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Fuzzy linear systems. (English) Zbl 0805.04005
Summary: Fuzzy linear systems of equations and inequalities over a bounded chain are studied both from theoretical and computational points of view. A unified approach is presented for solving such systems, completed with polynomial time algorithms. The main results are concerned with establishing the consistency of the system, computing all kinds of solutions, or marking the contradictory equations (respectively inequalities) if the system is inconsistent. Applications in fuzzy linear programming, multivalued logic, fuzzy matrix equations or inequalities, fuzzy relation equations or inclusions, fuzzy automata and medicine are presented.

03E72 Theory of fuzzy sets, etc.
68Q25 Analysis of algorithms and problem complexity
15A99 Basic linear algebra
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
Full Text: DOI
[1] Aho, A.V.; Hopcroft, J.E.; Ullman, J.D., The design and analysis of computer algorithms, () · Zbl 0286.68029
[2] Chen, Lichun; Peng, Boxing, The fuzzy relation equation with union or intersection preserving operator, Fuzzy sets and systems, 25, 191-204, (1988) · Zbl 0651.04005
[3] Cuninghame-Green, R.A., Minimax algebra, () · Zbl 0498.90084
[4] Di Nola, A., Fuzzy relation equations and their application to knowledge engineering, (1989), Kluwer Academic Press Dordrecht
[5] Di Nola, A.; Pedrycz, W.; Sessa, S.; Wang, P.Z., Fuzzy relation equations under triangular norms: A survey and new results, Stochastica, 8, 99-145, (1984) · Zbl 0581.04002
[6] Drewniak, J., Fuzzy relation calculus, (1989), Universitet Ślaski Katowice · Zbl 0701.04002
[7] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, () · Zbl 0605.03021
[8] Garey, M.R.; Johnson, D.S., Computers and intractability, A guide to the theory of NP-completeness, (1979), Freeman San Francisco, CA · Zbl 0411.68039
[9] Gratzer, G., General lattice theory, (1978), Akademic Verlag Berlin · Zbl 0385.06015
[10] Higashi, M.; Klir, G.J., Resolution of finite fuzzy relation equations, Fuzzy sets and systems, 13, 65-82, (1984) · Zbl 0553.04006
[11] Kovacs, M., On the g-fuzzy linear systems, Busefal, 37, 69-77, (1988) · Zbl 0668.90052
[12] MacLane, S.; Birkhoff, G., Algebra, (1979), Macmillan New York · Zbl 0153.32401
[13] Mivakoshi, M.; Shimbo, M., Lower solutions of systems of fuzzy equations, Fuzzy sets and systems, 19, 37-46, (1986)
[14] Miyakoshi, M.; Shimbo, M., Sets of solution-set-invariant matrices of simple fuzzy relation equations, Fuzzy sets and systems, 21, 59-83, (1987) · Zbl 0649.04003
[15] Pappis, C.P.; Sugeno, M., Fuzzy relational equations and the inverse problem, Fuzzy sets and systems, 15, 79-90, (1985) · Zbl 0561.04003
[16] Peeva, K., Linear systems and ordered semirings, () · Zbl 0584.68074
[17] Peeva, K., Systems of linear equations over a bounded chain, Acta cybernetica, 7, 2, 30-34, (1985) · Zbl 0584.68074
[18] Peeva, K.; Peeva, K., On behaviour, reduction and minimization of finite L-automata, (), 28, 2, 221-224, (1988), Japan
[19] Peeva, K., Fuzzy linear systems, () · Zbl 0584.68074
[20] Sanchez, E., Resolution of composite fuzzy relation equations, Inform. and control, 30, 38-48, (1976) · Zbl 0326.02048
[21] Sanchez, E., Solutions in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic, (), 221-234
[22] Sanchez, E., Solution of fuzzy equations with extended operations, Fuzzy sets and systems, 12, 237-248, (1984) · Zbl 0556.04001
[23] Sessa, S., Some results in the setting of fuzzy relation equations theory, Fuzzy sets and systems, 14, 281-297, (1984) · Zbl 0559.04005
[24] Sessa, S., Finite fuzzy relation equations with unique solution in complete Brouwerian lattices, Fuzzy sets and systems, 29, 103-113, (1989) · Zbl 0659.06007
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