Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment

Abstract

With the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SNHFS) is an efficient tool to process the vague information and contains the ideas of a single-valued neutrosophic hesitant fuzzy set (SVNHFS) and an interval neutrosophic hesitant fuzzy set (INHFS). In this paper, we propose a decision-making approach based on the maximizing deviation method and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) to solve the MADM problems, in which the attribute weight information is incomplete, and the decision information is expressed in simplified neutrosophic hesitant fuzzy elements. Firstly, we inaugurate an optimization model on the basis of maximizing deviation method, which is useful to determine the attribute weights. Secondly, using the idea of the TOPSIS, we determine the relative closeness coefficient of each alternative and based on which we rank the considered alternatives to select the optimal one(s). Finally, we use a numerical example to show the detailed implementation procedure and effectiveness of our method in solving MADM problems under simplified neutrosophic hesitant fuzzy environment.

Picture Fuzzy TOPSIS Method Based on CPFRS Model: An Application to Risk Management Problems

“…Since the TOPSIS method is suitable for the calculation of small samples and the calculation of large samples, it has been successfully applied to MCDM problems in various complicated fuzzy environments [13,35,44,[65][66][67][68][69]. We can see that the advantage of the CPFRS model and the TOPSIS method cannot be ignored.…”

Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers

“…In fuzzy decision-making problems, various new fuzzy decision-making methods [1][2][3] have received many applications under neutrosophic, simplified neutrosophic hesitant fuzzy, and bipolar neutrosophic environments.…”

“…To express both the continuous Z-numbers of truth, falsity, and indeterminacy membership functions and the reliability measures in MDM problems, it is necessary that this study needs to propose an MDM method based on trapezoidal neutrosophic Z-numbers (TrNZNs) to make up such insufficiencies of existing information expressions and MDM methods in the environments of TrNNs and NZNs. To do so, the main aims of this article are (1) to propose a TrNZN set and some basic operations of TrNZNs, (2) to introduce score and accuracy functions of TrNZN for ranking TrNZNs, (3) to put forward the TrNZNWAA and TrNZNWGA operators for aggregating TrNZNs, (4) to develop a MDM approach using the proposed aggregation operators and score and accuracy functions for solving MDM problems under the environment of TrNZNs, and (5) to apply the established MDM approach to an MDM example of software selection for revealing its efficiency in the setting of TrNZNs. e rest of the article is composed of the following sections.…”

“…, 1] indicate that the alternative Q i satisfies the degrees and reliability measures of the criteria s j , (I Vij1 , I Vij2 , I Vij3 , I Vij4 ) ⊆ [0, 1] and (I Rij1 , I Rij2 , I Rij3 , I Rij4 ) ⊆ [0, 1] indicate the indeterminate degrees and reliability measures of the alternative Q i over the criteria s j , and (F Vij1 , F Vij2 , F Vij3 , F Vij4 ) ⊆ [0, 1] and (F Rij1 , F Rij2 , F Rij3 , F Rij4 ) ⊆ [0,1] indicate that the alternative A i does not satisfy the degrees and reliability measures of the criteria s j , along with 0 ≤ T Vij4 + I Vij4 + F Vij4 ≤ 3 and 0 ≤ T Rij4 + I Rij4 + F Rij4 ≤ 3. Hence, all the specified TrNZNs can be constructed as the following decision matrix Z � (z ij ) 5×4 :…”

Certain Properties of Vague Graphs with a Novel Application

“…Ramakrishna [7] recommended the vague graph (VG) notion and evaluated some of its features. Akram et al [8][9][10][11][12][13][14] presented new definitions of FGs. Borzooei and Rashmanlou [15][16][17][18] investigated different concepts on VG.…”