Yager’s new class of implications Jf and some classical tautologies

Jayaram, Balasubramaniam

doi:10.1016/j.ins.2006.08.006

Cited by 82 publications

(33 citation statements)

References 22 publications

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“…Several definitions for fuzzy implications together with related properties have been given in the literature (see, e.g., [2,5,12,17,18,23,30,42,51,52,53]). The unique consensus in these definitions is that the fuzzy implication should have the same behavior as the classical implication for the crisp case.…”

Section: Fuzzy Implicationsmentioning

confidence: 99%

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Xor-Implications and E-Implications: Classes of Fuzzy Implications Based on Fuzzy Xor

Bedregal

Reiser

Dimuro

2009

Electronic Notes in Theoretical Computer Science

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The main contribution of this paper is to introduce an autonomous definition of the connective "fuzzy exclusive or" (fuzzy Xor, for short), which is independent from others connectives. Also, two canonical definitions of the connective Xor are obtained from the composition of fuzzy connectives, and based on the commutative and associative properties related to the notions of triangular norms, triangular conorms and fuzzy negations. We show that the main properties of the classical connective Xor are preserved by the connective fuzzy Xor, and, therefore, this new definition of the connective fuzzy Xor extends the related classical approach. The definitions of fuzzy Xor-implications and fuzzy E-implications, induced by the fuzzy Xor connective, are also studied, and their main properties are analyzed. The relationships between the fuzzy Xor-implications and the fuzzy E-implications with automorphisms are explored.

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Section: Fuzzy Implicationsmentioning

confidence: 99%

“…Fuzzy implications have been widely studied, playing important roles in different domains [18,19,46,48,51,52,54,55]. Recent papers studied different classes of fuzzy implications [2,4,5,12,18,44,53].…”

Section: Introductionmentioning

confidence: 99%

Xor-Implications and E-Implications: Classes of Fuzzy Implications Based on Fuzzy Xor

Bedregal

Reiser

Dimuro

2009

Electronic Notes in Theoretical Computer Science

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“…S :U 2 →U is an interval t-conorm (t-norm) if it is commutative, associative, monotonic w.r.t. the product and inclusion order and [0, 0] ( [1,1]) is the neutral element.…”

Section: Interval T-norms and T-conormsmentioning

confidence: 99%

“…Several definitions for fuzzy implications together with related properties have been given (see, e.g., [1,11,16,33,36]), where a binary function I : U 2 −→ U is a fuzzy implication if, at least, I satisfies the minimal boundary conditions: I(1, 1) = I(0, 1) = I(0, 0) = 1 and I(1, 0) = 0. However, other different properties may be required.…”

Section: Interval D-implicationsmentioning

confidence: 99%

Interval Valued D-Implications

Reiser¹,

Bedregal²,

Santiago³

et al. 2009

TEMA - Tendências Em Matemática Aplicada E Computacional

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“…Several definitions for fuzzy implication have been given, see for example [2,3,7,11,10,13,15,18,21,22,23]. The unique consensus in these definitions is that the fuzzy implication should have the same behavior as the classical implication for the crisp case.…”

Section: Fuzzy Implicationsmentioning

confidence: 99%