Paper:

# g-Calculus-Based Compositional Rule of Inference

## Marta Takács

Budapest Tech, H-1034 Budapest, Bécsi út 96/b, Hungary

We review a specific case, in which the investigated structure is a real semi-ring with pseudo-operations as a step toward investigating the problem of approximate reasoning in fuzzy systems. We focus on special-type fuzzy sets, i.e. *g* -generated quasi-triangular fuzzy numbers, and special *g* -generated t-norms and implication in fuzzy approximate reasoning.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.10, No.4, pp. 534-541, 2006.

- [1] B. D. Baets, “A note on Mamdani controllers,” Intelligent Systems and Soft Computing for Nuclear Science and Industry, D. Ruan, E. Kerre, Eds., Singapore: World Scientific, pp. 22-28, 1996.
- [2] U. Bodenhofer, “A similarity-Based Generalization of Fuzzy Orderings,” Universitätverlag Rudolf Trauner, Linz 1999.
- [3] J. Fodor, and M. Rubens, “Fuzzy Preference Modelling and Multicriteria Decision Support,” Kluwer Academic Pub., 1994.
- [4] B. Moser, and M. Navara, “Fuzzy Controllers with Conditionally Firing Rules,” IEEE Transactions on Fuzzy Systems, 10, pp. 340-348, 2002.
- [5] E. P. Klement, R Mesiar, and E. Pap, “Triangular Norms,” Kluwer Academic Publishers, ISBN 0-7923-6416-3, 2000.
- [6] I. J. Rudas, “Evolutionary operators: new parametric type operator families,” Fuzzy Sets and Systems 23, pp. 149-166, 1999.
- [7] I. J. Rudas, “Hybrid Systems (Integration of Neural Networks, Fuzzy Logic),” Expert Systems, and Genetic Algorithms, in Encyclopedia of Information Systems, Academic Press 2002, pp. 114-1 - 114-8, 2002.
- [8] M. Takács, “Investigation on a Special Group of Fuzzy Implication Operators and Fuzzy Inference Mechanism Using a Simplified Rule Base System,” Proceedings of the 1997 International Conference on Neural Information Processing and Intelligent Information Systems, New Zealand, Dunedin, Univ. of Otago, November 23-28, 1997, Vol.2, pp. 793-796.
- [9] D. Dubois, and H. Prade, “Fuzzy sets in approximate reasoning, part 2: Logical approaches,” Fuzzy Sets and Systems, 40, pp. 203-244, 1991b.
- [10] L. A. Zadeh, “A Theory of approximate reasoning,” In J. Hayes, and editors, Machine Intelligence, Vol.9, Halstead Press, New York, pp. 149-194, 1979.
- [11] L. A. Zadeh, “From Computing with Numbers to Computing with Words – From Manipulation of Measurements to manipulation of Perceptions,” In Proc. Of EUROFUSE – SIC Conf. 1999, Budapest, pp. 1-3, 1999.
- [12] H. J. Zimmermann, “Fuzzy Sets, Decision Making and Expert Systems,” Kluwer, Boston, 1991.
- [13] E. Pap, “Triangular norms in modelling uncertainly, non-linearity and decision,” in Proceedings of the 2
^{nd}International Symposium of Hungarian researchers Computational Intelligence, ISBN 963 7154 06 X, pp. 7-18. - [14] R. R. Yager, and D. P. Filev, “Essential of Fuzzy Modelling and Control,” Book, New York/John Wiley and Sons Inc., 1994.
- [15] E. Pap, “Pseudo-additive measures and their applications,” in Handbook of Measure Theory (Ed. E. Pap), Volume II, Elsevier, North-Holland, pp. 1403-1465, 2002.
- [16] L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Trans. Syst., Man Cybernetics 3, pp. 28-44, 1973.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.