Decision-Making with Bipolar Neutrosophic TOPSIS and Bipolar Neutrosophic ELECTRE-I

Akram, Muhammad; Shumaiza,; Smarandache, Florentín

doi:10.3390/axioms7020033

Cited by 59 publications

(26 citation statements)

References 22 publications

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“…Atanassov considered the human hesitancy and generalized the fuzzy sets to intuitionistic fuzzy sets (IFSs), which assigns a membership grade

μ

and a nonmembership grade

λ

to the objects under consideration, with the condition

μ + λ \leq 1

and the nonzero hesitancy part

normalπ = 1 - μ - λ

. Since its discovery, the IFSs have gained extensive attentions in extending the classical TOPSIS model in the IFS context along with its extensions and have been extensively applied in different areas of real world having MCDM problems …”

Section: Introductionmentioning

confidence: 99%

“…Since its discovery, the IFSs have gained extensive attentions in extending the classical TOPSIS model in the IFS context along with its extensions and have been extensively applied in different areas of real world having MCDM problems. [13][14][15][16][17][18] The restriction ≤ μ λ + 1 in IFS confines the selection of the membership and nonmembership grades. To evade the issue, Yager and colleague 19,20 discovered the notion of Pythagorean fuzzy set (PFS), represented by a membership function μ and a nonmembership function λ with the condition ≤ μ λ + 1 2 2 .…”

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confidence: 99%

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Group decision‐making based on pythagorean fuzzy TOPSIS method

2019

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Group decision‐making is a process wherein multiple individuals interact simultaneously, analyze problems, evaluate the possible available alternatives, characterized by multiple conflicting criteria, and choose suitable alternative solution to the problem. Technique for establishing order preference by similarity to the ideal solution (TOPSIS) is a well‐known method for multiple‐criteria decision‐making. The purpose of this study is to extend the TOPSIS method to solve multicriteria group decision‐making problems equipped with Pythagorean fuzzy data, in which the assessment information on feasible alternatives, provided by the experts, is presented as Pythagorean fuzzy decision matrices having each entry characterized by Pythagorean fuzzy numbers. A revised closeness index is utilized to obtain the ranking of alternatives and to identify the optimal alternative. The developed Pythagorean fuzzy TOPSIS (PF‐TOPSIS) is illustrated by a flow chart. At length, practical examples interpreting the applicability of our proposed PF‐TOPSIS are solved.

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“…Atanassov considered the human hesitancy and generalized the fuzzy sets to intuitionistic fuzzy sets (IFSs), which assigns a membership grade

μ

and a nonmembership grade

λ

to the objects under consideration, with the condition

μ + λ \leq 1

and the nonzero hesitancy part

normalπ = 1 - μ - λ

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Group decision‐making based on pythagorean fuzzy TOPSIS method

2019

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“…Garg and Nancy [16] defined the concept of Muirhead‐mean aggregation operators (MAO) in solving MCDA problems. Akram et al [17] introduced the concept of the bipolar neutrosophic set and solved MCDA problems using TOPSIS and ELECTRE methods.…”

Section: Introductionmentioning

confidence: 99%

Multiple‐criteria decision analysis process by using prospect decision theory in interval‐valued neutrosophic environment

Chinnadurai

Albert

2020

CAAI trans. intell. technol.

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This study intends to present an innovative study for ranking the alternatives in multiple‐criteria decision analysis (MCDA) problems under the interval‐valued neutrosophic soft set (IVNSS) environment. In this study, to illustrate the notion of objective and subjective weight, the prospect decision theory (PDT) performs an imperative role in determining decision‐making problems. PDT predicts human behaviour in terms of gains and losses and considers the expected utility relation to a reference point rather than complete outcomes. In the analysis of merged criteria weight and the prospect decision‐making matrix, the authors get a new dimension level for ranking the array of alternatives. This manuscript provides an improved score function (SF) to convert the interval‐valued membership grades of truth, indeterminacy and falsity into a mathematical and computational value. The advantage of this method is that it merges the objective and subjective weight during the proposed method. They propose an algorithm based on the SF to determine MCDA problems with IVNSSs. They illustrate a case study and provide various comparative analyses to show its significance over existing studies.

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“…Akram et al [45] introduced novel approach in decision-making with mF ELECTRE-I. With the passage of time, a number of extensions for fuzzy ELECTRE-I have been proposed by several researchers including [46][47][48][49][50][51][52][53][54][55]. For other notations, terminologies and applications, the readers are referred to [56][57][58][59][60].…”

Section: Introductionmentioning

confidence: 99%

Multi-Criteria Decision-Making under mHF ELECTRE-I and HmF ELECTRE-I

2019

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In a few years, hesitant fuzzy sets (HFSs) have had an impact on several different areas of decision science. However, a number of researches have utilized the Elimination and choice translating reality (ELECTRE) methods to determine the multi-criteria decision-making (MCDM) problems with hesitant information. The aim of this research article is to develop new multi-criteria group decision-making (MCGDM) methods, such as the m-polar hesitant fuzzy ELECTRE-I (mHF ELECTRE-I) method and hesitant m-polar fuzzy ELECTRE-I (HmF ELECTRE-I) method. Proposed MCGDM techniques based on the hybrid models, m-polar hesitant fuzzy sets (mHFS-sets) and hesitant m-polar fuzzy sets (HmF-sets), which are the natural generalizations of HFSs and m-polar fuzzy sets (mF sets). These models enable us to deal with multipolar information under hesitancy. We use the proposed methods to deal the complex problems in which the membership degree of an element of given set uses the m different numeric and fuzzy values, to rank all the alternatives and to determine the best alternative. We present two practical examples that illustrate the procedure of the proposed methods. We also discuss the differences and comparative analysis of the proposed methods. Finally, we develop an algorithm that implements our decision-making procedures by using computer programming.

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Decision-Making with Bipolar Neutrosophic TOPSIS and Bipolar Neutrosophic ELECTRE-I

Cited by 59 publications

References 22 publications

Group decision‐making based on pythagorean fuzzy TOPSIS method

Group decision‐making based on pythagorean fuzzy TOPSIS method

Multiple‐criteria decision analysis process by using prospect decision theory in interval‐valued neutrosophic environment

Multi-Criteria Decision-Making under mHF ELECTRE-I and HmF ELECTRE-I

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