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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| Published in: | Soft computing (Berlin, Germany) Vol. 23; no. 14; pp. 5605 - 5618 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2019
Springer Nature B.V |
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| ISSN: | 1432-7643, 1433-7479 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Ojha, Akshay Nayak, Suvasis |
| Author_xml | – sequence: 1 givenname: Suvasis surname: Nayak fullname: Nayak, Suvasis email: nksuvasis@gmail.com organization: School of Basic Sciences, Indian Institute of Technology Bhubaneswar – sequence: 2 givenname: Akshay surname: Ojha fullname: Ojha, Akshay organization: School of Basic Sciences, Indian Institute of Technology Bhubaneswar |
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| Keywords | Fuzzy goal programming Nonlinear fractional programming TOPSIS Bi-level multi-objective optimization Distance functions |
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| SubjectTerms | 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 |
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| Title | An approach of fuzzy and TOPSIS to bi-level multi-objective nonlinear fractional programming problem |
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