Research On Dual Hesitant Fuzzy Information Measurements And Granular Structure

With the rapid development of artificial intelligence technology,decision-making activities in various fields in real life are increasing day by day.Because dual hesitant fuzzy set can model the data environment with multiple membership degrees and multiple non-membership degrees at the same time,and can provide more sufficient and flexible decision-making information for decision-makers,it has become a hot issue for fuzzy decision-makers.Granular computing is a computing paradigm for people to solve complex problems.It uses granulation strategy to abstract,divide and transform complex problems.From the perspective of granular computing,it can study dual hesitant fuzzy information and its granularity.It is of great significance to reveal the correlation between information measurements and the nested relationship of granular structure.In this paper,the information measurements and granular structures of dual hesitant fuzzy sets are deeply studied.Firstly,the partial-order relationships on granular structures are defined.Secondly,different information measurements are proposed.Finally,the distances between the extension distance of dual hesitant fuzzy sets and granular structure are used to measure,The clustering algorithm of dual hesitant fuzzy sets and the clustering algorithm of dual hesitant fuzzy granular structures are proposed respectively.The specific work is as follows:(1)In the dual hesitant fuzzy environment,firstly,the important implicit data of hesitation degree is applied to the calculation of the distances between dual hesitant fuzzy sets.Secondly,the extended distances are used as an important basis for the clustering algorithm.Finally,an example shows that using the hesitation degrees to calculate the distances and applying extended distances to the clustering algorithm of dual hesitant fuzzy sets,compared with other distances,this distance can effectively improve the clustering accuracy at the same level of trust.(2)Combining dual hesitant fuzzy set and granular computing theory,a dual hesitant fuzzy granular computing model is established.Firstly,the dual hesitant fuzzy granular structure and basic operations are defined.Secondly,the dual hesitant fuzzy partial-order relations are proposed by using the elements,cardinality and sequence in the granular structures.Finally,the nested relationships between these partial-order relations are studied from the perspective of mathematics.(3)In the dual hesitant fuzzy granular computing model,firstly,the dual hesitant fuzzy information measurements system(including information entropy,rough entropy,information granularity,etc.)is defined.Secondly,the mathematical characteristics of these information measurements are discussed.Finally,the transformation laws between information measurements are obtained.(4)Based on the operations between dual hesitant fuzzy granular structures,firstly,the distance measure of dual hesitant fuzzy granular structures is defined,and then this distance is applied to the clustering algorithm.An example shows that using this distance for clustering can improve the intuitive reliability of human clustering results.The dual hesitant fuzzy granular computing model proposed in this paper provides a theoretical support for dual hesitant fuzzy information clustering computing and intelligent decision-making,and is of great significance for the further study of generalized fuzzy sets and their decision-making theory.