Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: t-conorm

Sortuj według:

Ogranicz wyniki do:

On two functional equations connected with distributivity of fuzzy implications

Ger R., Kuczma M. E., Niemyska W.

Commentationes Mathematicae

2015

Vol 55, No. 2

163--169

The distributivity law for a fuzzy implication I:[0,1]2→[0,1] with respect to a fuzzy disjunction S:[0,1]2→[0,1] states that the functional equation I(x,S(y,z))=S(I(x,y),I(x,z)) is satisfied for all pairs (x,y) from the unit square. To compare some results obtained while solving this equation in various classes of fuzzy implications, Wanda Niemyska has reduced the problem to the study of the following two functional equations: h(min(xg(y),1))=min(h(x)+h(xy),1), x∈(0,1), y∈(0,1], and h(xg(y))=h(x)+h(xy), x,y∈(0,∞), in the class of increasing bijections h:[0,1]→[0,1] with an increasing function g:(0,1]→[1,∞) and in the class of monotonic bijections h:(0,∞)→(0,∞) with a function g:(0,∞)→(0,∞), respectively. A description of solutions in more general classes of functions (including nonmeasurable ones) is presented.

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

Massanet S., Torrens J.

Journal of Artificial Intelligence and Soft Computing Research

2012

Vol. 2, No. 2

109--123

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.