If we know that an implication A ! B is to some extent true, and if we know that a statement A is true \to some extent", i.e., if we know that the statement m(A) is true, for some logical modiier m (\approximately", \slightly", etc.), then we can conclude that B is also true to some extent, i.e., that m 0 (B) is true for some logical modiier m 0. Thus, every fuzzy implication deenes a mapping f...

A fuzzy approximation method called fuzzy transforms for approximation of continuous function is presented in this paper. It is shown how can be fuzzy transforms naturally generalized for functions with more variables. A fuzzy function as an approximated mapping is considered. This leads to an extension of fuzzy transforms for fuzzy function as well as to an extension of generalized fuzzy trans...

A fuzzy mapping aggregation operator based on RIMER and its application in Chinese word semantic proofing system for special domain are discussed deeply in this paper. Firstly, the fuzzy mapping aggregation operator based on RIMER are introduced and followed by the corresponding fuzzy inference method. Secondly, the collection of the sensitive words and their substitutions and the soft inferenc...

Although the validation step can appear crucial in the case of clustering adopting fuzzy approaches, the problem of the partition validity obtained by those adopting the hard ones was not tackled. To cure this problem, we propose in this paper fuzzy-hard mapping processes of clustering while benefitting from those adopting the fuzzy case. These mapping processes concern: (1) local and global cl...

We establish some stability results concerning the general cubic functional equation f(x+ ky)− kf(x+ y) + kf(x− y)− f(x− ky) = 2k(k − 1)f(y) for fixed k ∈ N\{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any ap...

We introduce the new category VRel(H) consisting of H-fuzzy relation spaces and H-fuzzy mappings between them satisfying a certain condition, where the concept of H-fuzzy mapping is the modification of one of fuzzy mapping introduced by Demirci[6]. And we investigate VRel(H) in the sense of a topological universe and show that VRel(H) is Cartesian closed over Set. Moreover, we construct the cat...

The notion of a linear space is generalized to the case where the underlying algebra is a commutative monoid and the set of scalars is a semiring reduct of a BL-algebra or an MValgebra. The notions of linear dependence and independence are also introduced and necessary and sufficient conditions when vectors form a basis of a semi-linear space are given. A linear mapping between two semilinear s...