We introduce the notion of sensible fuzzy ideals of BCK-algebras with respect to a t-conorm and investigate some of their properties. We give the conditions for a sensible fuzzy subalgebra with respect to a t-conorm to be a sensible fuzzy ideal with respect to a t-conorm. Some properties of the direct product and S-product of fuzzy ideals of BCK-algebras with respect to a t-conorm are also disc...

In knowledge representation, when we have to use logical connectives, various continuous t-norms and t-conorms are used. In this paper, we show that every continuous t-norm and t-conorm can be approximated, to an arbitrary degree of accuracy, by a strict Archimedean t-norm (t-conorm).

The paper presents IF-inference systems of Takagi-Sugeno type. It is based on intuitionistic fuzzy sets (IF-sets), introduced by K.T. Atanassov, fuzzy t-norm and t-conorm, intuitionistic fuzzy t-norm and t-conorm. Thus, an IFinference system is developed for ozone time series prediction. Finally, we compare the results of the IF-inference systems across various operators.

The class of discrete uninorms U such that their underlying t-norm T and t-conorm S are smooth is studied. The different cases combining when T is the minimum or the Łukasiewicz t-norm and S is the maximum or the Łukasiewicz t-conorm, are characterized and the number of discrete uninorms with these underlying operators is given. It is also studied the general case when T and/or S are smooth, bu...

Introducing more types of integrals will provide more choices todeal with various types of objectives and components in real problems. Firstly,in this paper, a (T) fuzzy integral, in which the integrand, the measure andthe integration result are all multi-valued, is presented with the introductionof T-norm and T-conorm. Then, some classical results of the integral areobtained based on the prope...

The aim of this paper is to develop the calculus hesitant fuzzy numbers (HFNs), have been recently proposed as newest extension sets. At first, based on willingness decision maker each part HFNs, a new method has compare them. Then, several t-norm and t-conorm-based aggregation operators i.e., algebraic t-conorm, Einstein Hamacher Frank t-conorm defined, some their mathematical properties are a...

The characterization of (S,N)-implications when N is a non-continuous negation has remained one the most significant open problems in fuzzy logic for last decades. This paper constitutes first progress this topic. Namely, general family implication functions presented, which central property existence completion binary function defined on certain subregion [0,1]2 to t-conorm. In paper, dual pro...

There is given an axiomatization of the hybrid probabilistic-possibilistic mixture, based on a pair of t-conorm S and t-norm T satisfying (CD) condition, and the corresponding S-measure.

Abstract Aczel–Alsina t-norm and t-conorm are important t-conorm, they extended from algebraic t-conorm. Obviously, more general than some existing Furthermore, the power aggregation (PA) operator is also a very famous valuable which can consider relation between any two input parameters. In addition, Interval-valued Atanassov-intuitionistic fuzzy set (IVA-IFS) easily express uncertain informat...