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A characterization for residuated implications on the set of all the closed intervals in J[0,1]. Application to the L-fuzzy concept theory.

Cristina Alcalde, Ana Burusco, Ramón Fuentes-González (2005)

Mathware and Soft Computing

In this paper, a new characterization for the interval-valued residuated fuzzy implication operators is presented, with which it is possible to use them in a simple and efficient way, since the calculation of the values of an intervalvalued implication applicated to two intervals is reduced to the study of a fuzzy implication applicated to the extremes of these intervals. This result is very important in order to extract knowledge from an L-fuzzy context with incomplete information. Finally, some...

A characterization of uninorms on bounded lattices via closure and interior operators

Gül Deniz Çayli (2023)


Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.

A contour view on uninorm properties

Koen C. Maes, Bernard De Baets (2006)


Any given increasing [ 0 , 1 ] 2 [ 0 , 1 ] function is completely determined by its contour lines. In this paper we show how each individual uninorm property can be translated into a property of contour lines. In particular, we describe commutativity in terms of orthosymmetry and we link associativity to the portation law and the exchange principle. Contrapositivity and rotation invariance are used to characterize uninorms that have a continuous contour line.

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