A NOTE TO INTERPRETABLE FUZZY MODELS AND THEIR LEARNING

Document Type: Research Paper

Author

University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech Republic

Abstract

In this paper we turn the attention to a well developed theory of fuzzy/lin\-guis\-tic models that are interpretable and, moreover, can be learned from the data.
We present four different situations demonstrating both interpretability as well as learning abilities of these models.

Keywords


[1] A. Dvorak, H. Habiballa, V. Novak and V. Pavliska, The software package LFLC 2000 | its
speci city, recent and perspective applications, Computers in Industry, 51 (2003), 269{280.
[2] A. Dvorak, M. Stepnicka and L. Stepnickova, On Redundancies in Systems of
Fuzzy/Linguistic IF-THEN Rules under Perception-based Logical Deduction Inference, Fuzzy
Sets and Systems.
[3] E. Hullermeier, Does machine learning need fuzzy logic?, Fuzzy Sets and Systems, 281 (2015),
292{299.
[4] V. Novak, Linguistically oriented fuzzy logic controller, in: Proc. of the 2nd Int. Conf. On
Fuzzy Logic and Neural Networks IIZUKA'92, Fuzzy Logic Systems Institute, Iizuka, (1992),
579{582.
[5] V. Novak, Fuzzy relation equations with words, in: M. Nikravesh, L. Zadeh, V. Korotkikh
(Eds.), Fuzzy Partial Di erential Equations and Relational Equations, Springer, Berlin,
(2004), 167{185.
[6] V. Novak, Perception-based logical deduction, in: B. Reusch (Ed.), Computational Intelligence,
Theory and Applications, Springer, Berlin, (2005), 237{250.
[7] V. Novak, Mathematical fuzzy logic in modeling of natural language semantics, in: P. Wang,
D. Ruan, E. Kerre (Eds.), Fuzzy Logic { A Spectrum of Theoretical & Practical Issues,
Elsevier, Berlin, (2007), 145{182.
[8] V. Novak, A comprehensive theory of trichotomous evaluative linguistic expressions, Fuzzy
Sets and Systems, 159 (22) (2008), 2939{2969.
[9] V. Novak, On modelling with words, Int. J. of General Systems, 42 (2013), 21{40.

[10] V. Novak, Evaluative linguistic expressions vs. fuzzy categories?, Fuzzy Sets and Systems,
281 (2015), 81{87.
[11] V. Novak, Fuzzy Natural Logic: Towards Mathematical Logic of Human Reasoning, in:
E. Seising, R.and Trillas, J. Kacprzyk (Eds.), Fuzzy Logic: Towards the Future, Springer,
(2015), 137{165.
[12] V. Novak, Linguistic characterization of time series, Fuzzy Sets and Systems, 285 (2016),
52{72.
[13] V. Novak and J. Kova, Linguistic IF-THEN rules in large scale application of fuzzy control,
in: R. Da, E. Kerre (Eds.), Fuzzy If-Then Rules in Computational Intelligence: Theory and
Applications, Kluwer Academic Publishers, Boston, (2000), 223{241.
[14] V. Novak and S. Lehmke, Logical structure of fuzzy IF-THEN rules, Fuzzy Sets and Systems,
157 (2006), 2003{2029.
[15] V. Novak, V. Pavliska and Valasek, Specialized software for fuzzy natural logic and fuzzy
transform applications, in: Proc. Int. Conference FUZZ-IEEE'2014, Beijing, China, (2014),
2337{2344.
[16] V. Novak, V. Pavliska, M. Stepnicka and L. Stepnickova, Time series trend extraction and
its linguistic evaluation using F-transform and fuzzy natural logic, in: L. Zadeh, A. Abbasov,
R. Yager, S. Shahbazova (Eds.), Recent Developments and New Directions in Soft Computing,
Springer, Berlin, (2014), 429{442.
[17] V. Novak and I. Per lieva, Smooth fuzzy logic deduction with words, in: Proc. Int. Conf.
Fuzzy Information Processing: Theories and Applications, Vol. II, Tsinghua University
Press/Springer, Beijing, (2003), 599{604.
[18] V. Novak and I. Per lieva, On the semantics of perception-based fuzzy logic deduction, International
Journal of Intelligent Systems, 19 (2004), 1007{1031.
[19] V. Novak, I. Per lieva and A. Dvorak, Insight into Fuzzy Modeling, Wiley & Sons, Hoboken,
New Jersey, 2016.
[20] V. Novak, I. Per lieva and N. G. Jarushkina, A general methodology for managerial decision
making using intelligent techniques, in: E. Rakus-Anderson, R. Yager, N. Ichalkaranje, L. Jain
(Eds.), Recent Advances in Fuzzy Decision-Making, Springer, Heidelberg, (2009), 103{120.
[21] V. Novak, I. Per lieva, A. Romanov and N. Yarushkina, Time series grouping and trend
forecast using F1-transform and fuzzy natural logic, in: R. Marco se Moraes, E. E. Kerre,
L. dos Santos Machado, J. Lu (Eds.), Decision Making and Soft Computing, World Scienti c,
(2014), 143{148.
[22] I. Per lieva, Fuzzy transforms: theory and applications, Fuzzy Sets and Systems, 157 (2006),
993{1023.
[23] L. Zadeh, Toward a logic of perceptions based on fuzzy logic, in: V. Novak, I. Per lieva
(Eds.), Discovering the World With Fuzzy Logic, Studies in Fuzziness and Soft Computing,
Springer-Verlag, Heidelberg, (2000), 4{28.
[24] L. A. Zadeh, A rationale for fuzzy control, Trans. ASME, Ser. G, J. Dynamic. Systems,
Measurement and Control, 94 (1972), 3{4.
[25] L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision
processes, IEEE Trans. on Systems, Man, and Cybernetics SMC-3, (1973), 28{44.
[26] L. A. Zadeh, Quantitative fuzzy semantics, Information Sciences, 3 (1973), 159{176.
[27] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning
I, II, III, Information Sciences, 8-9 (1975), 199{257, 301{357, 43{80.
[28] L. A. Zadeh, Fuzzy logic = computing with words, IEEE Trans. Fuzzy Systems, 4 (1996),
103-111.
[29] L. A. Zadeh, From computing with numbers to computing with words & from manipulation
of measurements to manipulation of perceptions, Int. J. of Applied Math and Comp. Sci., 12
(2002), 307{324.
[30] L. A. Zadeh, Precisiated natural language, AI Magazine, 25 (2004), 74{91.