Fuzzy if-then rules for modeling interdependences in FMOP problems

There has been a growing interest and activity in the area of multiple criteria decision making (MCDM), especially in the last 25 years. modeling and optimization methods have been developed in both crisp and fuzzy environments. The overwhelming majority of approaches for finding best compromise solutions to MCDM problems do not make use of the interdependences among the objectives. However, as has been pointed out by [1, 2], in modeling real world problems (especially in management sciences and in group decisions) we often encounter MCDM problems with interdependent objectives. In multiple objective programs (MOP), application functions are established to measure the degree of fulfillment of the decision maker’s requirements (achievement of goals, nearness to an ideal point, satisfaction, etc.) about the objective functions (see e.g. [5, 11]) and extensively used in the process of finding ”good compromise” solutions. In [3] we demonstrated that the use of interdependences among objectives of a MOP in the definition of the application functions provides for more correct solutions and faster convergence. In [4], generalizing the principle of application function to fuzzy multiple objective programs (FMOP) with interdependent objectives, we defined a large family of application functions for FMOP in order to provide for a better understanding of the decision problem, and to find effective and more correct solutions. In this paper we define interdependencies among the objectives of FMOP by using fuzzy if-then rules.