On the Representation of Intuitionistic Fuzzy&amp;gt;tex&amp;lt;$t$&amp;gt;/tex&amp;lt;-Norms and&amp;gt;tex&amp;lt;$t$&amp;gt;/tex&amp;lt;-Conorms

Deschrijver, Glad; Cornelis, Chris; Kerre, Etienne

doi:10.1109/tfuzz.2003.822678

Cited by 485 publications

(282 citation statements)

References 18 publications

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“…Previously Deschrijver et al (see [77]) proved this theorem for A-IFSs. The only small difference between these two studies lies essentially in the fact that for the negations of the A-IFSs, K α operators are not used, whereas these operators are used in the characterization of the IV negations developed in [54].…”

Section: Representation Theorem For IV Negationsmentioning

confidence: 84%

“…Historically, this theorem provided the first construction method for such negations (see [21,53]). An in-depth study of strict IV negations can be found in [54,77].…”

Section: Negationsmentioning

confidence: 99%

“…The only small difference between these two studies lies essentially in the fact that for the negations of the A-IFSs, K α operators are not used, whereas these operators are used in the characterization of the IV negations developed in [54]. This fact enables us to prove the following lemma (which is a consequence of Lemma 3.5 proved in [77]):…”

Section: Representation Theorem For IV Negationsmentioning

confidence: 99%

“…Lemma 1, together with other properties (see [21,49,54,61]) of the operators K α , has made it possible to prove the following characterization theorem (which is an adaptation for IVFSs of Theorem 3.6 proved in [77]). …”

Section: Representation Theorem For IV Negationsmentioning

confidence: 99%

See 3 more Smart Citations

A Survey of Interval‐Valued Fuzzy Sets

Bustince

Montero

Pagola

et al. 2008

Handbook of Granular Computing

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Section: Representation Theorem For IV Negationsmentioning

confidence: 84%

“…Historically, this theorem provided the first construction method for such negations (see [21,53]). An in-depth study of strict IV negations can be found in [54,77].…”

Section: Negationsmentioning

confidence: 99%

Section: Representation Theorem For IV Negationsmentioning

confidence: 99%

Section: Representation Theorem For IV Negationsmentioning

confidence: 99%

See 2 more Smart Citations

A Survey of Interval‐Valued Fuzzy Sets

Bustince

Montero

Pagola

et al. 2008

Handbook of Granular Computing

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“…Furthermore, T W , T P and S W are natural extensions of T W , T P and S W respectively. In [2,4,7] it is shown that T W inherits more interesting properties from the Lukasiewicz t-norm on the unit interval than the t-representable extension of T W to L I .…”

Section: Then T Is Called the Representant Of T And T Is Denoted Bymentioning

confidence: 99%

Generalized arithmetic operators and their relationship to t-norms in interval-valued fuzzy set theory

Deschrijver

2009

Fuzzy Sets and Systems

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In this paper we study extensions of the arithmetic operators +, −, ·, ÷ to the lattice L I of closed subintervals of the unit interval. Starting from a minimal set of axioms that these operators must fulfill, we investigate which properties they satisfy. We also investigate some classes of t-norms on L I which can be generated using these operators; these classes provide natural extensions of the Lukasiewicz, product, Frank, Schweizer-Sklar and Yager t-norms to L I .

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Generation of interval-valued fuzzy and atanassov's intuitionistic fuzzy connectives from fuzzy connectives and fromKα operators: Laws for conjunctions and disjunctions, amplitude

Bustince¹,

Barrenechea²,

Pagola³

2008

Int. J. Intell. Syst.

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In this paper, we study in-depth certain properties of interval-valued fuzzy sets and Atanassov's intuitionistic fuzzy sets (A-IFSs). In particular, we study the manner in which to construct different interval-valued fuzzy connectives (or Atanassov's intuitionistic fuzzy connectives) starting from an operator. We further study the law of contradiction and the law of excluded middle for these sets. Furthermore, we analyze the following properties: idempotency, absorption, and distributiveness. We conclude relating idempotency with the capacity that some of the connectives studied have for maintaining, in certain conditions, the amplitude (or Atanassov's intuitionistic index) of the intervals on which they act. C 2008 Wiley Periodicals, Inc.

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On the Representation of Intuitionistic Fuzzy>tex<$t$>/tex<-Norms and>tex<$t$>/tex<-Conorms

Cited by 485 publications

References 18 publications

A Survey of Interval‐Valued Fuzzy Sets

A Survey of Interval‐Valued Fuzzy Sets

Generalized arithmetic operators and their relationship to t-norms in interval-valued fuzzy set theory

Generation of interval-valued fuzzy and atanassov's intuitionistic fuzzy connectives from fuzzy connectives and fromKα operators: Laws for conjunctions and disjunctions, amplitude

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