A Novel Distance Measure for Pythagorean Fuzzy Sets and its Applications to the Technique for Order Preference by Similarity to Ideal Solutions

Zhou, Fang; Chen, Ting‐Yu

doi:10.2991/ijcis.d.190820.001

Cited by 33 publications

(17 citation statements)

References 41 publications

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“…Grag [22] also presented the generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for Pythagorean fuzzy information. For more information related to PyFSs, we may refer to [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making

2019

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In this manuscript, the notions of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets (CFSs) are combined is to propose the complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental laws. The Cq-ROFSs are an important way to express uncertain information, and they are superior to the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the real part (similarly for imaginary part) of complex-valued membership degree and the qth power of the real part (similarly for imaginary part) of complex-valued non‐membership degree is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we develop the score function, accuracy function and comparison method for two Cq-ROFNs. Based on Cq-ROFSs, some new aggregation operators are called complex q-rung orthopair fuzzy weighted averaging (Cq-ROFWA) and complex q-rung orthopair fuzzy weighted geometric (Cq-ROFWG) operators are investigated, and their properties are described. Further, based on proposed operators, we present a new method to deal with the multi‐attribute group decision making (MAGDM) problems under the environment of fuzzy set theory. Finally, we use some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

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Section: Introductionmentioning

confidence: 99%

Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making

2019

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“…From this perspective, the third motivation of this article is to strictly carry out the fundamental procedure of the VIKOR method: determine the PFPIS and PFNIS according to relative distance and information reliability-based method [68], calculate the separation to the PFPIS and PFNIS via the novel distance measure between PF sets that reflects both length distance and angular distance [69], rank the suppliers in accordance with the consistency of the overall value, group utility, and individual regret, and test acceptable stability and advantage. The, the final solution for green supplier selection can be effectively addressed.…”

Section: B Fuzzy Methods For Green Supplier Evaluationmentioning

confidence: 99%

“…Firstly, we construct a set of hierarchical evaluation criteria in allusion to green supplier selection that can fully reflect the green performance of the suppliers, and utilize the AHP to determine the criterion weights that comprehensively reflect the intention of the DMs. Secondly, we extend the VIKOR to PF scenario, obtain the ratings of candidates regarding the criteria based on the seven-point scale linguistic terms, determine the magnitudes of PF set based on relative distance and reliability-based method [68], then compute the distance from PFPIS and PFNIS via the newest Hamming distance measure [69], then accurately acquire the compromise solution indices. Thirdly, we utilize the MRM to synthesize differentiated ranking order results along with the variable preference values, the weights of which are identified by OWA within normal distribution [72].…”

Section: Primary Study and Contributions Of This Papermentioning

confidence: 99%

“…Then, Li and Zeng [80], Zeng et al [81] presented the novel distance measures adding parameters  and d to the formulas. Afterwards, Zhou and Chen [69] identified some defects in available distance measures, and presented a new Hamming distance measure that considered both length distance and angular distance to comprehensively reflect greater spectrum of PFNs, and fulfill unique characteristics of distance measure that have been demonstrated. Definition 4 [69]: Given any two PFNs β can be described as below:…”

Section: B Distance Measures For Pfnsmentioning

confidence: 99%

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An Integrated Multicriteria Group Decision-Making Approach for Green Supplier Selection Under Pythagorean Fuzzy Scenarios

Zhou

Chen

2020

IEEE Access

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As a critical component in green supply chain activities, green supplier selection modelled as the typical multicriteria group decision-making (MCGDM) problem, has received tremendous attention both from scholars and practitioners. This article aims to advance an integrated approach for precisely addressing this urgent problem under Pythagorean fuzzy (PF) scenario. Firstly, analytic hierarchy process (AHP) is utilized for computing criterion weights that comprehensively reflect the intention of decision makers (DMs). Secondly, extend the Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) to PF scenario, and apply the newest magnitude comparison method and distance measure of PF sets in the p L − metric equation to accurately acquire the ranking indices, then obtain the different ranks of candidates along with the adjustment of DM's preference value to balance the group utility and individual regret. Thirdly, median ranking method (MRM) is employed to reach a consensus opinion for the differentiated ranks of candidates via the attribute-wise rank and linear programming model. Subsequently, a numerical example for an agrifood company in China is introduced to illustrate the feasibility of our AHP-VIKOR-MRM method. Finally, conduct the comparison with some available MCGDM methods with PF information to interpret the stability and practicability of our presented method. INDEX TERMS Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR), analytic hierarchy process (AHP), median ranking method (MRM), Pythagorean fuzzy (PF) sets, green supplier

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“…Zhang and Xu (2014) developed a distance measure between PFSs. Afterwards, to reflect the properties of PFSs, Li and Zeng (2018) and Zhou and Chen (2019) put forward novel distance measures for PFSs respectively. In addition, some distances between HFSs have been developed and applied to MADM (Xu & Xia, 2011a;Li et al, 2015;Liu et al, 2017).…”

Section: Literature Reviewmentioning

confidence: 99%

INVESTMENT DECISION MAKING ALONG THE B&R USING CRITIC APPROACH IN PROBABILISTIC HESITANT FUZZY ENVIRONMENT

Wang

Zhang

Chen

2020

Journal of Business Economics and Management

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The Belt and Road (B&R) Initiative receives enthusiastic response, the aim of which is to develop cooperative partnerships with countries along the routes and build a community of common destiny. So far, Chinese companies have invested in many different countries along the B&R. Generally, the investment decision making problems are characterized by high risk and uncertainty. Then how to make an appropriate investment decision will be a thorny issue. In this paper, probabilistic hesitant fuzzy set (PHFS) is used for handling uncertainty in multiple attribute decision making (MADM), and the criteria importance through intercriteria correlation (CRITIC) approach is extended to obtain attribute weights, no matter whether the weight information is incompletely known or not. Considering that the existing probabilistic hesitant fuzzy distance measures fail to meet the condition of distance measure, a new distance between PHFSs is proposed and applied to investment decision making for countries along the B&R. In the last, comparative analyses are performed to illustrate the advantages of the presented approach.

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A Novel Distance Measure for Pythagorean Fuzzy Sets and its Applications to the Technique for Order Preference by Similarity to Ideal Solutions

Cited by 33 publications

References 41 publications

Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making

Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making

An Integrated Multicriteria Group Decision-Making Approach for Green Supplier Selection Under Pythagorean Fuzzy Scenarios

INVESTMENT DECISION MAKING ALONG THE B&R USING CRITIC APPROACH IN PROBABILISTIC HESITANT FUZZY ENVIRONMENT

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