On defuzzyfication of ordered fuzzy numbers

Abstract

Ordered fuzzy number is an ordered pair of continuous real functions defined on the interval [0, 1]. Such numbers have been introduced by the author and his co-workers as an enlargement of classical fuzzy numbers by requiring a membership relation. It was done in order to define four algebraic operations between them, i.e. addition, subtraction, multiplication and division, in a way that renders them an algebra. Further, a normed topology is introduced which makes them a Banach space, and even more, a Banach algebra with unity. General form of linear functional on this space is presented which makes possible to define a large family of defuzzification methods of that class of numbers.