Research ArticleOpen AccessGoogle Scholar indexed
A Modified Interactive Stability Algorithm for Solving Multi-Objective NLP Problems with Fuzzy Parameters in Its Objective Functions
Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
Mathematics Department, Faculty of Science, Damietta University, Damietta, Egypt
Mathematics Department, Faculty of Science, Damietta University, Damietta, Egypt
- 1 Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
- 2 Mathematics Department, Faculty of Science, Damietta University, Damietta, Egypt
- 3 Mathematics Department, Faculty of Science, Damietta University, Damietta, Egypt
American Journal of Operations Research·Volume 06 (2016)·Pages 8–16·Published 11 January 2016·DOI10.4236/ajor.2016.61002
Copy link · social · email
Abstract
This paper presents a modified method to solve multi-objective nonlinear programming problems with fuzzy parameters in its objective functions and these fuzzy parameters are characterized by fuzzy numbers. The modified method is based on normalized trade-off weights. The obtained stability set corresponding to <i>α</i>-Pareto optimal solution, using our method, is investigated. Moreover, an algorithm for obtaining any subset of the parametric space which has the same corresponding <i>α</i>-Pareto optimal solution is presented. Finally, a numerical example to illustrate our method is also given.
KeywordsMulti-Objective Nonlinear ProgrammingStabilityTrade-Off MethodFuzzy Parameters
- Shih, C.J. and Lee, H.W. (2004) Level-Cut Approaches of First and Second Kind for Unique Solution Design in Fuzzy Engineering Optimization Problems. Tamkang Journal of Science and Engineering, 7, 189-198.
- Osman, M. (1977) Qualitative Analysis of Basic Notions in Parametric Convex Programming I (Parameters in the Constraints). Aplikace Matematiky, 22, 318-332.
- Osman, M. and El-Banna, A. (1993) Stability of Multiobjective Nonlinear Programming Problems with Fuzzy Parameters. Mathematics and Computers in Simulation, 35, 321-326. http://dx.doi.org/10.1016/0378-4754(93)90062-Y
- Kassem, M. (1995) Interactive Stability of Multiobjective Nonlinear Programming Problems with Fuzzy Parameters in the Constraints. Fuzzy Sets and Systems, 73, 235-243. http://dx.doi.org/10.1016/0165-0114(94)00317-Z
- Sakawa, M. and Yano, H. (1989) Interactive Decision Making for Multiobjective Nonlinear Programming Problems with Fuzzy Parameters. Fuzzy Sets and Systems, 29, 315-326. http://dx.doi.org/10.1016/0165-0114(89)90043-2
- Katagiri, H. and Sakawa, M. (2011) Interactive Multiobjective Fuzzy Random Programming through the Level Set-Based Probability Model. Information Sciences, 181, 1641-1650. http://dx.doi.org/10.1016/j.ins.2011.01.003
- Loganathan, G.V. and Sherali, H.D. (1987) A Convergent Interactive Cutting-Plane Algorithm for Multiobjective Optimization. Operations Research, 35, 365-377.
- Jameel, A. and Sadeghi, A. (2012) Solving Nonlinear Programming Problem in Fuzzy Enlivenment. International Journal of Contemporary Mathematical Sciences, 7, 159-170.
- Elshafei, M.M. (2006) Interactive Stability of Multiobjective Integer Nonlinear Programming Problems. Applied Mathematics and Computation, 176, 230-236.
- Pendharkar, P.C. (2013) Scatter Search Based Interactive Multi-Criteria Optimization of Fuzzy Objectives for Coal Production Planning. Engineering Applications of Artificial Intelligence, 26, 1503-1511. http://dx.doi.org/10.1016/j.engappai.2013.01.001
- Kassem, M. (2007) Interactive Stability Cutting-Plane Algorithm for Multiobjective Nonlinear Programming Problems. Applied Mathematics and Computation, 192, 446-456. http://dx.doi.org/10.1016/j.amc.2007.03.037
- Duboism, D. and Prade, H. (1980) Fuzzy Sets and Systems: Theory and Application. Academic Press, New York.