Uncertainties with memory in construction of strict monotonic t-norms and t-conorms for finite ordinal scales: Basic definitions and applications

Applied and Computational Mathematics

Volumn 10, Issue 3, 2011, Pages 498-513

  Batyrshin, Ildar ^a  

^a INSTITUTO MEXICANO DEL PETRÓLEO   (Mexico)

Author keywords

Chemical technology; Finite ordinal scale; Fuzzy logic; Fuzzy rule based system; Fuzzy simulator; Multiset; Petroleum industry; String; T conorm; T norm; Uncertainty

Indexed keywords

EID: 82055172163     PISSN: 16833511     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. Batyrshin, I. Z. Uncertainties with memory in decision-making and expert systems, Proc. Fifth IFSA World Congress'93, Seoul, Korea, 1993, pp. 737-740.
2. Batyrshin, I. Z. Lexicographic valuations of plausibility with universal bounds I, Technical Cybernetics, Izvestija Akademii Nauk, V.5, 1994, pp. 28-45, (in Russian).
3. Batyrshin, I. Z. Lexicographic valuations of plausibility with universal bounds II. Negation operations, theory and control systems, Izvestija Akademii Nauk, V.5, 1995, pp. 133-151, (in Russian).
4. Batyrshin, I. Z. Methods of representation and processing of fuzzy information in intelligent systems, News of Artificial Intelligence, 1996, V.2, pp. 9-65, (in Russian).
5. Batyrshin, I. Z., Batyrshin, I. I. Negations, strict monotonic t-norms and t-conorms for finite ordinal scales, 10th Intern. Conf. on Fuzzy Theory and Technology, 8th Joint Conf. on Information Sciences, JCIS, Salt Lake City, USA, 2005, pp. 50-53.
6. Batyrshin, I. Z., Nurullina, L. R., Zakuanov, R. A. Expert system for correction of parameters of electroplating process, In: Int. Conf. on Actual Problems of Mathematical Modeling and Automatic Design in Mechanical Engineering, Kazan, 1995, pp. 45-48 (in Russian).
7. Batyrshin, I., Zakuanov, R., Bikushev, G. Expert system based on algebra of uncertainties with memory in process optimization, In: D. Ruan, P. D'hondt, P. Govaerts and E. E. Kerre, Eds., Fuzzy Logic and Intelligent Technologies in Nuclear Science, FLINS 1994, World Scientific, Singapore, 1994, pp. 156-159.
8. Beliakov, G., Pradera, A., Calvo, T. Aggregation functions: a guide for practitioners, Springer-Verlag, Berlin, 2007.
9. Fodor, J. Smooth associative operations on finite ordinal scales, IEEE Transactions on Fuzzy Systems, V.8, N.6, 2000, pp. 791-795. (Pubitemid 32130580)
10. Forsyth, R. (Ed.) Expert systems: principles and case studies, Chapman and Hall, London, 1984.
11. Godo, L., Torra, V. On aggregation operators for ordinal qualitative information, IEEE Transactions on Fuzzy Systems, V.8, N.2, 2000, pp. 143-154.
12. Goguen, G. A. L-fuzzy sets, J. Math. Anal. Appl., V.18, 1967, pp. 145-174.
13. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E. Aggregation functions, Cambridge University Press, New York, 2009.
14. Kerre, E. E. The impact of fuzzy set theory on contemporary mathematics, Int. J. Applied and Computational Mathematics, V.10, N.1, 2011, pp. 20-34.
15. Klement, E. P., Mesiar, R., Pap, E. Triangular norms, Kluwer Academic Publishers, Dordrecht, 2000.
16. Mayor, G., Torrens, J. Triangular norms on discrete settings, In: Klement E. P., Mesiar R. (Eds.) Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, Elsevier, Amsterdam, 2005, pp. 189-230.
17. Miller, G. A. The magical number seven, plus or minus two: Some limits on our capacity for processing information, Psychological Review, V.63, 1956, pp. 81-97.
18. Pfanzagl, J. Theory of measurement, 2nd ed., Physica-Verlag, Wurzburg, 1971.
19. Sheremetov, L., Batyrshin, I., Filatov, D., Martinez, J., Rodriguez, H. Fuzzy expert system for solving lost circulation problem, Applied Soft Computing, V.8, 2008, pp. 14-29. (Pubitemid 47376927)
20. Sheremetov, L., Cosultchi, A., Batyrshin, I., Martínez- Muñoz, J., Berumen, S. New insights and applications of soft computing on analysis of water production from oil reservoirs, SPE 108702, 2nd Intern. Oil Conf. Exhibit, in Mexico, Veracruz, Mexico, 2007.
21. Siler, W., Buckley, J. J. Fuzzy expert systems and fuzzy reasoning, John Wiley & Sons, New Jersey, 2005.
22. Trillas, E. The principles of non-contradiction and excluded-middle in fuzzy logic, Revisited, Int. J. Appl. Comput. Math., V.10, N.1, 2011, pp. 78-87.
23. Zadeh, L. A. Fuzzy sets, Information and Control, V.8, 1965, pp. 338-353.
24. Zadeh, L. A. Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. SMC, V.3, 1973, pp. 28-44.
25. Zadeh, L. A. Knowledge representation in fuzzy logic, IEEE Transactions on Knowledge and Data Engineering, V.1, N.1, 1989, pp. 89-99.
26. Zadeh, L. A. From computing with numbers to computing with words - from manipulation of measurements to manipulation of perceptions, IEEE Trans, on Circuits and Systems - I: Fundamental Theory And Applications, V.45, N.1, 1999, pp. 105-119.
27. Zakuanov, R., Batyrshin, I., Bikushev, G., Arkhireev, V. P. Presentation of fuzzy concepts in hybrid expert system SMOPLEX, Intern. Workshop Soft Computing-96, 1996, pp. 122-128 (in Russian).