A multi-level non-linear multi-objective decision-making under fuzziness

This paper studies a three-level non-linear multi-objective decision-making (TLN-MODM) problem with linear (or non-linear) constraints, and in which the objective functions at every level are non-linear functions which are to be maximized. This paper makes an extension of work of Abo-Sinna which deals with a bi-level non-linear multi-objective decision-making problem under Fuzziness. The three level programming (TLP) problem, whether from the stand point of the three-planner Stackelberg behavior or from the interactive organizational behavior, is a very practical problem and encountered frequently in actual practice. This paper proposes a three-planner multi-objective decision-making model and solution method for solving this problem. This method uses the concepts of tolerance membership function and multi-objective optmization at each level to develop a fuzzy Max–Min decision model for generating Pareto optimal (satisfactory) solution for TLN-MODM problem; the first level decision-maker (FLDM) specifies his/her objective functions and decisions with possible tolerances which are described by membership functions of fuzzy set theory. Then, the second level decision-maker (SLDM) specifies his/her objective functions and decisions, in the view of the FLDM, with possible tolerances which are described by membership functions of fuzzy set theory. Finally, the third level decision-maker (TLDM) uses the preference information for the FLDM and SLDM to solve his/her problem subject to the two upper level decision-makers restrictions. An illustrative numerical example is given to demonstrate the obtained results.