Abstract
Crisp constraints in the case of linear optimization problem linked to max-aggregation function composition as rule may result in unsatisfactory solution. We propose and discuss a method of getting more feasible solutions, relaxing crisp inequalities/extremes by means of fuzzy sets.
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Baczynski, M., & Jayaram, B. (2008). Fuzzy implications. In Studies in fuzziness and soft computing (Vol. 231). Berlin: Springer.
Beliakov, G., Pradera, A., & Calvo, T. (2007). Aggregation functions: A guide for practitioners. Berlin: Springer.
Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in fuzzy environment. Management Science, 17, 141–164.
Durante, F., Quesada-Molina, J. J., & Sempi, C. (2006). Semicopulas: Characterizations and applicability. Kybernetika, 42, 287–302.
Fernandez, M. J., & Gil, P. (2004). Some specific types of fuzzy relation equations. Information Sciences, 164, 189–195.
Ghodousian, A., & Khorram, E. (2008). Fuzzy linear optimization in the presence of the fuzzy relation inequality constraints with max–min composition. Information Sciences, 178, 501–519.
Grabisch, M., Marichal, J. L., Mesiar, R., & Pap, E. (2009). Aggregation functions. Cambridge: Cambridge University Press.
Kouchakinejad, F., Khorram, E., & Mashinchi, M. (2015). Fuzzy optimization of linear objective function subject to max-average relational inequality constraints. Journal of Intelligent and Fuzzy Systems, 29, 635–645.
Kouchakinejad, F., Mashinchi, M., & Mesiar, R. (2016). Solution-set invariant matrices and vectors in fuzzy relation inequalities based on max-aggregation function composition. Iranian Journal of Fuzzy Systems, 13(7), 91–100.
Sakawa, M. (1993). Fuzzy sets and interactive multi-objective optimization. New York: Plenum.
Shieh, B. S. (2007). Solutions of fuzzy relation equations based on continuous t-norms. Information Sciences, 177, 4208–4215.
Stamou, G. B., & Tzafestas, S. G. (2001). Resolution of composite fuzzy relation equations based on Archimedean triangular norms. Fuzzy Sets and Systems, 120, 95–407.
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Radko Mesiar and Alexandra Šipošová acknowledge support from the APVV-14-0013.
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Mesiar, R., Kouchakinejad, F. & Šipošová, A. On fuzzy solution of a linear optimization problem with max-aggregation function relation inequality constraints. Ann Oper Res 269, 521–533 (2018). https://doi.org/10.1007/s10479-017-2483-6
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DOI: https://doi.org/10.1007/s10479-017-2483-6