Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant 0, namely ¬φ isφ → 0. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which i...

Recently, in [4], we have discussed the following distributive equation of implications I(x, T1(y, z)) = T2(I(x, y), I(x, z)) over t-representable t-norms, generated from strict t-norms, in interval-valued fuzzy sets theory. In this work we continue these investigations, but with the assumption that T1 is generated from nilpotent t-norms, while T2 is generated from strict t-norms. As a byproduc...

Uninorms are a generalization of t-norms and t-conorms for which the neutral element is an element of [0, 1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0, 1) to either 0 or 1. In real-life applications, this kind of aggregation may be counter-intuitive. Interval-...

In this paper are introduced some concepts of interval-valued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and local reflexivity. The existence and uniqueness of T-transitive closure of interval-valued fuzzy relations is proved. An algorithm to compute the T-transitive closure of finite interval-valued fuzzy relations is showed. Some propertie...

In this paper we consider general t-norm in the definition of fuzzy normed linear space which is introduced by the authors in an earlier paper. It is proved that if t-norm is chosen other than ”min” then decomposition theorem of a fuzzy norm into a family of crisp norms may not hold. We study some basic results on finite dimensional fuzzy normed linear spaces in general t-norm setting. 2010 AMS...

In this paper, the stability study of fuzzy control systems is presented. The approach developed is based on the convergence of regular vector norms, where the comparison, the overvaluing principle and the Borne and Gentina criterion are used. The controller is of type PI-fuzzy with different partition of the two fuzzy inputs. The system to be controlled is a nonlinear system and the applicatio...

The proposed article mainly comprises of ideas and motivations that led to the generalization usual or crisp sets. Moving forward we intend look into how definitions were modified suit meaning existing establish link between them, is say we, after giving formal aforementioned sets norms on these new would draw parallel them norm. We will then study some riveting algebraic properties same.

Fuzzy associative memories (FAMs) and, in particular, the class of implicative fuzzy associative memories (IFAMs) can be used to implement fuzzy rule-based systems. In this way, a variety of applications can be dealt with. Since there are infinitely many IFAM models, we are confronted with the problem of selecting the best IFAM model for a given application. In this paper, we restrict ourselves...

The concept of fuzzy flip-flop was introduced in the middle of 1980’s by Hirota (with his students). The Hirota Lab recognized the essential importance of the concept of a fuzzy extension of a sequential circuit and the notion of fuzzy memory. From this point of view they proposed alternatives for “fuzzifying” digital flip-flops. The starting elementary digital units were the binary J-K flipflo...