Bounds on the Value of Fuzzy Solution to Fuzzy Programming Problem

The paper is concerned with finding the refined bounds on the value of fuzzy solution to fuzzy programming prob- lem. In this paper we first present the definitions which are the sum of pairs expected value (SPEV), the expected value of the reference scenario (EVRS)and the expectation of pairs expected value (EPEV), and obtain the value of fuzzy solution (VFS) defined by difference between the re- course problem solution and the expected value of reference solution. In addition, several numerical examples are also given in order to explain the definitions specifically. Finally, the properties concerning the concepts are studied, which result in refined bounds on the value of fuzzy solution.