In the recent past Kernelized Fuzzy C-Means clustering technique has earned popularity especially in the machine learning community. This technique has been derived from the conventional Fuzzy C-Means clustering technique of Bezdek by defining the vector norm with the Gaussian Radial Basic Function instead of a Euclidean distance. Subsequently the fuzzy cluster centroids and the partition matri...

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...

The concept of intuitionistic fuzzy subhyperquasigroups in a hyperquasigroup with respect to an snorm and a t-norm on intuitionistic fuzzy sets is introduced and their properties of such hyperquasigroups are studied. Intuitionistic (S, T )-fuzzy relations on a hyperquasigroup G are discussed. In particular, we investigate connections hyperquasigroups with binary quasigroups.

This paper deals with the problem of searching basic properties for robust implication operators in fuzzy control. We use the word “robust” in the sense of good average behavior in different applications and in combination with different defuzzification methods. We study the behavior of the two main families of implication operators in the fuzzy control inference process. These two families are...

A fuzzification of the concept of functional dependency based on t-norms is presented. T-norms are equally used in the definition of the similarity relations in the domains and in the fuzziness degree assigned to functional dependencies. A sound and complete logic for this fuzzy functional dependencies is also introduced and, finally, its applicability to redundancy removing is shown.

In a previous paper, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of...

Recent development of mathematical fuzzy logic is brieey surveyed. The set of all formulas of predicate logic that are tautologies with respect to all continuous t-norms is shown to be heavily non-recursive ((2-hard).

Keywords: mathematical fuzzy logic, basic fuzzy logic, monoidal t-norm logic, hoop logic, non-commutative fuzzy logic. This paper is a companion to my [12]. The latter is a rather technical paper developing a generalized (mathematical) fuzzy logic. Main definitions and results of [12] are reproduced here without any proofs; but this is preceded by a survey on the basic proposi-tional fuzzy logi...

Fuzzy Description Logics are a family of logics which allow to deal with structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, current fuzzy DLs are open to be extend with several features worked out in the fuzzy logic literature. In this work, we extend fuzzy DLs with fuzzy truth values, allowing to state sentences su...

In this paper we propose computationally simple, pointwise formulas for extended t-norms and t-conorms on fuzzy truth values. The complex convolutions of the extended operations are shown to be equivalent to simple pointwise expressions for several special cases. Linear fuzzy truth values are defined and it is shown that the extended Łukasiewicz operations preserve linearity. Since linear fuzzy...