A Plea for the Usefulness of the Deductive Interpretation of Fuzzy Rules in Engineering Applications

This contribution is intended as a position paper that favors the viewpoint that inference based on deductive rules (i.e., the rules are interpreted using fuzzy implication) can indeed be considered as a valuable inference scheme in real-world applications. For this purpose, we highlight the basic concepts behind the most common fuzzy inference schemes and demonstrate their interpretation by means of illustrative examples. We conclude that, under some reasonable conditions, deductive inference is able to compete with or even outperform the well-known Mamdani-Assilian inference.

[1]  Robert Fullér,et al.  Introduction to neuro-fuzzy systems , 1999, Advances in soft computing.

[2]  Rajkumar Roy,et al.  Advances in Soft Computing , 2018, Lecture Notes in Computer Science.

[3]  Henri Prade,et al.  What are fuzzy rules and how to use them , 1996, Fuzzy Sets Syst..

[4]  J. Mendel.  Fuzzy logic systems for engineering: a tutorial , 1995, Proc. IEEE.

[5]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[6]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[7]  Petr Hájek,et al.  A Note on Fuzzy Inference as Deduction , 1999 .

[8]  J. A. Goguen,et al.  The logic of inexact concepts , 1969, Synthese.

[9]  Vilém Novák,et al.  Linguistically oriented fuzzy logic control and its design , 1995, Int. J. Approx. Reason..

[10]  Frank Klawonn,et al.  Foundations of fuzzy systems , 1994 .

[11]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  D. Coufal.  Radial implicative fuzzy inference systems , 2003 .

[13]  J. Baldwin,et al.  MODELLING CONTROLLERS USING FUZZY RELATIONS , 1980 .

[14]  Frank Klawonn,et al.  The relation between inference and interpolation in the framework of fuzzy systems , 1996, Fuzzy Sets Syst..

[15]  Radko Mesiar,et al.  Triangular Norms , 2000, Trends in Logic.

[16]  Wjm Walter Kickert,et al.  ANALYSIS OF A FUZZY LOGIC CONTROLLER , 1978 .

[17]  Vilém Novák,et al.  Logical structure of fuzzy IF-THEN rules , 2006, Fuzzy Sets Syst..

[18]  David Coufal.  Coherence of Radial Implicative Fuzzy Systems , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[19]  P. Martin Larsen,et al.  Industrial applications of fuzzy logic control , 1980 .

[20]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[21]  Jan Pavelka,et al.  On Fuzzy Logic I Many-valued rules of inference , 1979, Math. Log. Q..

[22]  Hashim Habiballa,et al.  The concept of LFLC 2000 - its specificity, realization and power of applications , 2003, Comput. Ind..

[23]  V. Novák,et al.  Mathematical Principles of Fuzzy Logic , 1999 .

[24]  E. H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Man Mach. Stud..

[25]  Angus Macintyre,et al.  Trends in Logic , 2001 .

[26]  Didier Dubois,et al.  Checking the coherence and redundancy of fuzzy knowledge bases , 1997, IEEE Trans. Fuzzy Syst..

[27]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[28]  H. Zimmermann,et al.  Comparison of fuzzy reasoning methods , 1982 .

[29]  Didier Dubois,et al.  Fuzzy Logic, Control Engineering and Artificial Intelligence , 1999 .