A novel table look-up scheme based on GFScom and its application
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This work considers Mamdani fuzzy systems constructed from finite input–output data pairs using the generalized fuzzy sets with contradictory, opposite and medium negation (GFScom). Considering that the information available often consists of a set of finite numerical data pairs, a new table look-up scheme for constructing Mamdani fuzzy systems is presented. The designed fuzzy system is proved to be capable of approximating any real continuous function on a compact set to arbitrary degree of accuracy. We use this fuzzy modeling method for the truck back-upper control problem. The effectiveness of the proposed method is demonstrated by a comparison with the traditional table look-up scheme.
KeywordsNegative information Generalized fuzzy sets GFScom Design of fuzzy systems Approximation of continuous functions Truck backer-upper problem
This research was partially supported by the Natural Science Foundation of China (Grant No. 11271237), the Higher School Doctoral Subject Foundation of Ministry of Education of China (Grant No. 20130202110001), the Key Program of Natural Science Research of Education Department of Guizhou Province of China under Grant No. 408 Contract KY and the Science and Technology Planning Project of Qianxinan Prefecture of Guizhou Province of China under Grant No. 2015-1-51.
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Conflicts of interest
Shengli Zhang and Yongming Li declare that they have no conflict of interest.
Human and animal rights
And this article does not contain any studies with human participants or animals performed by any of the authors.
- Beziau JY (2016) Disentangling contradiction from contrariety via incompatibility. Log Univers. doi: 10.1007/s11787-016-0151-2
- Ferré S (2006) Negation, opposition, and possibility in logical concept analysis. In: Ganter B, Kwuida L (eds) Proceedings of the fourth international conference on formal concept analysis, no. 3874 in lecture notes in artificial intelligence. Springer, Berlin, pp 130–145Google Scholar
- Gatti C (2014) Design of experiments for reinforcement learning. PhD thesis, Rensselaer Polytechnic Institute, New YorkGoogle Scholar
- Herre H, Jaspars J, Wagner G (1999) Partial logic with two kinds of negations as a foundation for knowledge-based reasoning. In: Gabby D, Wansing H (eds) What Is negation?. Kluwer, Dordrecht, pp 1–35Google Scholar
- Lepage F (2016) A square of oppositions in intuitionistic logic with strong negation. Log Univers. doi: 10.1007/s11787-016-0144-1
- Li YM (2005) Analysis of fuzzy system. Science Press, Beijing (in Chinese)Google Scholar
- Nguyen D, Widrow B (1989) The truck backer-upper: an example of self-learning in neural network. In: Proceedings of the international joint conference on neural networks, vol 2. IEEE Press, Washington DC, pp 357–363Google Scholar
- Pan ZH (2010) Fuzzy set with three kinds of negations in fuzzy knowledge processing. In: Proceedings of the ninth international conference on machine learning and cybernetics, vol 5. IEEE Computer Society Press, Piscataway, pp 2730–2735Google Scholar
- Pan ZH (2013) Three kinds of negation of fuzzy knowledge and their base of logic. In: Huang DS, Jo KH, Zhou YQ, Han K (eds) ProceedingS Of 9th international conference on intelligent computing, no. 7996 in lecture notes in artificial intelligence. Springer, Berlin, pp 83–93Google Scholar
- Wagner G (2003) Web rules need two kinds of negation. In: Bry F, Henze N, Maluszynski J (eds) Proceedings of the 1st international workshop on principles and practice of semantic web reasoning, no. 2901 in lecture notes in computer science. Springer, Berlin, pp 33–50Google Scholar
- Wang LX, Mendel JM (1991) Generating fuzzy rules from numerical data, with application. Report no. 169, University Southern California, Los AngelesGoogle Scholar
- Zhang SL (2014) Formal deductive system of fuzzy propositional logic with different negations. J Front Comput Sci Technol 8(4):494–505 (in Chinese)Google Scholar
- Zhang SL (2014) Fuzzy reasoning with contradictory, opposite and medium negation. Pattern Recog Artif Intell 27(7):431–444 (in Chinese)Google Scholar
- Zhang SL, Li YM (2015) Algebraic representation of negative knowledge and its application to design of fuzzy systems. Chin J Comput 38, Online Publishing No. 44 (in Chinese)Google Scholar
- Zimmermann HJ (2011) Fuzzy set theory and its applications, 4th edn. Kluwer, DordrechtGoogle Scholar