Abstract
The main purpose of this planned manuscript is to establish an algorithm for the solution of multiattribute decision-making (MADM) issues, where the experts utilizing linguistic variables provide the information about attributes in the form of picture hesitant fuzzy numbers. So, for the solution of these kinds of issues, we develop the TOPSIS algorithm under picture hesitant fuzzy environment using linguistic variables, which plays a vital role in practical applications, notably MADM issues, where the decision information is arranged by the decision-makers (DMs) in the form of picture hesitant fuzzy numbers. Finally, a sample example is given as an application and appropriateness of the planned method. At the end, we conduct comparison analysis of the planned method with picture fuzzy TOPSIS method and intuitionistic fuzzy TOPSIS method.
Highlights
E idea of intuitionistic fuzzy set (IFS) was first introduced by Atanassov, which is the generalization of fuzzy sets (FSs) and is denoted by the degree of membership and degree of nonmembership [8, 9], under the limitation that the sum of its membership degrees and nonmembership degrees is ≤ 1
Torra [14] coined the opinion of hesitant fuzzy sets (HFSs), which are the extension of fuzzy sets
Ere are many problems in real life, which must not be shown in IFS theory, for example, in the issue of voting system human notions which include other answers, for example, yes, no, abstinence, and refusal. en Coung covered these gaps by adding neutral-membership function in IFS theory
Summary
Let⌣hH: X ⟶ R([0, 1]), hesitant fuzzy set (HFS) H in X can be defined as follows: H. where hH(x⌣) denotes the set of possible values between 0 and 1. HFN is denoted by h hH(x⌣) and HFNs is the set of all hesitant fuzzy numbers. [14] Let h, h1 and h2 be three hesitant fuzzy numbers. A fuzzy sets distance measure between t€1 and t€2 is a mapping from (PHFS) up to unit closed interval [0, 1], satisfying the following conditions:. We present the relationship among linguistic variables and picture hesitant fuzzy numbers (PHFNs). TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is a very convenient practical method for selecting of suitable alternative and for ranking of alternatives with respect to their distance from the positiveideal solution and negative-ideal solution.
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