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Uncertainty in the conjunctive approach to fuzzy inference

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Języki publikacji
EN
Abstrakty
EN
Fuzzy inference using the conjunctive approach is very popular in many practical applications. It is intuitive for engineers, simple to understand, and characterized by the lowest computational complexity. However, it leads to incorrect results in the cases when the relationship between a fact and a premise is undefined. This article analyses the problem thoroughly and provides several possible solutions. The drawbacks of uncertainty in the conjunctive approach are presented using fuzzy inference based on a fuzzy truth value, first introduced by Baldwin (1979c). The theory of inference is completed with a new truth function named 0-undefined for two-valued logic, which is further generalized into fuzzy logic as α-undefined. Eventually, the proposed modifications allow altering existing implementations of conjunctive fuzzy systems to interpret the undefined state, giving adequate results.
Rocznik
Strony
431--444
Opis fizyczny
Bibliogr. 31 poz., rys., tab.
Twórcy
  • Institute of Computer Science, University of Silesia, Będzińska 39, 41-200 Sosnowiec, Poland
Bibliografia
  • [1] Azzini, A., Marrara, S., Sassi, R. and Scotti, F. (2008). A fuzzy approach to multimodal biometric continuous authentication, Fuzzy Optimization and Decision Making 7(243): 243–256.
  • [2] Baldwin, J. (1979a). Advances in Fuzzy Set Theory and Applications, North-Holland, Amsterdam, pp. 93–115.
  • [3] Baldwin, J. (1979b). Fuzzy logic and fuzzy reasoning, International Journal of Man-Machine Studies 11(4): 465–480.
  • [4] Baldwin, J. (1979c). A new approach to approximate reasoning using a fuzzy logic, Fuzzy Sets and Systems 2(4): 309–325.
  • [5] Bellman, R. and Zadeh, L. (1977). Modern Uses of Multiple-Valued Logic. Episteme, Springer, Dordrecht, pp. 103–165.
  • [6] Cordon, O., Herrera, F. and Peregrin, A. (1997). Applicability of the fuzzy operators in the design of fuzzy logic controllers, Fuzzy Sets and Systems 86(1): 15–41.
  • [7] Czabanski, R., Jezewski, M. and Leski, J. (2017). Introduction to Fuzzy Systems, Springer, Cham, pp. 23–43.
  • [8] Czogała, E. and Kowalczyk, R. (1996). Investigation of selected fuzzy operations and implications for engineering, IEEE 5th International Conference Fuzzy Systems, New Orleans, USA, pp. 879–885.
  • [9] Czogała, E. and Łęski, J. (2000). Fuzzy and Neuro-Fuzzy Intelligent Systems, Physica, Springer-Verlag, Heidelberg.
  • [10] Czogała, E. and Łęski, J. (2001). On equivalence of approximate reasoning results using different interpretations of if-then rules, Fuzzy Sets and Systems 117(2): 279–296.
  • [11] Dubois, D. and Prade, H. (1999). Fuzzy sets in approximate reasoning. Part 1: Inference with possibility distribution, Fuzzy Sets and Systems 100(Supp. 1): 73–132.
  • [12] Dubois, D. and Prade, H. (1996). What are fuzzy rules and how to use them, Fuzzy Sets and Systems 84(2): 169–185.
  • [13] Grzegorzewski, P., Hryniewicz, O. and Romaniuk, M. (2020). Flexible resampling for fuzzy data, International Journal of Applied Mathematics and Computer Science 30(2): 281–297, DOI: 10.34768/amcs-2020-0022.
  • [14] Ho, C., Li, J. and Gwak, S. (2010). Research of a new fuzzy reasoning method by moving of fuzzy membership functions, 2010 International Symposium on Intelligence Information Processing and Trusted Computing, Huanggang, China, pp. 297–300.
  • [15] Izquierdo, S.S. and Izquierdo, L.R. (2018). Mamdani fuzzy systems for modelling and simulation: A critical assessment, Journal of Artificial Societies and Social Simulation 21(3): 2.
  • [16] Klir, G.J., Clair, U.S. and Yuan, B. (1997). Fuzzy Set Theory: Foundations and Applications, Prentice Hall, Upper Saddle River.
  • [17] Kudłacik, P. (2010). Advantages of an approximate reasoning based on a fuzzy truth value, Medical Informatics & Technologies 16: 125–132.
  • [18] Kudłacik, P. (2012). Performance evaluation of Baldwin’s fuzzy reasoning for large knowledge bases, Medical Informatics & Technologies 20: 29–38.
  • [19] Kudłacik, P. (2013). An analysis of using triangular truth function in fuzzy reasoning based on a fuzzy truth value, Medical Informatics & Technologies 22: 103–110.
  • [20] Kudłacik, P. and Łęski, J. (2021). Practical aspects of equivalence of Baldwin’s and Zadeh’s fuzzy inference, Journal of Intelligent & Fuzzy Systems 40(3): 4617–4636.
  • [21] Mamdani, E. and Assilan, S. (1975). An experiment in linguistic synthesis with a fuzzy logic controller, International Journal of Man-Machine Studies 20(2): 1–13.
  • [22] Mazandarani, M. and Xiu, L. (2020). Fractional fuzzy inference system: The new generation of fuzzy inference systems, IEEE Access 8: 126066–126082.
  • [23] Mizumoto, M. and Zimmermann, H.-J. (1982). Comparison of fuzzy reasoning methods, Fuzzy Sets and Systems 8(3): 253–283.
  • [24] Piegat, A. and Dobryakova, L. (2020). A decomposition approach to type 2 interval arithmetic, International Journal of Applied Mathematics and Computer Science 30(1): 185–201, DOI: 10.34768/amcs-2020-0015.
  • [25] Rutkowski, L. (2008). Computational Intelligence, Methods and Techniques, Springer, Berlin/Heidelberg.
  • [26] Tong, R.M. and Festathiou, J. (1982). A critical assessment of truth function modification and its use in approximate reasoning, Fuzzy Sets and Systems 7(1): 103–108.
  • [27] Ughetto, L., Dubois, D. and Prade, H. (1999). Implicative and conjunctive fuzzy rules—A tool for reasoning from knowledge and examples, 16th National Conference on Artificial Intelligence/11th Annual Conference on Innovative Applications of Artificial Intelligence, Orlando, USA, pp. 214–219.
  • [28] Yagger, R. (1996). On the interpretation of fuzzy if-then rules, Applied Intelligence 6(2): 141–151.
  • [29] Zadeh, L. (1973). Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems, Man and Cybernetics 3(1): 28–44.
  • [30] Zadeh, L. (1975). Fuzzy logic and approximate reasoning, Syntheses 30(3): 407–428.
  • [31] Zimmermann, H.-J. (1985). Fuzzy Set Theory and Its Applications, Springer, Dordrecht.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bb1f7f24-2bee-47d3-8132-fcf55394e626
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