Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Castiñeira, Elena; Torres-Blanc, Carmen; Cubillo, Susana

doi:10.1080/03081079.2011.592040

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Proof (A) Let T'p(x) Be the Set Of All Finite Parts Of X C1

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Cited by 3 publications

(2 citation statements)

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“…We omit the proof of the above theorem because it is a particular case of Theorems 3.7 and 3.8 given in Ref. 15.…”

Section: Proof (A) Let T'p(x) Be the Set Of All Finite Parts Of X Cmentioning

confidence: 99%

Obtaining Contradiction Measures on Intuitionistic Fuzzy Sets From Fuzzy Connectives

Castiñeira

Torres-Blanc

Cubillo

2012

Int. J. Unc. Fuzz. Knowl. Based Syst.

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In a previous paper1, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of this paper is to construct some families of contradiction measures firstly using continuous t-norms and t-conorms, and secondly by means of strong negations. In both cases, we study the properties that they satisfy. These families are then classified according the different kinds of measures presented in the above paper.

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“…We omit the proof of the above theorem because it is a particular case of Theorems 3.7 and 3.8 given in Ref. 15.…”

Section: Proof (A) Let T'p(x) Be the Set Of All Finite Parts Of X Cmentioning

confidence: 99%

Obtaining Contradiction Measures on Intuitionistic Fuzzy Sets From Fuzzy Connectives

Castiñeira

Torres-Blanc

Cubillo

2012

Int. J. Unc. Fuzz. Knowl. Based Syst.

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“…The only runner-up is the paper by Nechansky (2011), which received three nominations. Each of the following four papers received two nominations: Castiñeira et al (2011), Checkland (2011, Klir (2011), andLouie andPoli (2011).…”

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confidence: 99%

Editorial

Klir

2012

International Journal of General Systems

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Self-contradiction for type-2 fuzzy sets whose membership degrees are normal and convex functions

Torres-Blanc

Hernández

Cubillo

2018

Fuzzy Sets and Systems

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Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Cited by 3 publications

References 12 publications

Obtaining Contradiction Measures on Intuitionistic Fuzzy Sets From Fuzzy Connectives

Obtaining Contradiction Measures on Intuitionistic Fuzzy Sets From Fuzzy Connectives

Editorial

Self-contradiction for type-2 fuzzy sets whose membership degrees are normal and convex functions

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