Multi-objective Optimization Proposal with Fuzzy Coefficients in both Constraints and Objective Functions.
Multi-objective Optimization Proposal with Fuzzy Coefficients in both Constraints and Objective Functions.
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Resumen
Propuesta de optimización multiobjetivo con coeficientes difusos en restricciones y en funciones objetivo.
Abstract
Fuzzy sets, and more specifically, fuzzy numbers can be a very suitable way to include uncertainty within the formulation and solution of linear problems with multiple goals. Goals in a decision problem do not need to be either maximized, or minimized, as in classical mathematical programming, but they are substituted by aspiration levels, and they need to be met in order to satisfy the decision-maker. Experience shows that it is easier for the decision-maker to formulate both objectives and constraints with fuzzy coefficients, rather than specify a defined quantity for the matrices A, b or g. This paper shows the versatility of a methodology that solves multi-objective linear problems, formulated with fuzzy coefficients. This conception becomes an alternative in contrast with the hard methodologies predominant in Operations Research, since the fuzzy approach allows the decision-maker to make uncertain assumptions both for the formulation and solution of optimization problems.
Keywords: Fuzzy logic, multi-criteria analysis, triangular fuzzy numbers.
Resumen
Los conjuntos difusos y específicamente los números difusos constituyen una manera efectiva de incluir la incertidumbre en la formulación y solución de problemas lineales de optimización multiobjetivo. Las metas en un problema de decisión no necesitan ser maximizadas ni minimizadas, como ocurre en las herramientas clásicas de programación matemática, sino que se pueden sustituir por niveles de aspiración, las cuales constituyen las expectativas para un decisor. La experiencia demuestra que es más fácil para el decisor formular los objetivos y las restricciones en un problema con coeficientes difusos, en vez de simplemente especificar un número concreto en las matrices A, b ó g. Este artículo presenta la versatilidad de una formulación metodológica que permite resolver problemas multiobjetivo de tipo lineal, los cuales son formulados con coeficientes difusos. Esta concepción constituye una alternativa a las metodologías duras que dominan la investigación de operaciones, dado que la aproximación difusa permite que los decisores realicen presunciones inciertas en la formulación y solución en los problemas de optimización.
Palabras Clave: Lógica difusa, análisis multiobjetivo, números triangulares difusos.
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Referencias (VER)
427-434.
Antonsson, E. K. & Sebastian, H. J. (1999). Fuzzy sets in engineering design, Practical Applications of Fuzzy Technologies. Springer.
Bellman, R. E. & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17 (4),
141-164.
Berredo, R. C., Ekel, P. Y., Martini, S. C., Palhares, R. M., Parreiras, R. O. & Pereira, J. G. (2013). Decision making in fuzzy environment and multicriteria power engineering problems. International Journal of Electrical Power & Energy Systems, 33 (3),
623-632.
Bit, A. K., Biswal, M. P. & Alam, S. S. (1992). Fuzzy programming approach to multicriteria decision making transportation problem. Fuzzy Sets and Systems, 50 (2),
135-141.
Carlsson, C. & Fuller, R. (2002). Fuzzy reasoning in decision making and optimization. Springer, Amsterdam.
Correa-Henao, G. J. (2015). Metodologías para la toma de decisiones apoyadas en modelos difusos. Editorial Académica Española, Hamburgo (Alemania),
304.
Correa-Henao, G. J., Peña-Zapata, G. E. & Álvarez, H. D. (2003). Propuestas metodológicas para la solución de problemas multiobjetivo, mediante el uso de conjuntos y de operadores difusos. Avances en Sistemas e Informática, 1 (1),
13-19.
Chanas, S. (1989). Fuzzy programming in multiobjective linear programming: a parametric approach. Fuzzy Sets and Systems, 29 (3),
303-313.
Chanas, S. & Kuchta, D. (1996). A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets and Systems, 82 (3),
299-305.
Chen, J. J., Hwang, L., Beckmann, M. J. & Krelle, W. (1992). Fuzzy multiple attribute decision making: methods and applications. New York: Springer-Verlag.
Chen, S. M., Yang, M. W., Yang, S. W., Sheu, T. W. & Liau, C. J. (2012). Multicriteria Fuzzy Decision Making Based on Interval-Valued Intuitionistic Fuzzy Sets. Expert Systems with Applications, 39 (15),
12085-12091.
Dubois, D., Kerre, E., Mesiar, R., & Prade, H. (2000). Fuzzy Interval Analysis, Fundamentals of Fuzzy Sets. Springer.
Dubois, D. & Prade, H., (1979). Decision-Making Under Fuzziness. Advances in Fuzzy Set Theory and Applications, 279-302.
Eiselt, H. A. & Laporte, G. (1992). The Use of Domains in Multicriteria Decision Making. European Journal of Operational Research, 61 (3),
292-298.
Ekel, P. Y., Martini, S. C. & Palhares, R. M. (2008). Multicriteria Analysis in Decision Making under Information Uncertainty. Applied Mathematics and Computation, 200 (2),
501-516.
Fullér, R. & Zimmermann, H. J. (1993). Fuzzy Reasoning for Solving Fuzzy Mathematical Programming Problems. Fuzzy Sets and Systems, 60 (2),
121-133.
Grzegorzewski, P. & Pasternak-Winiarska, K. (2014). Natural Trapezoidal Approximations of Fuzzy Numbers. Fuzzy Sets and Systems, 0.
