A New Positive and Negative Linguistic Variable of Interval Triangular Type-2 Fuzzy Sets for MCDM

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 287)


Fuzzy linguistic variable in decision making field has received significant attention from researchers in many areas. However, the existed research is given attention only in one side rather than two sides. Therefore, the aim of this paper is to introduce a new linguistic variable which considers both sides, positive and negative sides for symmetrical interval triangular type-2 fuzzy set (T2 FS). This new linguistic variable is developed in line with the interval type-2 fuzzy TOPSIS (IT2 FTOPSIS) method. Besides, a ranking value for aggregation process is modified to capture both positive and negative aspect for triangular. Then, this new method is tested using two illustrative examples. The results show that the new method is highly beneficial in terms of applicability and offers a new dimension to problem solving technique for the type-2 fuzzy group decision-making environment.


Interval type-2 fuzzy sets interval type-2 fuzzy TOPSIS 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zadeh, L.A.: The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Part I. Information Sciences. 8, 199–249 (1975a)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Zadeh, L.A.: Is there a Need for Fuzzy Logic? Information Sciences 13, 2751–2779 (2008)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Zadeh, L.A.: Toward a Generalized Theory of Uncertainty (GTU) – An outline. Information Sciences 172(1-2), 1–40 (2005)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Cheng, C.-H., Yang, K.-L., Hwang, C.-L.: Theory and Methodology Evaluating Attack Helicopters by AHP based on Linguistic Variable Weight. European Journal of Operational Research 116, 423–435 (1999)CrossRefMATHGoogle Scholar
  6. 6.
    Doukas, H.C., Andreas, B.M., Psarras, J.E.: Multi-Criteria Decision Aid for the Formulation of Sustainable Technological Energy Priorities using Linguistic Variables. European Journal of Operational Research 182, 844–855 (2007)CrossRefMATHGoogle Scholar
  7. 7.
    Wu, D., Mendel, J.M.: A Vector Similarity Measure for Linguistic Approximation: Interval Type-2 and Type-1 Fuzzy Sets. Information Sciences 178, 381–402 (2008)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Zhou, S.-M., Chiclana, F., John, R.I., Garibaldi, J.M.: Type-1 OWA Operators for Aggregating Uncertain Information with Uncertain Weights Induced by Type-2 Linguistic Quantifiers. Fuzzy Sets and Systems 159, 3281–3296 (2008)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Chen, S.-M., Lee, L.-W.: Fuzzy Multiple Attributes Group Decision-Making based on the Ranking Values and the Arithmetic Operations of Interval Type-2 Fuzzy Sets. Expert Systems with Applications 37, 824–833 (2010a)CrossRefGoogle Scholar
  10. 10.
    Ngan, S.-C.: A Type-2 Linguistic Set Theory and its Application to Multi-Criteria Decision Making. Computers & Industrial Engineering 64, 721–730 (2013)CrossRefGoogle Scholar
  11. 11.
    Zhang, Z., Zhang, S.: A Novel Approach to Multi Attribute Group Decision Making based on Trapezoidal Interval Type-2 Fuzzy Soft Sets. Applied Mathematical Modelling 37, 4948–4971 (2013)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Imran, C.T., Syibrah, M.N., Mohd Lazim, A.: New Condition for Conflicting Bifuzzy Sets based on Intuitionistic Evaluation. World Academy of Science, Engineering and Technology 19, 451–455 (2008)Google Scholar
  13. 13.
    Zhang, W.R., Zhang, L.: Yin-Yang Bipolar Logic and Bipolar Fuzzy Logic. Information Sciences 165, 265–287 (2004)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Nur Syibrah, M.N., Mohd Lazim, A., Che Mohd Imran, C.T., Abu Osman, M.T.: New Fuzzy Preference Relations and its Application in Group Decision Making. World Academy of Science, Engineering and Technology 54, 690–695 (2009)Google Scholar
  15. 15.
    Zhang, S.F., Liu, S.Y.: A GRA-Based Intuitionistic Fuzzy Multi-Criteria Group Decision Making Method for Personnel Selection. Experts Systems with Application 38, 11401–11405 (2011)CrossRefGoogle Scholar
  16. 16.
    Zamali, T., Abu Osman, M.T., Mohd Lazim, A.: Equilibrium Linguistic Computation Method for Fuzzy Group Decision-Making. Malaysian Journal of Mathematical Sciences 6(2), 225–242 (2012)MathSciNetGoogle Scholar
  17. 17.
    Zamali, T., Lazim, M.A., Abu Osman, M.T.: Sustainable Decision-Making Model for Municipal Solid-Waste Management: Bifuzzy Approach. Journal of Sustainability Science and Management 7(1), 56–68 (2012)Google Scholar
  18. 18.
    Xu, Z.S.: A Ranking Arithmetic for Fuzzy Mutual Complementary Judgment Matrices. Journal of Systems Engineering 16(4), 311–314 (2001)Google Scholar
  19. 19.
    Chen, C.T.: Extension of the TOPSIS for Group Decision Making under Fuzzy Environment. Fuzzy Sets and Systems 114(1), 1–9 (2000)CrossRefMATHGoogle Scholar
  20. 20.
    Chen, S.-M., Lee, L.-W.: Fuzzy Multiple Attributes Group Decision-Making based on the Interval Type-2 TOPSIS Method. Journal of Expert Systems with Application 37, 2790–2798 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.School of Informatics and Applied MathematicsUniversity Malaysia TerengganuKuala TerengganuMalaysia

Personalised recommendations