Construction of Fuzzy σ-algebras using triangular norms

(L, M)-Fuzzy σ-Algebras

Cardinalities of fuzzy sets with triangular norms

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.

Fuzzy Γ-Hyperideals in Γ-Hypersemirings by Using Triangular Norms

The concept of Γ-semihyperrings was introduced by Dehkordi and Davvaz as a generalization of semirings, semihyperrings, and Γ-semiring. In this paper, by using the notion of triangular norms, we define the concept of triangular fuzzy sub-Γ-semihyperrings as well as triangular fuzzy Γ-hyperideals of a Γ-semihyperring, and we study a few results in this respect.

Extended Triangular Norms on Gaussian Fuzzy Sets

So far, computational complextity of the general formula for the extended t-norm does not allow to construct fuzzy logic systems of type-2 other than interval type. In this paper, we derive new formulae for extended t-norms for arguments with Gaussian and piecewise-Gaussian membership functions basing on our original theorems.

Algebras of Fuzzy Sets in Logics Based on Continuous Triangular Norms

Associated with any [0, 1]-valued propositional logic with a complete algebraic semantics, one can consider algebras of families of fuzzy sets over a classical universe, endowed with the appropriate operations. For the three most important schematic extensions of Hájek’s Basic (Fuzzy) Logic, we investigate the existence and the structure of such algebras of fuzzy sets in the corresponding algeb...