Gupta, P. & Mehlawat, M. K. (2009). Bectorá “Chandra Type Duality in Fuzzy Linear Programming with Exponential Membership Functions. Fuzzy Sets and System, 160 (22),
3290-3308.
Hillier, F. S. & Lieberman, G. J. (2002). Investigación de operaciones. McGraw: Hill.
Joseph, A. (1995). Parametric Formulation of the General Integer Linear Programming Problem. Computers & Operations Research, 22 (9),
883-892.
Li, D. F. & Wan, S. P. (2013). Fuzzy Linear Programming Approach to Multiattribute Decision Making with Multiple Types of Attribute Values and Incomplete Weight Information. Applied Soft Computing, 13 (11),
4333-4348.
Luhandjula, M. K. (1987). Multiple Objective Programming Problems with Possibilistic Coefficients. Fuzzy Sets and Systems, 21 (2),
135-145.
Luo, J., Li, W. & Wang, Q. (2014. Checking Strong Optimality of Interval Linear Programming with Inequality Constraints and Nonnegative Constraints. Journal of Computational and Applied Mathematics, 260, 180-190.
Mahdavi-Amiri, N. & Nasseri, S. H. (2007). Duality Results and a Dual Simplex Method for Linear Programming Problems with Trapezoidal Fuzzy Variables. Fuzzy Sets and Systems, 158 (17),
1961-1978.
Maleki, H. R., Tata, M. & Mashinchi, M. (2000). Linear Programming with Fuzzy Variables. Fuzzy Sets and Systems, 109, (1),
21-33.
Martínez, E., Marquardt, W. & Pantelides, C. (2006). A Simplex Search Method for Experimental Optimization with Multiple Objectives, Computer Aided Chemical Engineering. Retrieved from: http://www.sciencedirect.com/science/article/pii/S1570794606800751
Ojha, A. K. & Biswal, K. K. (2006). Multi-Objective Geometric Programming Problem with ሊ-Constraint Method. Applied Mathematical Modelling, 38, (2),
47-758.
Ozgen, D. & Gulsun, B. (2013). Combining Possibilistic Linear Programming and Fuzzy AHP for Solving the Multi-Objective Capacitated Multi-Facility Location Problem. Information Sciences, 268.
Petrovic-Lazarevic, S. & Abraham, A. (2002). Optimizing Linear Programming Technique Using Fuzzy Logic, Hybrid Information Systems. Springer, 269-283.
Petrovic-Lazarevic, S. & Abraham, A. (2004). Hybrid Fuzzy-Linear Programming Approach for Multi Criteria Decision Making Problems. ArXiv preprint cs/0405019.
Ramík, J. & Ímánek, J. (1985). Inequality Relation between Fuzzy Numbers and Its Use in Fuzzy Optimization. Fuzzy Sets and Systems, 16 (2),
123-138.
Sakawa, M. (2002). Genetic Algorithms and Fuzzy Multiobjective Optimization. Springer.
Sakawa, M., Inuiguchi, M., Kato, K. & Ikeda, T. (1996). A Fuzzy Satisficing Method for Multiobjective Linear Optimal Control Problems. Fuzzy Sets and Systems, 78 (2),
223-229.
Sakawa, M., Katagiri, H. & Matsui, T. (2014). Interactive Fuzzy Stochastic Two-Level Linear Programming with Simple Recourse. Information Sciences, 1.
Sakawa, M. & Matsui, T. (2013a). Interactive Fuzzy Programming for Fuzzy Random Two-Level Linear Programming Problems through Probability Maximization with Possibility. Expert Systems with Applications, 40 (7),
2487-2492.
Sakawa, M. & Matsui, T. (2013b). Interactive Fuzzy Random Cooperative Two-Level Linear Programming through Level Sets Based Probability Maximization. Expert Systems with Applications. 40 (4),
1400-1406.
Tanaka, H., Guo, P. & Zimmermann, H. J. (2000). Possibility Distributions of Fuzzy Decision Variables Obtained from Possibilistic Linear Programming Problems. Fuzzy Sets and Systems, 113 (2),
323-332.
Wang, J. Q., Nie, R., Zhang, H. Y. & Chen, X. H. (2013). New Operators on Triangular Intuitionistic Fuzzy Numbers and Their Applications in System Fault Analysis. Information Sciences, 251, 79-95.
Wibowo, S. & Deng, H. (2013). Consensus-Based Decision Support for Multicriteria Group Decision Making. Computers & Industrial Engineering, 66 (4),
625-633.
Yager, R. (1978). Fuzzy Decision Making Including Unequal Objectives. Fuzzy Sets and Systems, 1 (2),
87-95.
Yang, M. F., Lin, Y., (2013). Applying Fuzzy Multi-Objective Linear Programming to Project Management Decisions with the Interactive Two-Phase Method. Computers & Industrial Engineering, 66, (4),
1061-1069.
Zare M, Y. & Daneshmand, A. (1995). A Linear Approximation Method for Solving a Special Class of the Chance Constrained Programming Problem. European Journal of Operational Research, 80 (1),
213-225.
Zimmermann, H. J. (1987). Fuzzy Sets, Decision Making, and Expert Systems. International Series in Management Science/Operations Research. Dordrecht: Kluwer Academic.
Zimmermann, H. J. (1978). Fuzzy Programming and Linear Programming with Several Objective Functions. Fuzzy Sets and Systems. 1 (1),
45-55.