The goal of this paper is to give a functional relationship between the membership functions of fuzzy intervals M1⊕...⊕Mn and M1 ... Mn, where Mi are positive LR fuzzy intervals of the same form Mi = M = (a, b, α, β)LR and the extended addition ⊕ and multiplication are defined in the sense of a triangular norm (i.e. via sup–t–norm convolution).

in this paper some algebraic structures for linguistic fuzzy models are defined for the first time. by definition linguistic fuzzy norm, stability of these systems can be considered. two methods (normed-based & graphical-based) for stability analysis of linguist fuzzy systems will be presented. at the follow a new simple method for linguistic fuzzy numbers calculations is defined. at the end tw...

In Mixed Fuzzy Rule Formation [Int. J. Approx. Reason. 32 (2003) 67] a method to extract mixed fuzzy rules from data was introduced. The underlying algorithm’s performance is influenced by the choice of fuzzy t-norm and t-conorm, and a heuristic to avoid conflicts between patterns and rules of different classes throughout training. In the following addendum to [Int. J. Approx. Reason. 32 (2003)...

The combination of Fuzzy Logics and Description Logics (DLs) has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. It has turned out, however, that in the presence of general concept inclusion axioms (GCIs) t...

The aim of this paper is to promote web geometry and, especially, the Reidemeister closure condition as a powerful and intuitive tool characterizing associativity of the Archimedean triangular norms. In order to demonstrate its possible applications, we provide the full solution to the problem of convex combinations of nilpotent triangular norms. Keywords— Archimedean triangular norm, web geome...

In this paper the notion of fuzzy ideals of a Γ-near-ring with respect to a t-norm is introduced and investigated some related properties. This concept of T -fuzzy ideals of a Γ-near-ring is a generalization of the concept of T -fuzzy ideals in near-rings. Also the notions of T -fuzzy ideals of a Γ-near-ring, quotient Γ-near-ring with respect to a t-norm and the sum of T -fuzzy ideals of a Γ-ne...

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 ...

Finding strongly standard complete axiomatizations for t-norm based fuzzy logics (i.e. complete for deductions with infinite sets of premises w.r.t. semantics on the real unit interval [0, 1]) is still an open problem in general, even though results are already available for some particular cases like some infinitary logics based on a continuous t-norm or certain expansions of Monoidal t-norm b...

Archimedean t-conorm and t-norm are generalizations of a lot of other t-conorms and t-norms, such as Algebraic, Einstein, Hamacher and Frank t-conorms and t-norms or others, and some of them have been applied to intuitionistic fuzzy set, which contains three functions: the membership function, the nonmembership function and the hesitancy function describing uncertainty and fuzziness more object...

Transitivity is a very important property in order to provide coherence to a preference relation. Usually, t-norms are considered to define the transitivity of fuzzy relations. In this paper we deal with conjunctors, a wider family than t-norm, to define the transitivity. This more general definition allows to impove the results found in the literature. We characterize the behaviour with respec...