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

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

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Article ID: iaor20022514
Country: India
Volume: 38
Issue: 5
Start Page Number: 484
End Page Number: 495
Publication Date: Oct 2001
Journal: OPSEARCH
Authors:
Keywords: fuzzy sets, programming: multiple criteria
Abstract:

This paper studies a bi-level non-linear multi-objective decision making (BLN-MODM) problem with linear (or nonlinear) constraints, and in which the objective function at each levels are nonlinear functions, which are to be maximized. The BLN-MODM problem can be thought of as a static version of the Stackelberg leader–follower game in which a Stackelberg strategy is used by the leader (or the higher-level decision maker (HLDM)), given the rational reaction of the follower (or the lower-level decision maker (LLDM)). From this point of view, this paper proposes a two-planner bi-level multi-objective decision-making model and solution method for solving this problem. This method uses the concepts of tolerance membership function and multi-objective optimization (MOO) (at each level) to develop a fuzzy max–min decision model for generating Pareto optimal (satisfactory) solution for BLN-MODM problem. The HLDM specifies his/her objective functions and decisions with possible tolerances, which are described by membership functions of fuzzy set theory. Then, the LLDM uses this preference information for HLDM and solves his/her problem subject to the HLDMs' restrictions. An illustrative numerical example is given to demonstrate the obtained results.

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