Advertisement

The Algebraic Properties of Linguistic Value “Truth” and Its Reasoning

  • Zheng Pei
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4529)

Abstract

From logic and algebra point of view, Computing with words is discussed in this paper. By analyzing the semantically ordering relation of linguistic variable Truth, orderings on linguistic hedges H and atomic evaluating syntagm Tr = {true, false} are obtained, respectively. Let H be finite chain, then Lukasiewicz product algebra of T = H×Tr of Truth is obtained, and term-set T(X) of Truth is embedded into an algebra Γ of type Δ = { ∨ , ∧ , ′,→ L }. In some cases, Γ can be applied in linguistic decision directly, also as truth domain of logic statements. Different with other truth domain, here truth values are linguistic terms rather than numerals (or symbolic).

Keywords

Fuzzy Logic Linguistic Term Algebraic Property Information Granulation Implication Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Zadeh, L.A.: Fuzzy logic = computing with words. Fuzzy Systems 4, 103–111 (1996)CrossRefGoogle Scholar
  2. 2.
    Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in houman reasoning and fuzzy logic. Fuzzy Sets and Systems 90, 103–111 (1997)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Novák, V., Perfilieva, I., Močkoř, J.: Mathematical principles of fuzzy logic. Kluwer Academic Publishers, Dordrecht (1999)zbMATHGoogle Scholar
  4. 4.
    Novák, V.: Antonyms and linguistic quantifiers in fuzzy logic. Fuzzy Sets and Systems 124, 335–351 (2001)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Dvořák, A., Novák, V.: Fromal theories and linguistic descriptions. Fuzzy Sets and Systems 143, 169–188 (2004)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Wang, P.P.: Computing with words. John Wiley and Sons, Chichester (2001)Google Scholar
  7. 7.
    Trillas, E.: On the use of words and fuzzy sets. Information Sciences 176, 1463–1487 (2006)CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Herrera, F., Herrera-Viedma, E.: Aggregation operators for linguistic weighted information. IEEE Trans. System, Man, Cybernet. - Part A: Systems Humans 27, 646–656 (1997)CrossRefGoogle Scholar
  9. 9.
    Herrera, F., Lopez, E., Rodriguez, M.A.: A linguistic decision model for promotion mix management solved with genetic algorithms. Fuzzy Sets and Systems 131, 47–61 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Pei, Z., Du, Y., Yi, L., Xu, Y.: Obtaining a complex linguistic data summaries from database based on a new linguistic aggregation operator. In: Cabestany, J., Prieto, A.G., Sandoval, F. (eds.) IWANN 2005. LNCS, vol. 3512, pp. 771–778. Springer, Heidelberg (2005)Google Scholar
  11. 11.
    Ho, N.C., Khang, T.D., Huynh, V.N.: An algebraic approach to linguistic hedges in Zadeh’s fuzzy logic. Fuzzy Sets and Systems 129, 229–254 (2002)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Zheng Pei
    • 1
  1. 1.School of Mathematics & Computer, Xihua University, Chengdu, Sichuan, 610039China

Personalised recommendations