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 function at every level are non-linear functions which are to be maximized. This paper makes an extension work of Abo-Sinna [J. Operat. R...

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Vydáno v:Applied mathematics and computation Ročník 153; číslo 1; s. 239 - 252
Hlavní autoři: Osman, M.S., Abo-Sinna, M.A., Amer, A.H., Emam, O.E.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Elsevier Inc 25.05.2004
Elsevier
Témata:
Calculus of variations and optimal control
Exact sciences and technology
Fuzzy decision-approach
Logic and foundations
Mathematical analysis
Mathematical logic, foundations, set theory
Mathematics
Measure and integration
Multi-level programming
Multi-objective decision-making
Numerical analysis
Numerical analysis. Scientific computation
Pareto optimal solution
Sciences and techniques of general use
Set theory
Stackelberg game
Multi-level programming
Pareto optimal solution
Stackelberg game
Multi-objective decision-making
Fuzzy decision-approach
Concept
Membership function
Solving
Constraint
Decision making
Optimization method
Non linear function
Programming
Tolerance
Fuzzy set
Decision
Constrained optimization
Numerical analysis
Applied mathematics
Preference
Optimal solution
Decision function
Problem solving
Set theory
Behavior
Objective function
ISSN:0096-3003, 1873-5649
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Shrnutí: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 function at every level are non-linear functions which are to be maximized. This paper makes an extension work of Abo-Sinna [J. Operat. Res. Soc. India (OPSEARCH) 38 (5) (2001) 484–495] which deal 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 optimization 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 solves his/her problem subject to the two upper level decision-makers restrictions. An illustrative numerical example is given to demonstrate the obtained results.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(03)00628-3