An approach of fuzzy and TOPSIS to bi-level multi-objective nonlinear fractional programming problem

This paper proposes a solution technique to bi-level multi-objective nonlinear fractional programming problem which is based on the concept of TOPSIS (technique for order preference by similarity to ideal solution) and fuzzy goal programming approach. Nonlinear polynomial functions are considered as...

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Veröffentlicht in:Soft computing (Berlin, Germany) Jg. 23; H. 14; S. 5605 - 5618
Hauptverfasser: Nayak, Suvasis, Ojha, Akshay
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2019
Springer Nature B.V
Schlagworte:
Artificial Intelligence
Computational Intelligence
Control
Decision making
Engineering
Functions (mathematics)
Goal programming
Linear programming
Mathematical Logic and Foundations
Mathematical programming
Mechatronics
Methodologies and Application
Objectives
Optimization
Polynomials
Robotics
Fuzzy goal programming
Nonlinear fractional programming
TOPSIS
Bi-level multi-objective optimization
Distance functions
ISSN:1432-7643, 1433-7479
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Zusammenfassung:This paper proposes a solution technique to bi-level multi-objective nonlinear fractional programming problem which is based on the concept of TOPSIS (technique for order preference by similarity to ideal solution) and fuzzy goal programming approach. Nonlinear polynomial functions are considered as the numerators as well as denominators of the fractional objectives at each level. The concept used implements simultaneous minimization and maximization of the functions (numerators and denominators of fractional objectives, decision variables controlled by the upper level decision makers) from their respective aspired (ideal) and acceptable (anti-ideal) values. Distance functions and their corresponding fuzzy membership functions are constructed at both levels for the objectives. Aspired and acceptable values of the decision variables of upper level are ascertained using a certain process. The sum of only under deviational variables obtained from the fuzzy membership goals of the distance functions and the decision variables controlled by upper level decision maker is minimized to obtain the best compromise solution of the concerned bi-level problem. Some comparative discussions with an existing approach are incorporated, and two illustrative numerical examples are discussed to demonstrate the effectiveness of the proposed method.
Bibliographie:ObjectType-Article-1
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ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-018-3217-7