On some properties of (h,e)-implications. distributivities with t-norms and t-conorms.

• Autorzy: Massanet S. , Torrens J.
• Języki publikacji: EN

Abstrakty

EN

In this paper some basic properties of (h, e)-implications are studied. This kind of implications has been recently introduced (see [29]). They are implications generated from an additive generator of a representable uninorm in a similar way of Yager’s f- and gimplications which are generated from additive generators of continuous Archimedean t-norms and t-conorms, respectively. In addition, they satisfy a classical property of some types of implications derived from uninorms that is I(e,y) = y for all y ∈ [0,1]. Moreover they are examples of fuzzy implications satisfying the exchange principle but not the law of importation for any t-norm, in fact for any function F : [0,1] 2 → [0,1]. On the other hand, the distributivities with conjunctions and disjunctions (t-norms and t-conorms) are also studied leading to new solutions of the corresponding functional equations. Finally, it is proved that they do not intersect with any of the most used classes of implications.

Słowa kluczowe

EN

(h, e)-implications; t-norm; t-conorm; fuzzy implications

• Wydawca: University of Social Sciences
• Czasopismo: Journal of Artificial Intelligence and Soft Computing Research
• Rocznik: 2012
• Tom: Vol. 2, No. 2
• Strony: 109--123
• Opis fizyczny: Bibliogr. 36 poz., rys.

Twórcy

autor

Massanet S.

• Department of Mathematics and Computer Science, University of the Balearic Islands, Crta. Valldemossa Km. 7,5, E-07122 Palma de Mallorca, Spain

autor

Torrens J.

• Department of Mathematics and Computer Science, University of the Balearic Islands, Crta. Valldemossa Km. 7,5, E-07122 Palma de Mallorca, Spain

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