Relating De Morgan triples with Atanassov’s intuitionistic De Morgan triples via automorphisms

Costa, Claudilene Gomes da; Bedregal, Benjamín R. C.; Neto, Adrião Duarte Dória

doi:10.1016/j.ijar.2010.11.004

Cited by 43 publications

(13 citation statements)

References 32 publications

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“…Thus, by the Remark 2 in Ref. 19 and Proposition 28, it follows that the composition operator • :Ũ →Ũ is an order-preserving bijection. In addition, for all φ ∈ Aut(U ) andX ∈Ũ, the operator ( • ) (φ)(X) = φ (X) can be expressed as: So, Theorem 5 guarantees equivalent compositions related to the φ-representability of automorphisms from Aut(U ) to Aut(Ũ).…”

Section: Now Letmentioning

confidence: 70%

“…19, it guarantees that an IvA Φ preserves diagonal elements onŨ , which means, for Φ ∈ Aut(Ũ ), Φ(D) =D is verified.…”

Section: Atanassov's Intuitionistic Automorphismsmentioning

confidence: 99%

“…(14), is an order-preserving bijection from Aut(U ) to Aut(Ũ ), based on Remark 2 from da Costa et al 19 Automorphisms in Aut(U ) can be obtained by projection functions of Φ ∈ Aut(Ũ ). Additionally, by results in Prop.…”

Section: Relationships Between Aut(ũ ) and Aut(u )mentioning

confidence: 99%

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Correlation in Interval-Valued Atanassov’s Intuitionistic Fuzzy Sets — Conjugate and Negation Operators

Reiser

Bedregal

2017

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

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This paper studies the conjugate functions related to main connectives of the Intervalvalued Atanassov's Intuitionistic Fuzzy Logic. The relationships among automorphism classes are formalized by the φ-representability theorem, passing from automorphisms to interval-valued intuitionistic automorphisms, also visiting other two ones, intuitionistic automorphisms and interval-valued automorphisms. Additionally, the φ-conjugate of an interval-valued Atanassov's intuitionistic fuzzy negation can be obtained either from an interval-valued fuzzy negation or from an Atanassov's intuitionistic fuzzy negation, including a discussion presenting such reverse constructions. The φ-conjugate of an interval-valued Atanassov's intuitionistic fuzzy negation not only preserves the main properties of its corresponding fuzzy negation but also of two other ones, the intuitionistic fuzzy negation and interval-valued fuzzy negation. Moreover, an extension of the intuitionistic fuzzy index as well as the correlation coefficient is discussed in terms of fuzzy negations, by considering the Atanassov's Intuitionistic Fuzzy Logic.

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Section: Now Letmentioning

confidence: 70%

“…19, it guarantees that an IvA Φ preserves diagonal elements onŨ , which means, for Φ ∈ Aut(Ũ ), Φ(D) =D is verified.…”

Section: Atanassov's Intuitionistic Automorphismsmentioning

confidence: 99%

See 1 more Smart Citation

Correlation in Interval-Valued Atanassov’s Intuitionistic Fuzzy Sets — Conjugate and Negation Operators

Reiser

Bedregal

2017

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

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“…In [17], the Atanassov's operator was considered together with representable Atanassov's Intuitionistic De Morgan triples in order to generate new De Morgan triples, providing an extension of the notions of De Morgan triples and automorphisms on unitary interval for IFSs.…”

Section: Related Workmentioning

confidence: 99%

“…Let I be a I ðIa;I b ;Ka;KbÞ -representable implication, as defined in Proposition 4.2, by Eq (17). and F ðI;KaÞ be ðI; K a Þ-generated implication given according with Definition 5.1.…”

mentioning

confidence: 99%

K-operators: An approach to the generation of interval-valued fuzzy implications from fuzzy implications and vice versa

Reiser

Bedregal

2014

Information Sciences

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Typical Hesitant Fuzzy Negations

Bedregal

Santiago

Bustince

et al. 2014

Int. J. Intell. Syst.

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Since the seminal paper of fuzzy set theory by Zadeh in 1965, many extensions have been proposed to overcome the difficulty for assigning the membership degrees. In recent years, a new extension, the hesitant fuzzy sets, has attracted a lot of interest due to its usefulness to handle those problems in which it is difficult to provide accurately a single membership value; since for hesitant sets, membership values are given by a whole set of values. On the other hand, since fuzzy negations have an important role in applications as well as in the theoretical approach to of fuzzy logics, it is important to study an extension of the concept of fuzzy negation for hesitant fuzzy degrees (elements). In this paper, we propose such a definition and we study some of the main properties of this new concept.

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Relating De Morgan triples with Atanassov’s intuitionistic De Morgan triples via automorphisms

Cited by 43 publications

References 32 publications

Correlation in Interval-Valued Atanassov’s Intuitionistic Fuzzy Sets — Conjugate and Negation Operators

Correlation in Interval-Valued Atanassov’s Intuitionistic Fuzzy Sets — Conjugate and Negation Operators

K-operators: An approach to the generation of interval-valued fuzzy implications from fuzzy implications and vice versa

Typical Hesitant Fuzzy Negations

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