The recent advances in the research of left-continuous t-norms is summarized in this talk. The main focus is on construction methods, geometric description, and structural characterization. We point out further research directions and open problems.

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 ...

Min-independence has been proved to be a sufficient condition of a vector of fuzzy random variables to be a fuzzy random vector. The objective of this paper is to study further on the independence condition for fuzzy random vector based on continuous triangular norms. We first discuss measurability criteria for fuzzy random vector, and present two more new equivalent formulations of the measura...

fuzzy set based methods have been proved to be effective in handling many types of uncertainties in different fields, including reliability engineering. this paper presents a new approach on fuzzy reliability, based on the use of beta type distribution as membership function. considering experts' ideas and by asking operators linguistic variables, a rule base is designed to determine the level ...

and Applied Analysis 3 As a result of 2.2 we obtain, for each x, y ∈ 0, 1 , T ( x, y ) ≤ T x, 1 x, T ( x, y ) ≤ T ( 1, y ) y. 2.5 Since, for all x, y ∈ 0, 1 , trivially T x, y ≥ 0 TD x, y , we get for an arbitrary t-norm T , TD ≤ T ≤ TM. 2.6 That is, TD is weaker and TM is stronger than any other t-norms. Also since TL < TP , we obtain the following ordering for four basic t-norms TD < TL < TP ...

in this paper, we deal with molaei’s generalized groups. we definethe notion of a fuzzy generalized subgroup with respect to a t-norm (ort-fuzzy generalized subgroup) and give some related properties. especially,we state and prove the representation theorem for these fuzzy generalizedsubgroups. next, using the concept of continuity of t-norms we obtain a correspondencebetween tf(g), the set of ...

In fuzzy logic in wider sense t norms got a prominent r ole in recent times In many valued logic the Lukasiewicz systems the G odel sytems and also the product logic are t norm based The present paper discusses the more general problem of the adequate axiomatizability for such t norm based logical systems in general survey ing results of the last years