The notion of feasibility, applicable in various areas related to logic, is arguably of gradual nature—some tasks are more feasible than others. The possibility of modeling a gradual notion of feasibility in t-norm logics is brought forward and illustrated on the gradual notions of feasible number, feasible knowledge, feasible formula, and feasible computability.

Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g. T -transitivity. It will be shown that preservation of T -transitivity is closely relat...

In this paper we generalize the well known construction of ”classic” measure theory to the fuzzy case. We consider such T-norm based classes of fuzzy sets as T-semirings and T-tribes (T sigmaalgebras), such fuzzy valued functions as elementary T-measures, exterior T-measures and T-measures, and we suggest the construction of a TM-measure by extension of an elementary TM-measure on a TM-semiring...

On the basis of the concept of interval valued intuitionistic fuzzy set introduced by K. Atanassov [3], the notion of interval valued intuitionistic fuzzy subsemigroup (ideal, bi-ideal, (1, 2)-ideal) of a semigroup with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help o...

Periods of matrix power sequences in max-drast fuzzy algebra and methods of their computation are considered. Matrix power sequences occur in the theory of complex fuzzy systems with transition matrix in max-t algebra, where t is a given triangular fuzzy norm. Interpretation of a complex system in max-drast algebra reflects the situation when extreme demands are put on the reliability of the sy...

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 ...

In fuzzy logic in wider sense, i.e. in the field of fuzzy sets applications, t-norms got a prominent rôle in recent times. In many-valued logic, the Lukasiewicz systems, the Gödel sytems, and also the product logic all are t-norm based systems. The present paper discusses the more general problem of the adequate axiomatizability for such t-norm based logical systems in general, surveying result...

The paper is devoted to a general aggregation operator acting on L-fuzzy real numbers. It is defined as a t-norm based extension of an ordinary aggregation operator. The aim of our research is to analyze properties of the general aggregation operator depending on properties of the ordinary aggregation operator and the t-norm. By using the general aggregation operator we consider the properties ...

The extension principle defines the arithmetic operations on fuzzy numbers. In the extension principle one can use any t-norm for modeling the conjunction operator. It is therefore important to know, which t-norms are consistent with a particular type of fuzzy number. We call a t-norm consistent, if the arithmetic operation is closed. In this paper we investigate the addition of sigmoid and two...