The main goal of this paper is to apply the method of extension of fuzzy connectives proposed in our previous work for fuzzy implications valued on a bounded lattice. Also we discuss about which properties of implications are preserved by this method and we prove some results involving extension and automorphisms. Finally, we investigate the behavior of the extensions of two special classes of ...

In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

The concepts of fuzzy semi-ideals of R with respect to H≤R and generalized fuzzy quotient rings are introduced. Some properties of fuzzy semiideals are discussed. Finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some...