Abstract
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.
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References
Zadeh, L.A.: The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Part I. Information Sciences. 8, 199–249 (1975a)
Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)
Zadeh, L.A.: Is there a Need for Fuzzy Logic? Information Sciences 13, 2751–2779 (2008)
Zadeh, L.A.: Toward a Generalized Theory of Uncertainty (GTU) – An outline. Information Sciences 172(1-2), 1–40 (2005)
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)
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)
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)
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)
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)
Ngan, S.-C.: A Type-2 Linguistic Set Theory and its Application to Multi-Criteria Decision Making. Computers & Industrial Engineering 64, 721–730 (2013)
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)
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)
Zhang, W.R., Zhang, L.: Yin-Yang Bipolar Logic and Bipolar Fuzzy Logic. Information Sciences 165, 265–287 (2004)
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)
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)
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)
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)
Xu, Z.S.: A Ranking Arithmetic for Fuzzy Mutual Complementary Judgment Matrices. Journal of Systems Engineering 16(4), 311–314 (2001)
Chen, C.T.: Extension of the TOPSIS for Group Decision Making under Fuzzy Environment. Fuzzy Sets and Systems 114(1), 1–9 (2000)
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)
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Zamri, N., Abdullah, L. (2014). A New Positive and Negative Linguistic Variable of Interval Triangular Type-2 Fuzzy Sets for MCDM. In: Herawan, T., Ghazali, R., Deris, M. (eds) Recent Advances on Soft Computing and Data Mining. Advances in Intelligent Systems and Computing, vol 287. Springer, Cham. https://doi.org/10.1007/978-3-319-07692-8_7
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DOI: https://doi.org/10.1007/978-3-319-07692-8_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07691-1
Online ISBN: 978-3-319-07692-8
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