A New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making
Ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs) is an important task for solving real-life Decision-Making problems. It is a potential area of research that has attracted the researchers working in fuzzy mathematics. Researchers worldwide are looking for a unique ranking principle t...
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2021
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oai:doaj.org-article:ca162a70bff44340b3625f2429dc6df42021-11-11T18:13:38ZA New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making10.3390/math92126472227-7390https://doaj.org/article/ca162a70bff44340b3625f2429dc6df42021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2647https://doaj.org/toc/2227-7390Ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs) is an important task for solving real-life Decision-Making problems. It is a potential area of research that has attracted the researchers working in fuzzy mathematics. Researchers worldwide are looking for a unique ranking principle that can be used to discriminate any two arbitrary IVIFNs. Various ranking functions on the set of IVIFNs have been proposed. However, every method has some drawbacks in ranking arbitrary IVIFNs due to the partial ordering. This paper introduces a new ranking principle for comparing two arbitrary IVIFNs by defining a new score function based on the non-membership value of IVIFNs. In this paper, firstly, the limitations of a few well-known and existing ranking methods for IVIFNs have been discussed. Secondly, a new non-membership score on the class of IVIFNs has been introduced. Thirdly, the superiority of the proposed score function in ranking arbitrary IVIFNs over the existing methods has been demonstrated. Finally, the proposed non-membership score function has been utilized in interval-valued intuitionistic fuzzy TOPSIS (IVIF-TOPSIS) using numerical examples.Jeevaraj SelvarajAbhijit MajumdarMDPI AGarticleinterval-valued intuitionistic fuzzy numbernon-membership score functionMCDMIVIF-TOPSISIVIF-MCDMdefuzzificationMathematicsQA1-939ENMathematics, Vol 9, Iss 2647, p 2647 (2021) |
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interval-valued intuitionistic fuzzy number non-membership score function MCDM IVIF-TOPSIS IVIF-MCDM defuzzification Mathematics QA1-939 |
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interval-valued intuitionistic fuzzy number non-membership score function MCDM IVIF-TOPSIS IVIF-MCDM defuzzification Mathematics QA1-939 Jeevaraj Selvaraj Abhijit Majumdar A New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making |
| description |
Ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs) is an important task for solving real-life Decision-Making problems. It is a potential area of research that has attracted the researchers working in fuzzy mathematics. Researchers worldwide are looking for a unique ranking principle that can be used to discriminate any two arbitrary IVIFNs. Various ranking functions on the set of IVIFNs have been proposed. However, every method has some drawbacks in ranking arbitrary IVIFNs due to the partial ordering. This paper introduces a new ranking principle for comparing two arbitrary IVIFNs by defining a new score function based on the non-membership value of IVIFNs. In this paper, firstly, the limitations of a few well-known and existing ranking methods for IVIFNs have been discussed. Secondly, a new non-membership score on the class of IVIFNs has been introduced. Thirdly, the superiority of the proposed score function in ranking arbitrary IVIFNs over the existing methods has been demonstrated. Finally, the proposed non-membership score function has been utilized in interval-valued intuitionistic fuzzy TOPSIS (IVIF-TOPSIS) using numerical examples. |
| format |
article |
| author |
Jeevaraj Selvaraj Abhijit Majumdar |
| author_facet |
Jeevaraj Selvaraj Abhijit Majumdar |
| author_sort |
Jeevaraj Selvaraj |
| title |
A New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making |
| title_short |
A New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making |
| title_full |
A New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making |
| title_fullStr |
A New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making |
| title_full_unstemmed |
A New Ranking Method for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Multi-Criteria Decision-Making |
| title_sort |
new ranking method for interval-valued intuitionistic fuzzy numbers and its application in multi-criteria decision-making |
| publisher |
MDPI AG |
| publishDate |
2021 |
| url |
https://doaj.org/article/ca162a70bff44340b3625f2429dc6df4 |
| work_keys_str_mv |
AT jeevarajselvaraj anewrankingmethodforintervalvaluedintuitionisticfuzzynumbersanditsapplicationinmulticriteriadecisionmaking AT abhijitmajumdar anewrankingmethodforintervalvaluedintuitionisticfuzzynumbersanditsapplicationinmulticriteriadecisionmaking AT jeevarajselvaraj newrankingmethodforintervalvaluedintuitionisticfuzzynumbersanditsapplicationinmulticriteriadecisionmaking AT abhijitmajumdar newrankingmethodforintervalvaluedintuitionisticfuzzynumbersanditsapplicationinmulticriteriadecisionmaking |
| _version_ |
1718431910921764864 |