A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem
This paper presents an optimization method to solve a multi-objective model of a bi-level linear programming problem with intuitionistic fuzzy coefficients. The idea is based on TOPSIS (technique for order preference by similarity to ideal solution) method. TOPSIS method is a multiple criteria metho...
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| Veröffentlicht in: | Complex & intelligent systems Jg. 8; H. 4; S. 3263 - 3278 |
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| Sprache: | Englisch |
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Springer International Publishing
01.08.2022
Springer Nature B.V |
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| ISSN: | 2199-4536, 2198-6053 |
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| Abstract | This paper presents an optimization method to solve a multi-objective model of a bi-level linear programming problem with intuitionistic fuzzy coefficients. The idea is based on TOPSIS (technique for order preference by similarity to ideal solution) method. TOPSIS method is a multiple criteria method that identifies a satisfactory solution from a given set of alternatives based on the minimization of distance from an ideal point and maximization of distance from the nadir point simultaneously. A new model of multi-objective bi-level programming problem in an intuitionistic fuzzy environment has been considered. The problem is first reduced to a conventional multi-objective bi-level linear programming problem using accuracy function. Then the modified TOPSIS method is proposed to solve the problem at both the leader and the follower level where various linear/non-linear membership functions are used to represent the flexibility in the approach of decision-makers (DMs). The problem is solved hierarchically, i.e., first the problem at the leader level is solved and then the feasible region is extended by relaxing the decision variables controlled by the leader. The feasible region is extended to obtain a satisfactory solution for the DMs at both levels. Finally, the application of the proposed approach in the production planning of a company has been presented. An illustrative numerical example is also given to explain the methodology defined in this paper. |
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| AbstractList | This paper presents an optimization method to solve a multi-objective model of a bi-level linear programming problem with intuitionistic fuzzy coefficients. The idea is based on TOPSIS (technique for order preference by similarity to ideal solution) method. TOPSIS method is a multiple criteria method that identifies a satisfactory solution from a given set of alternatives based on the minimization of distance from an ideal point and maximization of distance from the nadir point simultaneously. A new model of multi-objective bi-level programming problem in an intuitionistic fuzzy environment has been considered. The problem is first reduced to a conventional multi-objective bi-level linear programming problem using accuracy function. Then the modified TOPSIS method is proposed to solve the problem at both the leader and the follower level where various linear/non-linear membership functions are used to represent the flexibility in the approach of decision-makers (DMs). The problem is solved hierarchically, i.e., first the problem at the leader level is solved and then the feasible region is extended by relaxing the decision variables controlled by the leader. The feasible region is extended to obtain a satisfactory solution for the DMs at both levels. Finally, the application of the proposed approach in the production planning of a company has been presented. An illustrative numerical example is also given to explain the methodology defined in this paper. |
| Author | Ebrahimnejad, Ali Sharma, Kirti Singh, V. P. Chakraborty, Debjani |
| Author_xml | – sequence: 1 givenname: V. P. surname: Singh fullname: Singh, V. P. email: vpsingh@mth.vnit.ac.in organization: Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur – sequence: 2 givenname: Kirti surname: Sharma fullname: Sharma, Kirti organization: Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur – sequence: 3 givenname: Debjani surname: Chakraborty fullname: Chakraborty, Debjani organization: Department of Mathematics, Indian Institute of Technology Kharagpur – sequence: 4 givenname: Ali surname: Ebrahimnejad fullname: Ebrahimnejad, Ali organization: Department of Mathematics, Qaemshahr Branch, Islamic Azad University |
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| Cites_doi | 10.1007/s40747-021-00299-9 10.1007/s40815-020-00878-x 10.1007/978-3-030-52119-6_13 10.1016/j.apm.2013.11.008 10.1109/ACCESS.2020.3013568 10.1016/S0165-0114(97)00377-1 10.1016/j.ejor.2007.12.019 10.1016/j.apm.2012.03.002 10.1016/0165-0114(78)90031-3 10.1007/s10479-017-2551-y 10.1287/mnsc.17.4.B141 10.1016/j.ejor.2005.08.024 10.1201/b11032 10.1109/FSKD.2008.537 10.1109/CFIS.2018.8336644 10.3233/JIFS-179451 10.1007/s00500-021-05791-5 10.1016/j.esr.2020.100492 10.1007/s10700-017-9280-1 10.1007/s40747-021-00326-9 10.17535/crorr.2019.0025 10.1007/s00500-019-04286-8 10.1016/0305-0548(82)90006-5 10.1016/S0165-0114(02)00362-7 10.3233/JIFS-152354 10.1007/s10479-017-2734-6 10.1007/3-540-45631-7_13 10.1007/s40747-020-00251-3 10.1016/j.eswa.2016.10.063 10.1080/02331934.2020.1768253 |
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| Keywords | TOPSIS method Intuitionistic fuzzy number Fuzzy optimization Bi-level programming problem Multi-objective optimization problem |
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| SubjectTerms | Complexity Computational Intelligence Data Structures and Information Theory Decision making Engineering Fuzzy logic Fuzzy sets Linear programming Multiple criterion Optimization Original Article Production planning |
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| Title | A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem |
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