The type-2 fuzzy sets was introduced by L. Zadeh as an extension of ordinary fuzzy sets. So the concept of type-2 fuzzy sets is also extended from type-1 fuzzy sets. If A is a type-1 fuzzy set and membership grade of x ∈ X in A is μA(x), which is a crisp number in [0, 1]. A type-2 fuzzy set in X is Ã, and the membership grade of x ∈ X in à is μÃ(x), which is a type-1 fuzzy set in [0, 1]. The el...

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...

This paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. The classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. Finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

the aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. in thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle htimes h, otimesrangle$ in a particularcase.

Recently there has been significant growth in research interest in type-2 fuzzy logic. Type-2 fuzzy logic is extension of type-1 (regular) fuzzy logic where the membership grade in a fuzzy set is itself measured as a fuzzy number. Much of this growth has only been concerned with type-2 interval fuzzy systems, a subset of type-2 fuzzy systems, where the membership grade of a fuzzy set is given a...

Within the RERAU methodology, each rehabilitation criterion is assigned a grade out of 4 possible ones. This grade results from successive aggregations of performance indicators. Issues related to base data (uncertain or imprecise data) and to fusion (conflicting or reinforcing indicators) lead to envisage a fuzzy method for processing the proposed set of performance indicators. Five issues are...

First of all, in this paper we propose a family of fuzzy implication operators, which the generalised Luckasiewicz ́s one, and to analyse the impacts of Smets and Magrez properties on these operators. The result of this approach will be a characterisation of a proposed family of inclusion grade operators (in Bandler and Kohout ́s manner) that satisfies the axioms of Divyendu and Dogherty. Second,...

In this research paper, it was studied about degree of vertices of a semitotal blocks in fuzzy graphs. In process we obtain some interesting results regarding the degree of the vertices in semitotal blocks in fuzzy graphs. We observed that when ‘B’ is a block of a given fuzzy graph G:(V, σ, μ), then degree of the vertex B in semi total block fuzzy graph TSTBF(G) is equal to the sum of the membe...

To overcome the difficulty in understanding quantitative evaluation on actually safety assessment, This research proposed a qualitative comprehensive assessment method of fuzzy state based on fuzzy Analytic Hierarchy Process (AHP) and Fuzzy Transform. First of all, the fuzzy comment of multiple assessments by experts should focus on the quantitative evaluation of corresponding triangular fuzzy ...

A pattern-recognition method for flatness defect based on CMAC neural network is proposed, and a flatness fuzzy controller based on the pattern-recognition results is designed in this paper. Pattern-recognition and controller are designed into a single unit, in which CMAC recognizes the membership grade relative to six basic modes of common flatness defect and realizes the seeking function of t...