The Linguistic Picture Fuzzy Set and Its Application in Multi-Criteria Decision-Making: An Illustration to the TOPSIS and TODIM Methods Based on Entropy Weight Article Swipe

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YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.3390/sym12071170

The paper considers the multi-criteria decision-making problem based on linguistic picture fuzzy information. Firstly, we propose the concept of linguistic picture fuzzy set(LPFS), where the positive-membership, the neutral-membership and the negative-membership are represented by linguistic variables, and its operation rules are also discussed. The linguistic picture fuzzy weighted averaging (LPFWA) operator and linguistic picture fuzzy weighted geometric (LPFWG) operator are developed based on the proposed operation rules. Secondly, we propose the generalized weighted distance measure, the generalized weighted Hausdorff distance measure, and the generalized hybrid weighted distance measure between LPFSs and discuss their properties. Thirdly, we extend the technique for order of preference by similarity to the ideal solution (TOPSIS) method and the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method to the proposed distance measure, and the linguistic picture fuzzy entropy method is proposed to calculate the weights of the criteria. Finally, an illustrative example is given to verify the feasibility and effectiveness of the proposed methods, the comparative analysis with other existing methods and sensitivity analysis of the proposed methods are also discussed.

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Mathematics

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TOPSIS Mathematics Entropy (arrow of time) Measure (data warehouse) Ideal solution Operator (biology) Fuzzy logic Similarity measure Fuzzy set Group decision-making Distance measures Artificial intelligence Computer science Data mining Operations research Thermodynamics Physics Transcription factor Gene Chemistry Law Repressor Political science Quantum mechanics Biochemistry

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Type: article
Language: en
Landing Page: https://doi.org/10.3390/sym12071170
PDF: https://www.mdpi.com/2073-8994/12/7/1170/pdf?version=1594779134
OA Status: gold
Cited By: 31
References: 43
Related Works: 10
OpenAlex ID: https://openalex.org/W3043699408

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DOI: https://doi.org/10.3390/sym12071170

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Title: The Linguistic Picture Fuzzy Set and Its Application in Multi-Criteria Decision-Making: An Illustration to the TOPSIS and TODIM Methods Based on Entropy Weight

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Language: en

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Publication year: 2020

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Publication date: 2020-07-14

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Authors: Donghai Liu, Yan Luo, Zaiming Liu

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Landing page: https://doi.org/10.3390/sym12071170

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Concepts: TOPSIS, Mathematics, Entropy (arrow of time), Measure (data warehouse), Ideal solution, Operator (biology), Fuzzy logic, Similarity measure, Fuzzy set, Group decision-making, Distance measures, Artificial intelligence, Computer science, Data mining, Operations research, Thermodynamics, Physics, Transcription factor, Gene, Chemistry, Law, Repressor, Political science, Quantum mechanics, Biochemistry

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Cited by: 31

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Citations by year (recent): 2025: 6, 2024: 4, 2023: 7, 2022: 8, 2021: 6

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