An Order Relation and Fundamental Operations on Fuzzy Numbers and Their Applications to Fuzzy Linear Programming

An order relation, which satisfies the axioms of a partial ordering, is defined on the set of general fuzzy numbers. An L fuzzy number is defined as a fuzzy numbcr specialized to a certain extent, and fundamental linear operations are introduced on the set of the L fuzzy numbers. After that, characterization theorems of the order among the L fuzzy numbers is given in terms of the parameters of the fuzzy numbers, and it is investigated, on the basis of the theorems, that how the order relation is adapted for the fundamental operations. Finally, some of these results are applied to two types of fuzzy linear programming problems, in which the coefficients of constraint functions are L fuzzy numbers, to show that both types of the problems can be reduced to nonfuzzy problems. One type of them is reduced to a usual linear programming problem, and another type generates a nonfuzzy new programming problem.