Exponential similarity measures for Pythagorean fuzzy sets and their applications to pattern recognition and decision-making process

Nguyen, Xuan Thao; Nguyen, Vinh; Nguyen, Van Hanh; Garg, Harish

doi:10.1007/s40747-019-0105-4

Cited by 54 publications

(28 citation statements)

References 53 publications

(111 reference statements)

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“…The geometric mean is used to aggregate expert opinions. Weakly important (Wk) (1,3,5) Essentially important (Es) (3,5,7)…”

Section: Comparative Analysismentioning

confidence: 99%

“…Very strongly important (Vs) (5,7,9) Absolutely important (Ab) (7,9,9) Step 2: Weights are calculated. Firstly, the fuzzy weight matrix is calculated by Buckley's method.…”

Section: Comparative Analysismentioning

confidence: 99%

“…Decision-making theory is one of the most fundamental issues used to find feasible solutions in decisionmaking situations where many factors should be taken into account. Considering the uncertainty and multi-factor inherent in new product development, applying multi-criteria decision making (MCDM) theory in the process will be useful [5].…”

Section: Introductionmentioning

confidence: 99%

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Prioritizing the Factors for Customer-Oriented New Product Design in Industry 4.0

Erdoğan

Bilişik

2020

Sakarya University Journal of Science

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Customer-oriented new product design is one of the most important processes in the production environment to improve product quality and reliability and maximize their productivity. It is also necessary to consider customer expectations in this process for an effective design. In this paper, we present a methodology which is called Pythagorean Fuzzy Analytic Hierarchy Process (PF-AHP) for prioritizing criteria which should be considered for an efficient customer-oriented new product design in Industry 4.0 transition primarily. We use Pythagorean Fuzzy Sets (PFSs) to allow experts to make more flexible evaluations and handle the uncertain and vague information in a wider way. We determine five main and eighteen sub-criteria that affect the new product design process and after applying PF-AHP, we find that the most important main-criterion determined as "Production" and sub-criterion determined as "Return on Investment".

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“…The geometric mean is used to aggregate expert opinions. Weakly important (Wk) (1,3,5) Essentially important (Es) (3,5,7)…”

Section: Comparative Analysismentioning

confidence: 99%

“…Very strongly important (Vs) (5,7,9) Absolutely important (Ab) (7,9,9) Step 2: Weights are calculated. Firstly, the fuzzy weight matrix is calculated by Buckley's method.…”

Section: Comparative Analysismentioning

confidence: 99%

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Prioritizing the Factors for Customer-Oriented New Product Design in Industry 4.0

Erdoğan

Bilişik

2020

Sakarya University Journal of Science

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“…Khan et al [ 21 ] proposed the Dombi aggregation operators using Dombi norm for PyF information and discussed their application in decision making. Nguyen and Garg [ 22 ], proposed the exponential based similarity measure for PyFS. Garg [ 23 ], developed the neutrality geometric operations under PyF information.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Fuzzy TOPSIS Method Based on Entropy Measure under Spherical Fuzzy Information

Barukab

Abdullah

Ashraf

et al. 2019

Entropy

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Spherical fuzzy set (SFS) is one of the most important and extensive concept to accommodate more uncertainties than existing fuzzy set structures. In this article, we will describe a novel enhanced TOPSIS-based procedure for tackling multi attribute group decision making (MAGDM) issues under spherical fuzzy setting, in which the weights of both decision-makers (DMs) and criteria are totally unknown. First, we study the notion of SFSs, the score and accuracy functions of SFSs and their basic operating laws. In addition, defined the generalized distance measure for SFSs based on spherical fuzzy entropy measure to compute the unknown weights information. Secondly, the spherical fuzzy information-based decision-making technique for MAGDM is presented. Lastly, an illustrative example is delivered with robot selection to reveal the efficiency of the proposed spherical fuzzy decision support approach, along with the discussion of comparative results, to prove that their results are feasible and credible.

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“…Because of stronger expressiveness than IFSs, PFSs have also achieved a wide range of applications in MCGDM. A number of research topics regarding PFSs for MCGDM, such as operational rules of Pythagorean fuzzy numbers (PFNs) [18,19], correlation and correlation coefficient of PFSs [20], information measures of PFSs [21][22][23], aggregation operators of PFNs [24][25][26][27], and MCDM or MCGDM methods based on PFSs [28][29][30], have received widespread attention during the past few years.…”

Section: Introductionmentioning

confidence: 99%

Archimedean Muirhead Aggregation Operators of q-Rung Orthopair Fuzzy Numbers for Multicriteria Group Decision Making

et al. 2019

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q-Rung orthopair fuzzy number (qROFN) is a flexible and superior fuzzy information description tool which can provide stronger expressiveness than intuitionistic fuzzy number and Pythagorean fuzzy number. Muirhead mean (MM) operator and its dual form geometric MM (GMM) operator are two all-in-one aggregation operators for capturing the interrelationships of the aggregated arguments because they are applicable in the cases in which all arguments are independent of each other, there are interrelationships between any two arguments, and there are interrelationships among any three or more arguments. Archimedean T-norm and T-conorm (ATT) are superior operations that can generate general and versatile operational rules to aggregate arguments. To take advantage of qROFN, MM operator, GMM operator, and ATT in multicriteria group decision making (MCGDM), an Archimedean MM operator, a weighted Archimedean MM operator, an Archimedean GMM operator, and a weighted Archimedean GMM operator for aggregating qROFNs are presented to solve the MCGDM problems based on qROFNs in this paper. The properties of these operators are explored and their specific cases are discussed. On the basis of the presented operators, a method for solving the MCGDM problems based on qROFNs is proposed. The effectiveness of the proposed method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons. The demonstration results suggest that the proposed method has satisfying generality and flexibility at aggregating q-rung orthopair fuzzy information and capturing the interrelationships of criteria and the attitudes of decision makers and is feasible and effective for solving the MCGDM problems based on qROFNs.

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Exponential similarity measures for Pythagorean fuzzy sets and their applications to pattern recognition and decision-making process

Cited by 54 publications

References 53 publications

Prioritizing the Factors for Customer-Oriented New Product Design in Industry 4.0

Prioritizing the Factors for Customer-Oriented New Product Design in Industry 4.0

A New Approach to Fuzzy TOPSIS Method Based on Entropy Measure under Spherical Fuzzy Information

Archimedean Muirhead Aggregation Operators of q-Rung Orthopair Fuzzy Numbers for Multicriteria Group Decision Making

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