Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

In order to improve students' teaching/learning processes computational systems have been developed allowing to adapt virtual courses based on the students' profiles. There are currently various kinds of adaptation such as instruccional adaptation of plans, assessments adaptation, and adaptation of educational contents, among others.The aim of this paper is to propose a fuzzy inference model fo...

This paper presents a multiple criteria decision aiding approach in order to build a ranking and suggest a choice 2 on a set of alternatives. The partial evaluations of the alternatives on the points of view can be fuzzy numbers. The aggregation is performed through the use of a fuzzy extension of the Choquet integral. We detail how to assess the parameters of the aggregator by using alternativ...

At the first, we revise the Kosinski’s definition of the sum of ordered fuzzy numbers. The associativity of revised sum is investigated here. In addition, we show that the multiple revised sum of finite sequence of trapezoidal ordered fuzzy numbers depends on its summands ordering. .AMS Classification: 03E72

Recently, there has been a growing interest in the application of Fuzzy ARTMAP for use in building energy management systems or EMS. However, a number of papers have indicated that there are important weaknesses to the Fuzzy ARTMAP approach, such as sensitivity to noisy data and category proliferation. Gaussian ARTMAP was developed to help overcome these weaknesses, raising the question of whet...

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

By using the notion of fuzzy functions introduced by Dib and Youssef, we obtain fuzzy analogues of some results concerning ordinary functions. In particular, we give the definition different from one of invertible fuzzy function introduced by Dib and Youssef. And we show that the two definitions are equivalent. Furthermore, we introduce the concepts of fuzzy increasing functions and fuzzy isomo...

In this contribution, we will recall graded fuzzy rules introduced in [6] and explain the difference from the classical fuzzy rules. Moreover, properties of formulae, which are used to formalize the graded fuzzy rules, will be analyzed.

In this paper, a solution procedure for the solution of the system of fuzzy differential equations ẋ(t) = α(A− In) [t(A− In) + In]−1 x(t), x(0) = x0 where A is real n × n matrix which does not have eigenvalues on R− and x0 is a vector consisting of n fuzzy numbers is developed. In addition, the necessary and sufficient condition for the existence of fuzzy solution is presented. An example is pr...