Fuzzy modus ponens (briefly, FMP) is the most fundamental form of fuzzy reasoning and has been extensively discussed by diverse researchers. The aim of the present paper is to propose a formalized form of FMP, called generalized modus ponens, in the fuzzy logic system L and solve it in L, and then provide its numerical version as a new algorithm for solving FMP. As a preparation, some related q...

and Applied Analysis 3 Definition 2.2 Kramosil and Michálek 3 . The triple X,M, ∗ is called a fuzzy metric space if X is an arbitrary set, ∗ is a continuous t-norm, andM is a fuzzy set onX×X× 0,∞ satisfying the following conditions: for all x, y, z ∈ X and s, t > 0, FM-1 M x, y, 0 0, FM-2 M x, y, t 1 if and only if x y, FM-3 M x, y, t M y, x, t , FM-4 M x, y, t ∗M y, z, s ≤ M x, z, t s , FM-5 a...

This paper is directed to the question of how to model and design an efficient tool for the intelligent mapping which is based on both dynamic and efficient storage of data and soft computing. The former is performed by our method that learns how to store, search and delete the data. After pointing out the limitation of the crisp evaluation of the distance between two points, we argue in favor ...

We shall discuss further regularity properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pre...

Abstract: The purpose of this paper is to discuss the properties of regularity and strong regularity of fuzzy measure on metric spaces following the previous results. Some properties are defined with the help of nulladditivity such as inner\outer regularity and the regularity of fuzzy measure. We define the strong regularity of fuzzy measures and show our result that the null-additive fuzzy mea...

We shall continue to discuss further properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pr...

generalized geraghty type fuzzy mappings oncomplete metric spaces are introduced and a fixed point theorem thatgeneralizes some recent comparable results for fuzzy mappings incontemporary literature is obtained. example is provided to show thevalidity of obtained results over comparable classical results for fuzzymappings in fixed point theory. as an application, existence of coincidencefuzzy p...

In this paper we give a fixed-point theorem for fuzzy contractive mappings in the George and Veeramani p-complete fuzzy metric spaces.