chapter  12
16 Pages

- Fuzzy Interdependent Multi-Objective Programming

Since Bellman and Zadeh (1970) originally proposed the concepts of decision making in a fuzzy environment, much research has been proposed to guide study in the field of fuzzy multi-objective programming (FMOP). The first step of FMOP is to view objectives and constraints as fuzzy sets and characterize them by their individual membership functions. Then, a crisp (non-fuzzy) solution is generated by transforming FMOP into multi-objective programming (MOP) and determining the optimal solution to achieve the highest degree of satisfaction in the decision set. For further discussions, readers can refer to Zimmermann (1978); Verners (1987); Martinson (1993); and Lee and Li (1993). As with MOP, the problem of FMOP can be defined by calculating the following model:

= ∈ ≤ = ∈x X

x x x

X x X x

f f f

s t g k m

max/ min { ( ), ( ), , ( )}

. . { | ( ) 0, 1, , }.