Weakest T-norm Research Articles

Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T ω -based addition preserves the shape of L- R type fuzzy numbers. In this paper, we show T ω -based multiplication also preserves the shape of L- R type fuzzy numbers. We then apply T ω -based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L- R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.

A new look at fuzzy connectives

A new and general approach is suggested to revise definitions and properties of logical connictives for fuzzy sets. This is based on solutions of a functional equation between implications and conjunctions reflecting the residuation principle. Using that equation, properties of R-implications are characterized by corresponding properties of conjunctions. Representation theorems for weak t-norms and strict negations are also obtained.

Strict preference relations based on weak t-norms

In this paper we introduce and investigate weak t-norms and related concepts in order to give a general representation of valued strict preference relations associated with a given valued preference relation. All the well-known forms of valued strict preference relations are particular cases of our results. Moreover, when some types of ‘rationality’ assumptions are made, our unified approach seems to be the only possible one.

On fuzzy implication operators

Abstract There exist several constructions for fuzzy implication operators via conjunctions. In this paper we present a unifying approach to the generation of implications and we prove that for a rather general class of conjuctions the generation process is closed. In addition, all well-known families of fuzzy implications are within our framework. The results support that the class of weak t-norms having the Exchange Property seems to be a good model of the conjunction (or equivalently, of intersection) operator in fuzzy set theory.