L-transform Based Algebraic Operations on fuzzy LR-numbers

Y. A. Vorontsov, Postgraduate Student, e-mail: voroncov_ya@sc.vsu.ru, M. G. Matveev, Professor, Head of Chair, e-mail: mgmatveev@yandex.ru, Voronezh State University

This paper proposes fuzzy calculations technique which is based on L-transform of α-cuts of fuzzy numbers. It covers the properties of the transform in order to demonstrate applicability of L-transform for fuzzy problems which are solved as a union of crisp problems on each predefined α-level. The paper also introduces an algebra for modified fuzzy numbers and proves the properties of basic algebraic operations, neutral and inverse elements of modified fuzzy numbers set. Usage of these operations is illustrated through some examples. The results of the research show that the proposed L-transform for triangular fuzzy numbers allows to overcome drawbacks of existing algebras of LR-numbers. The transform itself is proven to be a general case of existing methods of selection of point valuation on -cuts. Since the set K of L-transform results is viewed as a linear space, it allows the further development of L-transform-based calculations for fuzzy numbers in perspective.

Keywords: fuzzy parameters, α-cut, L-transform, algebra of fuzzy numbers, point valuations, modified fuzzy numbers

pp. 23–29