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.

In this paper,  The Picard method is proposed to solve the system of first-order fuzzy  differential equations  $(FDEs)$ with fuzzy initial conditions under generalized $H$-differentiability. Theexistence and uniqueness of the solution and convergence of theproposed method are proved in details. Finally, the method is illustrated by solving some examples.

This article introduces the fuzzy theory. At first, the definition of fuzzy set characterized by membership function is described. Next, definitions of empty fuzzy set and universal fuzzy set and basic operations of these fuzzy sets are shown. At last, exclusive sum and absolute difference which are special operation are introduced. [6] provide the notation and terminology for this paper. In th...

Type-1 Fuzzy Logic Systems (FLSs) have been applied to date with great success to different applications. However, for many real-world applications, there is a need to cope with large amounts of uncertainties. The traditional Type-1 FLSs that use crisp Type-1 fuzzy sets cannot directly handle such uncertainties. Type-2 FLSs that use Type2 fuzzy sets can handle such uncertainties to produce a be...