Solving Assignment Problem Using L-R Fuzzy Numbers

Abstract

Let and be two simple graphs. Let (,  1) and (,  2) be two vertex measure spaces. In this paper we introduce a σ algebra  1  2 , which consists of all vertex induced sub graphs of , and it contains every vertex measurable rectangle graph of the form H 1 H 2 , H 1 ∈  1 and H 2 ∈  2. Here, we prove  1  2 is the smallest σ algebra of such that the maps and defined by and for all vertex measurable graphs H in and K in respectively are measurable.