Abstract
We study optimization problem with linear objective function subject to fuzzy linear system of equations as constraint, when the composition is in f − − →in BL - algebra. The algorithm for solving fuzzy linear system of equations is provided by algebraic-logical properties of the solutions. We present algorithms for computing the extremal solutions of fuzzy linear system of equations and implement the results for solving the linear optimization problem.
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Aho, A., Hopcroft, J., Ullman, J.: The Design and Analysis of Computer Algorithms. Addison-Wesley Publ. Co., London (1976)
Bourke, M.M., Fisher, D.G.: Solution algorithms for fuzzy relational equations with max-product composition. Fuzzy Sets and Systems 94, 61–69 (1998)
De Baets, B.: Analytical solution methods for fuzzy relational equations. In: Dubois, D., Prade, H. (eds.) Fundamentals of Fuzzy Sets. Handbooks of Fuzzy Sets Series, vol. 1, pp. 291–340. Kluwer Academic Publishers, Dordrecht (2000)
Di Nola, A., Lettieri, A.: Relation Equations in Residuated Lattices. Rendiconti del Circolo Matematico di Palermo, s. II, XXXVIII, pp. 246–256 (1989)
Di Nola, A., Pedrycz, W., Sessa, S., Sanchez, E.: Fuzzy Relation Equations and Their Application to Knowledge Engineering. Kluwer Academic Press, Dordrecht (1989)
Grätzer, G.: General Lattice Theory. Akademie-Verlag, Berlin (1978)
Guu, S.M., Wu, Y.-K.: Minimizing a linear objective function with fuzzy relation equation constraints. Fuzzy Optimization and Decision Making 4(1), 347–360 (2002)
Klir, G., Clair, U.H.S., Bo, Y.: Fuzzy Set Theory Foundations and Applications. Prentice Hall PRT, Englewood Cliffs (1977)
Loetamonphong, J., Fang, S.-C.: An efficient solution procedure for fuzzy relational equations with max-product composition. IEEE Transactions on Fuzzy Systems 7(4), 441–445 (1999)
Loetamonphong, J., Fang, S.-C.: Optimization of fuzzy relation equations with max-product composition. Fuzzy Sets and Systems 118(3), 509–517 (2001)
Loetamonphong, J., Fang, S.-C., Young, R.E.: Multi-objective optimization problems with fuzzy relation equation consrtaints. Fuzzy Sets and Systems 127(3), 141–164 (2002)
MacLane, S., Birkhoff, G.: Algebra. Macmillan, New York (1979)
Noskova, L., Perfilieva, I.: System of fuzzy relation equations with sup− * −composition in semi-linear spaces: minimal solutions. In: Proc. FUZZ-IEEE Conf. on Fuzzy Systems, London, July 23-26, pp. 1520–1525 (2007)
Peeva, K.: Universal algorithm for solving fuzzy relational equations. Italian Journal of Pure and Applied Mathematics 19, 9–20 (2006)
Peeva, K., Petrov, D.: Algorithm and Software for Solving Fuzzy Relational Equations in some BL-algebras. In: 2008 IVth International IEEE Conference ”Intelligent Systems”, Varna, September 2008, vol. 1, pp. 2-63–2-68 (2008) ISBN 978-I-4244-1739
Peeva, K., Kyosev, Y.: Fuzzy Relational Calculus-Theory, Applications and Software (with CD-ROM). In: The series Advances in Fuzzy Systems - Applications and Theory, vol. 22. World Scientific Publishing Company, Singapore (2004)
Perfilieva, I., Noskova, L.: System of fuzzy relation equations with \(\inf-\rightarrow\) composition: complete sets of solutions. Fuzzy Sets and Systems 150(17), 2256–2271
Sanchez, E.: Resolution of composite fuzzy relation equations. Information and Control 30, 38–48 (1976)
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Peeva, K., Petrov, D. (2010). Optimization of Linear Objective Function under Fuzzy Equation Constraint in BL − Algebras – Theory, Algorithm and Software. In: Sgurev, V., Hadjiski, M., Kacprzyk, J. (eds) Intelligent Systems: From Theory to Practice. Studies in Computational Intelligence, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13428-9_20
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DOI: https://doi.org/10.1007/978-3-642-13428-9_20
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