Calculation and reasoning with ordered fuzzy numbers

The fundamental concept of the fuzzy logic has been weakened by requiring a mere membership relation; consequently an ordered fuzzy number (OFN) arises as an ordered pair of continuous real functions defined on the interval [0, 1]. Four algebraic operations are constructed in a way that renders them an algebra. Further, a norm is introduced which makes them a Banach space. A class of linear defuzzyfication operations on the algebra of OFN’s is introduced. New algebraic methods of determining activation levels of multiconditional fuzzy If–Then rules are proposed. Examples of compositional rules of inference are given. The proposed operations and methods have been implemented in the form of a fuzzy calculator working under Windows and a class of controllers.