Intuitionistic fuzzy sets in the sense of Atanassov and interval-valued fuzzy sets can be seen as L-fuzzy sets w.r.t. a special lattice L . Deschrijver [2] introduced additive and multiplicative generators on L based on a special kind of addition introduced in [3]. Actually, many other additions can be introduced. In this paper we investigate additive generators on L as far as possible independ...

This report treats the relation between substructural logics and fuzzy logics, especially focuses on the noncommutativity of conjunctive operators i.e. substructural logics without the exchange rule. As the results, the authors show that fuzzy logics based on the left continuous pseudo-t-norms are the extensions of FLw. Also, we introduce the definition of pseudouninorms and give some methods t...

In this paper we consider algebras of fuzzy truth values equipped with an implication operation. Generalizing the definition of type-1 fuzzy implications, we discuss extended fuzzy S-implications and coimplications and also extended residual implications and coimplications, in particular to the extended residual of minimum. We study the algebraic properties of these operations and their relatio...

We introduce nearly Frank t-norms as t-norms which are generated from Frank t-norms by means of a negation-preserving automorphism. We state basic properties of nearly Frank t-norms and we show their speci c role in the characterization of T -measures. 1 Basic facts about T -norms A t-norm (fuzzy conjunction) is a binary operation T : [0; 1]2 ! [0; 1] which is commutative, associative, nondecre...

We introduce and discuss a notion of fuzzy uniform structure that provides a direct link with the classical theory of uniform spaces. More exactly, for each continuous t-norm we prove that the category of all fuzzy uniform spaces in our sense (and fuzzy uniformly continuous mappings) is isomorphic to the category of uniform spaces (and uniformly continuous mappings) by means of a covariant func...

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...

INTRODUCTION There have been a number of generalizations of metric spaces. One such generalization is Menger space introduced in 1942 by Menger[9] who used distribution functions instead of nonnegative real numbers as values of the metric. This space was expanded rapidly with the pioneering works of Schweizer and Sklar [11, 12]. Modifying the idea of Kramosil and Michalek [7], George and Veeram...

Originally, fuzzy logic was proposed to describe human reasoning. Lately, it turned out that fuzzy logic is also a convenient approximation tool, and that moreover, sometimes a better approximation can be obtained if we use real values outside the interval 0; 1]; it is therefore necessary to describe possible extension of t-norms and t-conorms to such new values. It is reasonable to require tha...

Some fuzzy expert systems have used fuzzy rules with numerical values which represent degrees of conndence for rules. We discuss two kinds of interpretations for these numerical degrees of conndence for rules, called "di-rect degrees " and "indirect degrees". Then, we apply Zadeh's, Baldwin's, and Tsukamoto's reasoning method to the rules under the two interpretations using general T-norms, and...

This paper first exposes an algorithm that leads to fuzzy segmentation of color images. This algorithm performs, as in the watershed method, a progressive flood of the gradient image from pixels of lowest gradients. Membership degrees of pixels to regions depend on topographic distance, which takes into account both the distance to the core and the gradient norms. Geometric and colorimetric fea...