Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making

Akram, Muhammad; Habib, Amna; Ilyas, Farwa; Dar, Jawaria Mohsan

doi:10.3390/mca23030042

Cited by 52 publications

(30 citation statements)

References 24 publications

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“…However,

{(\sqrt{3} / 4)}^{2} + {(1 / \sqrt{7})}^{2} \leq 1

, that is why the PFN is able to capture this preference information. Hence, the space of Pythagorean fuzzy membership grades is greater than the space of intuitionistic fuzzy membership grades because of the corresponding constraint conditions as shown in Figure and is in general capable to accommodate greater degrees of uncertainty in MCDM problems . Zhang and Xu explored potent mathematical operations on PFNs and generalized the classical TOPSIS approach to MCDM with PFSs.…”

Section: Introductionmentioning

confidence: 99%

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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“…However,

{(\sqrt{3} / 4)}^{2} + {(1 / \sqrt{7})}^{2} \leq 1

Section: Introductionmentioning

confidence: 99%

Group decision‐making based on pythagorean fuzzy TOPSIS method

2019

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“…Liang et al created Pythagorean fuzzy Bonferroni mean aggregation operator and gave its accelerative calculating algorithm with the multithreading. For other terminologies and applications, one can view …”

Section: Introductionmentioning

confidence: 99%

Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision‐making

2019

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A Pythagorean fuzzy set, an extension of intuitionistic fuzzy sets, is very helpful in representing vague information that occurs in real world scenarios. The Dombi operators with operational parameters, have excellent flexibility. Due to the flexible nature of these Dombi operational parameters, this research paper introduces some new aggregation operators under Pythagorean fuzzy environment, including Pythagorean Dombi fuzzy weighted arithmetic averaging (PDFWAA) operator, Pythagorean Dombi fuzzy weighted geometric averaging (PDFWGA) operator, Pythagorean Dombi fuzzy ordered weighted arithmetic averaging operator and Pythagorean Dombi fuzzy ordered weighted geometric averaging operator. Further, this paper presents several advantageous characteristics, including idempotency, monotonicity, boundedness, reducibility and commutativity of preceding operators. By utilizing PDFWAA and PDFWGA operators, this article describes a multicriteria decision-making (MCDM) technique for solving MCDM problems. Finally, a numerical example related to selection of a leading textile industry is presented to illustrate the applicability of our proposed technique. K E Y W O R D S multicriteria decision-making, ordered weighted aggregation operators, Pythagorean Dombi fuzzy weighted, Pythagorean fuzzy sets, Τ-norms

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“…Akram and Naz [15] discussed the energy of Pythagorean fuzzy graphs with applications. Recently, certain operations on PFGs and IFG of the three-type and n-type were discussed by Akram et al [16]. The same authors discussed certain Pythagorean fuzzy graphs and also defined q-rung orthopair fuzzy competition graphs with applications in [17].…”

Section: Introductionmentioning

confidence: 99%

q-Rung Orthopair Fuzzy Hypergraphs with Applications

2019

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The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the q th power of the truth-membership and the q th power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter q, q ≥ 1 . In this research study, we design a new framework for handling uncertain data by means of the combinative theory of q-rung orthopair fuzzy sets and hypergraphs. We define q-rung orthopair fuzzy hypergraphs to achieve the advantages of both theories. Further, we propose certain novel concepts, including adjacent levels of q-rung orthopair fuzzy hypergraphs, ( α , β ) -level hypergraphs, transversals, and minimal transversals of q-rung orthopair fuzzy hypergraphs. We present a brief comparison of our proposed model with other existing theories. Moreover, we implement some interesting concepts of q-rung orthopair fuzzy hypergraphs for decision-making to prove the effectiveness of our proposed model.

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Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making

Cited by 52 publications

References 24 publications

Group decision‐making based on pythagorean fuzzy TOPSIS method

Group decision‐making based on pythagorean fuzzy TOPSIS method

Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision‐making

q-Rung Orthopair Fuzzy Hypergraphs with Applications

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