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...

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...

This paper presents a variety of cardinality concepts offered by cardinality theory of triangular norm-based fuzzy sets, including the scalar and the "fuzzy" streams.

Mathematical fuzzy logic (or fuzzy logic in a narrow sense) is a many-valued symbolic logic with a comparative notion of truth. The present state of development of t-norm based fuzzy propositional and predicate logic will be surveyed and some recent results will be described (on witnessed models and others).

We present a simple framework which enables us to consider the well-known sup-t-norm and inf-residuum products of relations as two particular cases of a single, more general type of product. We present basic properties of the framework and consequences for the theory of fuzzy relations. Informally, the paper implies that in many cases of fuzzy relational modeling, such as in solving fuzzy relat...