considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. this paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong hausdorff topology.we study interrelationships between this theory and other fuzzy theories suchas intuitionis...

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...

Fuzzy controller’s design depends mainly on the rule base and membership functions over the controller’s input and output ranges. This paper presents two different approaches to deal with these design issues. A simple and efficient approach; namely, Fuzzy Subtractive Clustering is used to identify the rule base needed to realize Fuzzy PI and PD type controllers. This technique provides a mechan...

abstract. in the case of process capability index several methods are identified. in this paper ,a new process capability index using fuzzy number and fuzzy probability concept, in order to remove the weakness of other famous method is suggested. after introduction of fuzzy index in univariate case, fuzzy multivariate process capability index is investigated. finally, this new method is compare...

We studied the Cauchy problem of fuzzy di erential equations on the basis of introducing the concept of di erentiation which is a generalization of the de nition of H-di erentiability due to Puri and Ralescu (1983), for fuzzy set-valued mappings of real variables whose values are in the fuzzy number space (E; D). The existence and uniqueness theorem is obtained for the Cauchy problem x′=f(t; x)...

Several necessary and suucient conditions for the pseudometric generating property of non-additive set functions are given. The relation among the pseudometric generating property and autocontinuity of fuzzy measures is depicted by using the absolute continuity and exhaustivity. Moreover, any uniformly autocontinuous nite fuzzy measure is equivalent to a subadditive nite fuzzy measure. A furthe...

In this paper we propose the extension of some aggregation or arithmetic operations between discrete fuzzy numbers to discrete fuzzy number-valued multisets such as the addition, the union and the intersection and, even, the order. For this reason, we prove or recall some properties of discrete fuzzy numbers and we undertake their study on multisets.

in this paper the solution of a second order linear dierential equations with intu-itionistic fuzzy boundary value is described. it is discussed for two dierent cases: coecientis positive crisp number and coecient is negative crisp number. here fuzzy numbers aretaken as generalized trapezoidal intutionistic fuzzy numbers (gtrifns). further a numericalexample is illustrated.

Most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. For making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. In line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or de...