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International Conference on Conceptual Structures

ICCS 2019: Graph-Based Representation and Reasoning pp 204–217Cite as

The Compositional Rule of Inference Under the Composition Max-Product

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11530))

Abstract

Approximate reasoning is used in Fuzzy Inference Systems to handle imprecise knowledge. It aims to be close as possible to human reasoning. The main approach of approximate reasoning is the compositional rule of inference, which generates different methods by varying its parameters: a t-norm and an implication. In most cases, combinations of t-norms and implications do not fit human intuitions. Based on these methods, we suggest the use of the product t-norm in the compositional rule of inference. We combine this t-norm with different known implications. We then study these combinations and check if they give reasonable consequences.

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References

  1. Bandemer, H., Gottwald, S.: Fuzzy Sets, Fuzzy Logic, Fuzzy Methods. Wiley, Chichester (1995)

    MATH  Google Scholar 

  2. Fukami, S., Mizumoto, M., Tanaka, K.: Some considerations on fuzzy conditional inference. Fuzzy Sets Syst. 4(3), 243–273 (1980)

    Article  MathSciNet  Google Scholar 

  3. Mizumoto, M.: Fuzzy inference using max-\({\wedge }\) composition in the compositional rule of inference. Approx. Reason. Decis. Anal., 67–76 (1982)

    Google Scholar 

  4. Mizumoto, M.: Fuzzy conditional inference under max-\(\odot \) composition. Inf. Sci. 27(3), 183–209 (1982)

    Article  MathSciNet  Google Scholar 

  5. Mizumoto, M., Zimmermann, H.J.: Comparison of fuzzy reasoning methods. Fuzzy Sets Syst. 8(3), 253–283 (1982)

    Article  MathSciNet  Google Scholar 

  6. Nguyen, T., Khosravi, A., Creighton, D., Nahavandi, S.: Classification of healthcare data using genetic fuzzy logic system and wavelets. Expert. Syst. Appl. 42(4), 2184–2197 (2014)

    Article  Google Scholar 

  7. Sahu, S., Kumar, P.B., Parhi, D.R.: Intellegent hybrid fuzzy logic system for damage detection of beam-like structural elements. J. Theor. Appl. Mech. 55(2), 509–521 (2017)

    Article  Google Scholar 

  8. Tick, J., Fodor, J.: Fuzzy implications and inference processes. In: Computational Cybernetics, pp. 105–109 (2005)

    Google Scholar 

  9. Zadeh, L.A.: Fuzzy sets. Inf. Control. 8(3), 338–353 (1965)

    Article  Google Scholar 

  10. Zadeh, L.A.: A fuzzy-set-theoretic interpretation of linguistic hedges. J. Cybern. 2(3), 4–34 (1972)

    Article  MathSciNet  Google Scholar 

  11. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-III. Inf. Sci. 9(1), 43–80 (1975)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. National School of Computer Sciences, COSMOS Research Laboratory, University of Manouba, 2010, Manouba, Tunisia

    Nourelhouda Zerarka, Saoussen Bel Hadj Kacem & Moncef Tagina

  2. Faculty of Economic Sciences and Management of Nabeul, University of Carthage, 8000, Nabeul, Tunisia

    Saoussen Bel Hadj Kacem

Authors
  1. Nourelhouda Zerarka
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  2. Saoussen Bel Hadj Kacem
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  3. Moncef Tagina
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Corresponding author

Correspondence to Nourelhouda Zerarka .

Editor information

Editors and Affiliations

  1. Philipps-Universität Marburg, Marburg, Germany

    Dominik Endres

  2. FIZ Karlsruhe – Leibniz Institute for Information Infrastructure, Eggenstein-Leopoldshafen, Germany

    Mehwish Alam

  3. Babes-Bolyai University, Cluj-Napoca, Romania

    Diana Şotropa

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Zerarka, N., Bel Hadj Kacem, S., Tagina, M. (2019). The Compositional Rule of Inference Under the Composition Max-Product. In: Endres, D., Alam, M., Şotropa, D. (eds) Graph-Based Representation and Reasoning. ICCS 2019. Lecture Notes in Computer Science(), vol 11530. Springer, Cham. https://doi.org/10.1007/978-3-030-23182-8_15

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  • DOI: https://doi.org/10.1007/978-3-030-23182-8_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-23181-1

  • Online ISBN: 978-3-030-23182-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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