the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.

In this paper, a new way of optimizing fuzzy logic is introduced. This way is used to optimize the output of Interval Type-2 Fuzzy Logic controller by replacing the Defuzzification stage by the Optimization algorithm. The algorithm chooses the best crisp output variable from the type-reduced set which is the output of the Type-Reduction stage instead of averaging the set extremes which was perf...

Type-2 fuzzy sets have come to play an increasingly important role in both applications and in the general theory of fuzzy sets. The basis of type-2 fuzzy sets is a certain algebra of truth values, as set forth by Zadeh. This paper is a survey of results about this algebra, along with some new material.

This article introduces a general framework of multi-granulation fuzzy probabilistic roughsets (MG-FPRSs) models in multi-granulation fuzzy probabilistic approximation space over twouniverses. Four types of MG-FPRSs are established, by the four different conditional probabilitiesof fuzzy event. For different constraints on parameters, we obtain four kinds of each type MG-FPRSs...

Fuzzy Technique for Order Preference by Similarly to Ideal Solution (TOPSIS) is one of the most commonly used approaches in solving numerous multiple criteria decision making problems. It has been widely used in ranking of multiple alternatives with respect to multiple criteria with the superiority of fuzzy set type-1 and subjective weights. Recently, fuzzy TOPSIS has been merged with interval ...

in this study, we introduce and study a concept of distributed fuzzymodeling. fuzzy modeling encountered so far is predominantly of a centralizednature by being focused on the use of a single data set. in contrast to this style ofmodeling, the proposed paradigm of distributed and collaborative modeling isconcerned with distributed models which are constructed in a highly collaborativefashion. i...

This paper is concerned with the defuzzification of the discretised generalised type-2 fuzzy set. In 2008 Liu proposed the α-Plane Representation — a decomposition of the generalised type-2 set into horizontal slices termed ‘α-planes’. An α-plane is akin to an interval type-2 fuzzy set. The α-Plane Representation must be used in conjunction with an interval defuzzification method: The three mai...

After the introduction of fuzzy set by Zadeh in 1965 [1], there have been a number of generalizations of this fundamental concept. In 1967, Goguen [2] proposed the concept of L-fuzzy set. The idea of interval valued fuzzy set is given by Zadeh in 1975 [3]. Type 2 fuzzy sets were poposed by Zadeh in [4]. Attanasove introduced intuitionistic fuzzy sets in 1986 [5]. Interval valued intuitionistic ...

in this paper, we consider the production possibility set with n production units such that the following four principles that governs: inclusion observations, conceivability, immensity and convexity. our goal is to estimate the output of a same and new production unit with existing production possibility and amount of input is specified. so, initially we find the interval changes of each input...