Calculi of Information Granules: Fuzzy Relational Equations

Handbook of Granular Computing

Volumn , Issue , 2008, Pages 225-248

  Gottwald, Siegfried ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Approximation and interpolation; Fuzzy control and relation equations; Information granule calculi; Interpolation strategies and aggregation operators; MA pseudo solution optimality; Mamdani Assilian relation RMA; Proportional integral derivative (PID) control strategies; Pseudosolution strategy; Rule based fuzzy mathematical treatment control

Indexed keywords

EID: 58149377350     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9780470724163.ch11     Document Type: Chapter

References (24)

1. S. Gottwald. Generalised solvability behaviour for systems of fuzzy equations. In: V. Novák and I. Perfilieva (eds), Discovering the World with Fuzzy Logic, Advances in Soft Computing. Physica-Verlag, Heidelberg, 2000, pp. 401-430.
2. S. Gottwald. Mathematical fuzzy control. A survey of some recent results. Log. J. IGPL 13 (5) (2005) 525-541.
3. S. Gottwald, V. Novák, and I. Perfilieva. Fuzzy control and t-norm-based fuzzy logic. Some recent results. In: Proceedings of the 9th International Conference of IPMU'2002, ESIA - Université de Savoie, Annecy, 2002, pp. 1087-1094.
4. I. Perfilieva and S. Gottwald. Fuzzy function as a solution to a system of fuzzy relation equations. Int. J. Gen. Syst. 32 (2003) 361-372.
5. S. Gottwald. A Treatise on Many-Valued Logics. Studies in Logic and Computation, Vol. 9. Research Studies Press, Baldock, 2001.
6. L.A. Zadeh. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybcrn. SMC-3 (1973) 28-44.
7. R.D. Luce. A note on Boolean matrix theory. Proc. Am. Math. Soc. 3 (1952) 382-388.
8. A. DiNola, S. Sessa,W. Pedrycz, and E. Sanchez. Fuzzy Relation Equations and Their Applications to Knowledge Engineering. Theory and Decision Library, Series D. Kluwer, Dordrecht, 1989.
9. E. Sanchez. Resolution of composite fuzzy relation equations. Inf. Control 30 (1976) 38-48.
10. S. Gottwald. Characterizations of the solvability of fuzzy equations. Elektron. Inf. Kybern. 22 (1986) 67-91.
11. S. Gottwald. Fuzzy Sets and Fuzzy Logic. The Foundations of Application - From a Mathematical Point of View. Vieweg: Braunschweig/Wiesbaden and Teknea, Toulouse, 1993.
12. A. Mamdani and S. Assilian. An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man-Mach. Stud. 7 (1975) 1-13.
13. F. Klawonn. Fuzzy points, fuzzy relations and fuzzy functions. In: V. Novák and I. Perfilieva (eds), Discovering the World with Fuzzy Logic, Advances in Soft Computing. Physica-Verlag, Heidelberg, 2000, pp. 431-453.
14. S. Gottwald. Criteria for non-interactivity of fuzzy logic controller rules. In: A. Straszak(ed), Large Scale Systems: Theory and Applications, Proceedings of the 3rd IFAC/IFORS Sympasium Warsaw 1983. Pergamon Press, Oxford, 1984, pp. 229-233.
15. W. Wu. Fuzzy reasoning and fuzzy relation equations. Fuzzy Sets Syst. 20 (1986) 67-78.
16. G. Klir and B. Yuan. Approximate solutions of systems of fuzzy relation equations. In: FUZZ-IEEE '94. Proceedings of the 3rd International Conference on Fuzzy Systems, Orlando, FL, 1994, pp. 1452-1457.
17. I. Perfilieva. Fuzzy function as an approximate solution to a system of fuzzy relation equations. Fuzzy Sets Syst. 147 (2004) 363-383.
18. I. Perfilieva and A. Tonis. Compatibility of systems of fuzzy relation equations. Int. J. Gen. Syst. 29 (2000) 511-528.
19. T. Calvo, G. Mayor, and R. Mesiar (eds). Aggregation Operators: New Trends and Applications. Physica-Verlag, Heidelberg, 2002.
20. D. Dubois and H. Prade. On the use of aggregation operations in information fusion processes. Fuzzy Sets Syst. 142 (2004) 143-161.
21. S. Gottwald. On a generalization of fuzzy relation equations. In: Proceedings of the 11th International Conference of IPMU 2006, Edition EDK, Paris, 2006, Vol. 2, pp. 2572-2577.
22. N.N. Morsi and A.A. Fahmy. On generalized modus ponens with multiple rules and a residuated implication. Fuzzy Sets Syst. 129 (2002) 267-274.
23. L.P. Holmblad and J.J. Ostergaard. Control of a cement kiln by fuzzy logic. In: M.M. Gupta and E. Sanchez (eds), Fuzzy Information and Decision Processes. North-Holland, Amsterdam, 1982, pp. 389-399.
24. A. DiNola, A. Lettieri, I. Perfilieva, and V. Novák. Algebraic analysis of fuzzy systems. Fuzzy Sets Syst. 158 (2007) 1-22.