Closure theory for semirings-valued fuzzy sets with applications to new fuzzy structures

Močkoř, Jǐŕı

doi:10.1016/j.ijar.2023.108953

Cited by 2 publications

(1 citation statement)

References 22 publications

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“…In traditional mathematics, an element belongs to a single set, whereas in fuzzy set theory, an element can belong to multiple sets, with its membership degree expressed by a real number between 0 and 1. Fuzzy set concepts are intuitive and flexible, making them suitable for dealing with real-world uncertain and vague issues, such as in engineering, artificial intelligence, and control systems [4][5][6](Močkoř J 2023;Liu Z 2023;Tan T 2023). The core idea of fuzzy set theory lies in the concept of membership function, which views the relationship between an element and a set as a continuous process rather than a discrete boundary.…”

Section: Introductionmentioning

confidence: 99%

A novel Clark distance measure method for intuitionistic fuzzy sets with pattern classification applications

WU,

Wang

2024

Preprint

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Fuzzy sets possess remarkable abilities in expressing and handling information uncertainty, which has resulted in their widespread application in various fields. Nevertheless, distance measurement between IFSs for quantitating their differences and levels of differentiation has remained an open problem that deserves attention. Despite the development of various metrics, they either lack intuitive insight or do not satisfy the axioms of distance measurement, leading to counterintuitive results. To address these issues, this paper proposed a distance measurement method based on Clark divergence, which satisfies the distance measurement axioms and exhibits nonlinearity. Numerical examples demonstrate that our method effectively distinguishes different indicators, yielding more reasonable results. Moreover, when comparing relative differences of the results, our method demonstrated superior adaptability to complex environmental decision-making, providing decision-makers with more accurate and confidential judgments. The pattern classification algorithm designed in this paper will offer a promising solution to inference problems.

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Section: Introductionmentioning

confidence: 99%

A novel Clark distance measure method for intuitionistic fuzzy sets with pattern classification applications

WU,

Wang

2024

Preprint

View full text Add to dashboard Cite

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A Novel Clark Distance-Based Decision-Making Algorithm on Intuitionistic Fuzzy Sets

Wu,

Wang,

Zhang

2024

Electronics

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Fuzzy sets possess remarkable abilities in expressing and handling information uncertainty, which has resulted in their widespread application in various fields. Nevertheless, distance measurement between IFSs for quantitating their differences and levels of differentiation has remained an open problem that deserves attention. Despite the development of various metrics, they either lack intuitive insight or do not satisfy the axioms of distance measurement, leading to counterintuitive results. To address these issues, this paper proposed a distance measurement method based on Clark divergence, which satisfies the distance measurement axioms and exhibits nonlinearity. Numerical examples demonstrate that our method effectively distinguishes different indicators, yielding more reasonable results. Moreover, when comparing relative differences of the results, our method demonstrated superior adaptability to complex environmental decision-making, providing decision-makers with more accurate and confidential judgments. In our numerical and pattern classification application tests, we achieve an accuracy of 98%, a 40% increase in computing time efficiency and a relative diversity improvement of 35%. The pattern classification algorithm designed in this paper will offer a promising solution to inference problems.

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Closure theory for semirings-valued fuzzy sets with applications to new fuzzy structures

Cited by 2 publications

References 22 publications

A novel Clark distance measure method for intuitionistic fuzzy sets with pattern classification applications

A novel Clark distance measure method for intuitionistic fuzzy sets with pattern classification applications

A Novel Clark Distance-Based Decision-Making Algorithm on Intuitionistic Fuzzy Sets

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