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In this paper, we define the arrangement of rectangles with fuzzy sizes in a breadth -- tangency, intersection, non-intersection. We also define the arrangement of rectangles with fuzzy sizes in the fuzzy size breadth -- tangency, intersection, non-intersection. Finally, we construct a new mathematical model of the one problem of the rectangle packing as a problem of the Euclidian combinatorial optimization on a set of fuzzy permutations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of the characteristic function of a fuzzy number. Through the samples provided, we demonstrate the operation of addition and the order relation of fuzzy numbers. Moreover, we study the properties of proposed operations and relations. We determine that these concepts can be used in simulation of optimization problems with indefinite data. [ABSTRACT FROM AUTHOR]