Abstract
Similarity measures have a great importance in the decision-making process. In order to identify the similarity between the options, many experts have established several types of similarity measures on the basis of vectors and distances. The Cosine, Dice, and Jaccard are the vector similarity measures. The present work enclosed the modified Jaccard and Dice similarity measures. Founded on the Dice and Jaccard similarity measures, we offered a multiple criteria decision-making (MCDM) model under the dual hesitant fuzzy sets (DHFSs) situation, in which the appraised values of the alternatives with respect to criteria are articulated by dual hesitant fuzzy elements (DHFEs). Since the weights of the criteria have a much influence in making the decisions, therefore decision makers (DMs) allocate the weights to each criteria according to their knowledge. In the present work, we get rid of the doubt to allocate the weights to the criteria by taking an objective function under some constraints and then extended the linear programming (LP) technique to evaluate the weights of the criteria. The Dice and Jaccard weighted similarity measures are practiced amongst the ideal and each alternative to grade all the alternatives to get the best one. Eventually, two practical examples, about investment companies and selection of smart phone accessories are assumed to elaborate the efficiency of the proposed methodology.
Highlights
In everyday life, decision-making plays a central role in choosing the best option out of certain choices
Researchers divert their attention towards hesitant fuzzy sets (HFSs) and ample work is carried out in the multiple criteria decision-making (MCDM) process with the help of HFSs [7,8,9]. e decision makers (DMs) feel that the above extensions of fuzzy sets (FSs) have inadequacy of data because FSs treat only one membership value; intuitionistic fuzzy sets (IFSs) deal two kinds of information that are membership and nonmembership while HFSs consider the set values in its membership value but ignore the nonmembership value
We propose a MCDM model based on the two weighted vector similarity under dual hesitant fuzzy data, which can be formulated as follows: Step 1: construct a dual hesitant fuzzy decision matrix (DHFM) denoted by D [dij]n×m according to the given data presented by the DM
Summary
Decision-making plays a central role in choosing the best option out of certain choices. Torra [6] presented a novel extension of FSs, the hesitant fuzzy sets (HFSs), which augmented by adding diverse values to the membership Researchers divert their attention towards HFSs and ample work is carried out in the MCDM process with the help of HFSs [7,8,9]. Many experts have presented a number of similarity measures for MCDM problems to select the most favorable alternative from the various options having identical features under the certain criteria, for example, similarity measures based on distance, Cosine similarity measure, Jaccard similarity measure, and Dice similarity measure. A comparative analysis and conclusions are given in Sections 6 and 7, respectively
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