, the DHFRS is transferred into a fuzzy set, where the membership of any given element to it has multi-grouped values. By the idea of bootstrap sampling, a group of four sets are generated to describe the membership degree on DHFRS, where the elements of the aforementioned sets are all considered as assessment values. Secondly, the generated sets are dealt with by assessment deviation theories, and specifically, two variables are proposed to describe the systematic and random deviations of the sets. Thirdly, the true-value of the membership degree of any elements to the set is estimated by a deviation-based dual hesitant fuzzy rough weighted aggregating operator. Fourthly, a dual hesitant fuzzy rough pattern recognition approach based on assessment deviation theories is proposed. Finally, an urban traffic modes recognition example is given to illustrate the validity of the proposed theories on DHFRSs.
Highlights
Rough set, first described by Pawlak [1], is a formal approximation of a crisp set in terms of a pair of sets, which gives the lower and the upper approximations of an original set
The four sets are weighted according to two parameters, where one quantifies the systematic deviations of the four sets, while the other one quantifies the random deviations of them; subsequently, the true-value of the membership degree of an element to a set is estimated by an operator; a dual hesitant fuzzy rough pattern recognition approach based on assessment deviation theories is proposed
The weighted membership degree sets of an object to different patterns are obtained by the dual hesitant fuzzy rough weighted aggregating (DHFRWA) operator proposed in the previous subsection; subsequently, according to the comparative results of any two degree sets generated by Definition 7, an pattern recognition result is obtained
Summary
First described by Pawlak [1], is a formal approximation of a crisp set in terms of a pair of sets, which gives the lower and the upper approximations of an original set. The four sets are weighted according to two parameters, where one quantifies the systematic deviations of the four sets, while the other one quantifies the random deviations of them; subsequently, the true-value of the membership degree of an element to a set is estimated by an operator; a dual hesitant fuzzy rough pattern recognition approach based on assessment deviation theories is proposed.
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