Implication Operator of Linguistic Truth-Valued Intuitionistic Fuzzy Lattice

  • Chunying Guo
  • Fengmei Zhang
  • Li Zou
  • Kaiqi Zou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6401)


We construct linguistic truth-valued intuitionistic fuzzy lattice b based on linguistic truth-valued lattice implication algebra to deal with linguistic truth-valued. The proposed system can better express both comparable and incomparable information. Also it can deal with both positive and negative evidences which are represented by linguistic truth values at the same time during information processing system. This paper discusses the intuitionistic fuzzy implication operator on the linguistic truth-valued intuitionistic fuzzy lattice and its properties.


Linguistic truth-valued lattice implication algebra Linguistic truth-valued intuitionistic fuzzy lattice Intuitionistic fuzzy implication 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Herrera, F., Martnez, L.: The 2-Tuple linguistic computational model. Advantages of its linguistic description, accuracy and consistency. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9, 33048 (2001)Google Scholar
  2. 2.
    Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems 15(11), 1179–1187 (2007)CrossRefGoogle Scholar
  3. 3.
    Huynh, V.N., Ho, T.B., Nakamori, Y.: A Parametric Representation of Linguistic Hedges in Zadeh’s Fuzzy Logic. International Journal of Approximate Reasoning 30, 203–223 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Ho, N.C.: A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms and hedges. Fuzzy Sets and Systems 158, 436–451 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Xu, Y., Liu, J., Ruan, D., Lee, T.T.: On the consistency of rule bases based on lattice-valued first-order logic LF(X). International Journal of Intelligent Systems 21, 399–424 (2006)zbMATHCrossRefGoogle Scholar
  6. 6.
    Atanassov, K.T.: Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade’s paper Terminological difficulties in fuzzy set theory the case of ‘Intuitionistic Fuzzy Sets’. Fuzzy Sets and Systems 156, 496–499 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Zadeh, L.A.: The comcept of linguistic variable and its application to approximate reasoning (I)(II). Information Sciences 8, 199–249, 310–357 (1975)Google Scholar
  8. 8.
    Zou, L., Ruan, D., Pei, Z., Xu, Y.: A linguistic truth-valued reasoning approach in decision making with incomparable information. Journal of Intelligent and Fuzzy Systems 19(4-5), 335–343 (2008)zbMATHGoogle Scholar
  9. 9.
    Zou, L., Pei, Z., Liu, X., Xu, Y.: Semantic of Linguistic Truth-Valued Intuitionistic Fuzzy Proposition Calculus. International Journal of Innovative Computing, Information and Control 5(12), 4745–4752 (2009)Google Scholar
  10. 10.
    Zou, L., Liu, X., Wu, Z., Xu, Y.: A Uniform Approach of Linguistic Truth Values in Sensor Evaluation. International Journal of Fuzzy Optimization and Decision Making 7(4), 387–397 (2008)zbMATHCrossRefGoogle Scholar
  11. 11.
    Zou, L., Ma, J., Xu, Y.: A Framework of Linguistic Truth-valued Propositional Logic Based on Lattice Implication Algebra. In: Proceedings of 2006 IEEE International Conference on Granular Computing, pp. 574–577 (2006)Google Scholar
  12. 12.
    Wang, D.G., Song, W.Y., Li, H.X.: Unified forms of Fuzzy Similarity Inference Method for Fuzzy Reasoning and Fuzzy Systems. International Journal of Innovative Computing Information and Control 4(10), 2285–2294 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Chunying Guo
    • 1
  • Fengmei Zhang
    • 2
  • Li Zou
    • 2
  • Kaiqi Zou
    • 3
  1. 1.Vocational CollegeLiaoning Technical UniversityFu XinP.R. China
  2. 2.School of Computer and Information TechnologyLiaoning Normal UniversityDalianP.R. China
  3. 3.College of Information Engineering, University Key Lab of Information Science and EngineeringDalian UniversityDalianChina

Personalised recommendations