Calculus of fuzzy numbers
Treść / Zawartość
From the introduction: "In this article we attempt to use concepts of fuzzy set theory to formalize such ideas as `about 30', `approximately 5', few, many, etc. These ideas describe some numbers, but are not precise; hence, we call them imprecise, or fuzzy numbers. Despite their fuzzy character, one can perform various arithmetical and logical operations: X earns more than Y (even though both of them earn very little), Z earns as much as X and Y earn between them (a sum of two numbers), etc. The purpose of this paper is to define operations on these numbers so that they would reflect our intuitive ideas and would in some sense generalize corresponding operations performed on the `ordinary' real numbers. Attainment of the first objective is difficult because of its subjective character and the lack of formal criteria. For this reason, a large part of this article is devoted to the justification of this or that type of formalism.''