Mathematical fuzzy control. A survey of some recent results

Logic Journal of the IGPL

Volumn 13, Issue 5, 2005, Pages 525-541

  Gottwald, Siegfried ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Approximation and interpolation; Compositional rule of inference; Fuzzy control; Fuzzy relation equations; Optimality of pseudo solutions; Pseudo solutions; Solvability criteria; Solvability index

Indexed keywords

AUTOMATION; FUNCTIONS; FUZZY INFERENCE; INTERPOLATION; SURVEYS;

APPROXIMATION AND INTERPOLATION; COMPOSITIONAL RULES OF INFERENCES; CONTROL APPROACH; FUZZY RELATION EQUATIONS; OPTIMALITY; OPTIMALITY OF PSEUDO-SOLUTION; PSEUDO SOLUTION; SOLVABILITY CRITERIA; SOLVABILITY INDEX;

FUZZY CONTROL;

EID: 33750102803     PISSN: 13670751     EISSN: 13689894     Source Type: Journal    
DOI: 10.1093/jigpal/jzi040     Document Type: Conference Paper

References (17)

1. A. DiNola, S. Sessa, W. Pedrycz and E. Sanchez, Fuzzy Relation Equations and Their Applications to Knowledge Engineering. Theory and Decision Libr., ser. D, Kluwer Acad. Publ.: Dordrecht, 1989.
2. S. Gottwald, Criteria for non-interactivity of fuzzy logic controller rules. In: Large Scale Systems: Theory and Applications, Proc. 3rd IFAC/ IFORS Symp. Warsaw 1983 (A. Straszak, ed.), Pergamon Press: Oxford, 1984, 229-233.
3. S. Gottwald, Characterizations of the solvability of fuzzy equations. Elektron. Informationsverarb. Kybernet. 22 (1986) 67-91.
4. S. Gottwald, Fuzzy Sets and Fuzzy Logic. The Foundations of Application - From a Mathematical Point of View, Vieweg: Braunschweig/Wiesbaden and Teknea: Toulouse, 1993.
5. S. Gottwald, Generalised solvability behaviour for systems of fuzzy equations, in: V. Novák, I. Perfilieva (Eds.), Discovering the World with Fuzzy Logic, Advances in Soft Computing, Physica-Verlag: Heidelberg, 2000, 401-430.
6. S. Gottwald, A Treatise on Many-Valued Logics. Studies in Logic and Computation, vol. 9, Research Studies Press: Baldock, 2001.
7. S. Gottwald, V. Novák, I. Perfilieva, Fuzzy control and t-norm-based fuzzy logic. Some recent results, in: Proc. 9th Internat. Conf. IPMU'2002, ESIA - Université de Savoie, Annecy, 2002, 1087-1094.
8. Klawonn, F. (2001): Fuzzy points, fuzzy relations and fuzzy functions. In: Discovering the World with Fuzzy Logic (V. Novák, I. Perfilieva eds.) Advances in Soft Computing, Physica-Verlag: Heidelberg 2000, 431-453.
9. G. Klir, B. Yuan, Approximate solutions of systems of fuzzy relation equations, in: FUZZ-IEEE '94. Proc. 3rd Internat. Conf. Fuzzy Systems, Orlando FL, 1994, 1452-1457.
10. R.D. Luce, A note on Boolean matrix theory, Proc. Amer. Math. Soc. 3 (1952) 382-388.
11. A. Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller, Internat. J. Man-Machine Studies 7 (1975) 1-13.
12. I. Perfilieva, Fuzzy function as an approximate solution to a system of fuzzy relation equations, Fuzzy Sets Systems, 147 (2004), 363-383.
13. I. Perfilieva, S. Gottwald, Fuzzy function as a solution to a system of fuzzy relation equations, Internat. J. General Systems, 32 (2003) 361-372.
14. I. Perfilieva, A. Tonis, Compatibility of systems of fuzzy relation equations, Internat. J. General Systems, 29 (2000) 511-528.
15. E. Sanchez, Resolution of composite fuzzy relation equations, Information and Control, 30 (1976) 38-48.
16. W. Wu, Fuzzy reasoning and fuzzy relation equations, Fuzzy Sets Systems, 20 (1986) 67-78.
17. L.A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Systems, Man and Cybernet. SMC-3 (1973) 28-44.