New operations on fuzzy numbers and intervals

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Authors: Efremov A. A.

Annotation: New operations on fuzzy numbers and intervals which keep the type and the shape of membership functions intact and allow producing complex terms of linguistic variables corresponding linguistic hedges «very» and «more or less» are suggested in this paper. We derive mathematical expressions which allow determining characteristic points of fuzzy results of introduced operations for particular types of membership functions without integral evaluation.

Keywords: fuzzy set, fuzzy number, linguistic hedges, polynomial membership functions, piecewise continuous functions