Abstract
Dual hesitant fuzzy sets (DHFSs) is the refinement and extension of hesitant fuzzy sets and encompasses fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as a special case. DHFSs have two parts, that is, the membership function and the non-membership function, in which each function is defined by two sets of some feasible values. Therefore, according to the practical demand, DHFSs are more adjustable than the existing ones and provide the information regarding different objects in much better way. The set pair analysis (SPA) illustrates unsureness in three angles, called “identity”, “discrepancy” and “contrary”, and the connection number (CN) is one of its main features. In the present article, the axiom definition of distance measure between DHFSs and CN is introduced. The distance measures are established on the basis of Hamming distance, Hausdorff distance and Euclidean distance. The previous identities and relationship between them are discussed in detail. On the basis of the geometric distance model, the set-theoretic approach, and the matching functions several novel distance formulas of CN are introduced. The novel distance formulas are then applied to multiple-attribute decision making for dual hesitant fuzzy environments. Finally, to demonstrate the validity of the introduced measures, a practical example of decision-making is presented. The benefits of the new measures over the past measures are additionally talked about.
Highlights
When we use the fuzzy theory to make decision in real life, we face the fuzzy problems which cannot be only represented by certainty or uncertainty
THE NOVEL DISTANCE MEASURE AND connection number (CN) OF set pair analysis (SPA) THEORY In this segment, we have introduced a collection of some new distance formulas using Euclidean, Hamming, and Hausdorff metrics, which will be helpful in real scientific and engineering applications to select the best alternative under the SPA
Where the combination of Dual hesitant fuzzy sets (DHFSs) and SPA provides a technique of transforming dual hesitant fuzzy numbers into corresponding connection number, with no loss of dual hesitant fuzzy information. (ii) The distance measures based on CN of SPA gives clear and transparent results than previously existing measure and distinguish between all the alternatives clearly have simple calculations. (iii) The novel distance formulas discuss the certainty and uncertainty as one consolidated system
Summary
When we use the fuzzy theory to make decision in real life, we face the fuzzy problems which cannot be only represented by certainty or uncertainty. Liu et al.: Distance Measures for Multiple-Attributes Decision-Making Based on CNs of SPA With DHFSs. Wangb [9] used the concept of least common principle with hesitant fuzzy information in decision making. The decision making issues for various fuzzy conditions have moved toward becoming logically significantly more intricate and unsure, MADM issues with dual hesitant fuzzy data have progressively earned more consideration Be that as it may, the greater part of the methods dependent on prospect hypothesis for managing such kind of problems. The present examination outfits an idea of data measures by presenting the class of separation measures in the light of CN of the SPA to deal with dual hesitant fuzzy decision-making issues.
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