We survey the main results characterizing partial isometries in C∗algebras and tripotents in JB∗-triples obtained in terms of regularity, conorm, quadratic-conorm, and the geometric structure of the underlying Banach spaces.

Fuzzy integrals are commonly used as aggregation operators. In this paper we present new composite models based on fuzzy integrals with several t-conorms. These models permit to further increase the computational power of the previous models. Basic properties of new composite models are studied. In particular, it is shown that for composite models, the only meaningful case is when not all the t...

We define and study the concept of non-Archimedean intuitionistic fuzzy normed space by using the idea of t-norm and t-conorm. Furthermore, by using the non-Archimedean intuitionistic fuzzy normed space, we investigate the stability of various functional equations. That is, we determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framewor...

Abstract: In this paper, the theory of T-norm and T-conorrn is reviewed and the T-norm, T-conorm and negation function are defined as a set of T-operators. Some typical T-operators and their mathematical properties are presented. Finally, the T-operators are extended to the conventional fuzzy reasoning methods which are based on the MIN and MAX operators. This extended fuzzy reasoning provides ...

We consider the generalized method-of-case (GMC) inference scheme with fuzzy antecedents, which has been introduced by Da in [1]. We show that when the fuzzy numbers involved in the observation part of the scheme have continuous membership functions; and the t-norm, t-conorm used in the definition of the membership function of the conclusion are continuous, then the conclusion defined by the co...

In this paper we use a comparison measure which can be adapted to various different applications and has many good properties for further analysis. This comparison measure is based on the adaptive aggregation of the t-norms and t-conorms. We test this measure in classification tasks, with Dombi and Yager type of t-norm and t-conorm operators. The classification results are compared to plain t-n...

In this article we are presenting two new classes of t-norm and t-conorm based generalized means with weights. We are going to test usability of these measures which we get by combining classes of t-norms and t-conorms to the generalized mean operator. Since we are using the generalized mean we have an additional parameter that controls the power which the argument values are raised. Dombi and ...

Using Generalized Modus Ponens reasoning, we examine the values of the inferred conclusion by using Fodor's implication in order to interpret a fuzzy if-then rule with a single input single output and the tnorm ( ) ( )( ) ( xy y x max y , x t ) λ λ − − + + = 1 1 , 1 − ≥ λ , for composition operation. This t-norm is important to use because for 1 − = λ and 0 = λ it gives the commonly used t-norm...

We consider the problem of choosing an alternative in a set A = {A1, A2, ..., Am} of alternatives, given a set D = {d1, d2, ..., dh} of decision makers and a set Ω = {O1, O2, ..., On} of objectives. We assume that any decision maker dk assigns to any pair (alternative Ai, objective Oj) a number aijk that measures to what extent Ai satisfies Oj . We assume that Ω is a subset of a universal set U...