Introducing Similarity Relations in a Framework for Modelling Real-World Fuzzy Knowledge

  • Víctor Pablos-Ceruelo
  • Susana Muñoz-Hernández
Part of the Communications in Computer and Information Science book series (CCIS, volume 444)


There is no need for justifying the use of fuzzy logic (FL) to model the real-world knowledge. Bi-valued logic cannot conclude if a real-world sentence like “the restaurant is close to the city center” is true or false because it is neither true nor false. Letting apart paradoxes’ sentences, there are sentences (as the previous one) that are not true nor false but true up to some degree of truth or true at least to some degree of truth. In order to represent the truth or falsity of such sentences we need FL.

Similarity is a relation between real-world concepts. As in the representation of the truth of the first sentence, the representation of the similarity between two (fuzzy or not) concepts can be true, false or true up to (or at least to) some degree. We present syntactic constructions (and their semantics) for modelling such relation between concepts. The interest is in, for example, obtaining “spanish food restaurants” when asking for “mediterranean food restaurants” (only if the similarity between spanish and mediterranean food is explicitly stated in the program file). We hope this allows to represent in a better way the real-world knowledge, specially the concepts that are defined just by their similarity relations to some other concepts.


fuzzy logic framework similarity relations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baldwin, J.F., Martin, T.P., Pilsworth, B.W.: Fril-Fuzzy and Evidential Reasoning in Artificial Intelligence. John Wiley & Sons, Inc., New York (1995)Google Scholar
  2. 2.
    Bobillo, F., Straccia, U.: fuzzydl: An expressive fuzzy description logic reasoner. In: 2008 International Conference on Fuzzy Systems (FUZZ 2008), pp. 923–930. IEEE Computer Society (2008)Google Scholar
  3. 3.
    Dubois, D., Prade, H.: Comparison of two fuzzy set-based logics: similarity logic and possibilistic logic. In: Proceedings of 1995 IEEE Int. Fuzzy Systems, International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium, vol. 3, pp. 1219–1226 (1995)Google Scholar
  4. 4.
    Esteva, F., Garcia, P., Godo, L., Ruspini, E., Valverde, L.: On similarity logic and the generalized modus ponens. In: Proceedings of the Third IEEE Conference on Computational Intelligence, Fuzzy Systems, IEEE World Congress on Computational Intelligence, vol. 2, pp. 1423–1427 (1994)Google Scholar
  5. 5.
    Godo, L., Rodriguez, R.O.: A fuzzy modal logic for similarity reasoning. In: Cai, K.-Y., Chen, G., Ying, M. (eds.) Fuzzy Logic And Soft Computing. Kluwer Academic (1999)Google Scholar
  6. 6.
    Guadarrama, S., Muñoz-Hernández, S., Vaucheret, C.: Fuzzy prolog: a new approach using soft constraints propagation. Fuzzy Sets and Systems 144(1), 127–150 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Ishizuka, M., Kanai, N.: Prolog-elf incorporating fuzzy logic. In: IJCAI 1985: Proceedings of the 9th International Joint Conference on Artificial Intelligence, pp. 701–703. Morgan Kaufmann Publishers Inc., San Francisco (1985)Google Scholar
  8. 8.
    Li, D., Liu, D.: A fuzzy Prolog database system. John Wiley & Sons, Inc., New York (1990)Google Scholar
  9. 9.
    Medina, J., Ojeda-Aciego, M., Vojtáš, P.: A completeness theorem for multi-adjoint logic programming. In: FUZZ-IEEE, pp. 1031–1034 (2001)Google Scholar
  10. 10.
    Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Multi-adjoint logic programming with continuous semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 351–364. Springer, Heidelberg (2001)Google Scholar
  11. 11.
    Medina, J., Ojeda-Aciego, M., Vojtáš, P.: A procedural semantics for multi-adjoint logic programming. In: Brazdil, P., Jorge, A. (eds.) EPIA 2001. LNCS (LNAI), vol. 2258, pp. 290–297. Springer, Heidelberg (2001)Google Scholar
  12. 12.
    Medina, J., Ojeda-Aciego, M., Vojtáš, P.: A multi-adjoint approach to similarity-based unification. Electronic Notes in Theoretical Computer Science 66(5), 70–85 (2002), UNCL’2002, Unification in Non-Classical Logics (ICALP 2002 Satellite Workshop)Google Scholar
  13. 13.
    Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Similarity-based unification: a multi-adjoint approach. Fuzzy Sets and Systems 146(1), 43–62 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Moreno, J.M., Ojeda-Aciego, M.: On first-order multi-adjoint logic programming. In: 11th Spanish Congress on Fuzzy Logic and Technology (2002)Google Scholar
  15. 15.
    Morcillo, P.J., Moreno, G.: Floper, a fuzzy logic programming environment for research. In: Fundación Universidad de Oviedo (ed.) Proceedings of VIII Jornadas sobre Programación y Lenguajes (PROLE 2008), Gijón, Spain, pp. 259–263 (october 2008)Google Scholar
  16. 16.
    Muñoz-Hernández, S., Pablos-Ceruelo, V., Strass, H.: Rfuzzy: Syntax, semantics and implementation details of a simple and expressive fuzzy tool over prolog. Information Sciences 181(10), 1951–1970 (2011), Special Issue on Information Engineering Applications Based on LatticesGoogle Scholar
  17. 17.
    Pablos-Ceruelo, V., Muñoz-Hernández, S.: Introducing priorities in rfuzzy: Syntax and semantics. In: CMMSE 2011: Proceedings of the 11th International Conference on Mathematical Methods in Science and Engineering, Benidorm, Alicante, Spain, vol. 3, pp. 918–929 (June 2011)Google Scholar
  18. 18.
    Pablos-Ceruelo, V., Muñoz-Hernández, S.: Getting answers to fuzzy and flexible searches by easy modelling of real-world knowledge. In: FCTA 2013: Proceedings of the 5th International Conference on Fuzzy Computation Theory and Applications (2013)Google Scholar
  19. 19.
    Vaucheret, C., Guadarrama, S., Muñoz-Hernández, S.: Fuzzy prolog: A simple general implementation using CLP(R). In: Baaz, M., Voronkov, A. (eds.) LPAR 2002. LNCS (LNAI), vol. 2514, pp. 450–464. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Vojtáš, P.: Fuzzy logic programming. Fuzzy Sets and Systems 124(3), 361–370 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Wang, J.-B., Xu, Z.-Q., Wang, N.-C.: A fuzzy logic with similarity. In: Proceedings of the 2002 International Conference on Machine Learning and Cybernetics, vol. 3, pp. 1178–1183 (2002)Google Scholar
  22. 22.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Víctor Pablos-Ceruelo
    • 1
  • Susana Muñoz-Hernández
    • 1
  1. 1.The Babel Research Group, Facultad de InformáticaUniversidad Politécnica de MadridSpain

Personalised recommendations