Title: Functional Equations Involving Fuzzy Implication Functions

Speaker: Prof. Michał Baczyński, Institute of Mathematics, University of Silesia, Poland

Date: October 13, 2016

Time:9:00 am-10:00 am

Location: Room B1032, Tenth Floor, Zhixin Building, Central Campus

Abstract:  Researches on fuzzy implication functions, where the truth values belong to the unit interval [0,1], are carried out from the beginning of fuzzy set theory and fuzzy logic. In recent years, investigations has been deepened, which resulted in publishing some surveys [4, 3] and two research monographs [1, 2] entirely devoted to this class of fuzzy connectives. In my talk I concentrate on different functional equations (or inequalities) involving fuzzy implications and their role in approximate reasoning. In particular, we discuss the exchange principle, the distributivity equations of fuzzy implications over different fuzzy logic operations, the law of importation, the T-conditionality inequalities in generalized modus ponens, etc. For each of the above functional equation or inequality with fuzzy implication functions, we describe the current state of theoretical research, we discuss their role in fuzzy logic and we show what are the open problems.

References

1. M. Baczyński, G. Beliakov, H. Bustince, and A. Pradera (Eds.), Advances in Fuzzy Implication Functions, volume 300 of Studies in Fuzziness and Soft Computing, Springer, Berlin Heidelberg, 2013.

2. M. Baczyński and B. Jayaram, Fuzzy Implications, volume 231 of Studies in Fuzziness and Soft Computing, Springer, Berlin Heidelberg, 2008.

3. M. Baczyński, B. Jayaram, S. Massanet and J. Torrens, Fuzzy Implications: Past, Present, and Future, in: J. Kacprzyk and W. Pedrycz (Eds.), Springer Handbook of Computational Intelligence, Springer, Berlin Heidelberg 2015, pp. 183-202.

4. M. Mas, M. Monserrat, J. Torrens, and E. Trillas, A survey on fuzzy implication functions, IEEE Trans. Fuzzy Syst., 15(6):1107–1121, 2007.

Bio:Professor Michał Baczyński is currently with the Institute of Mathematics, University of Silesia, Poland. He has co-authored a research monograph on Fuzzy Implications published by Springer in 2008 and is the author or co-author of more than 50 published papers in refereed international journals and conferences. He has been invited to be an invited speaker for 7 international conferences. He has also presented his research works at some 55 conferences with proceedings, such as EUSFLAT, IPMU, AGOP, FUZZ-IEEE, and FSTA, as well as in many workshops and seminars. He is also a regular reviewer for many respected international journals and a member of various committees in international conferences.

His current research interests include fuzzy aggregation operations, chiefly fuzzy implications, approximate reasoning, fuzzy systems, and functional equations. M. Baczyński is a member of the European Society for Fuzzy Logic and Technology (EUSFLAT) and the Polish Mathematical Society (PTM).