A New Cotangent-based Entropy Measure and Application to Intuitionistic Fuzzy Multi-attribute Decision Making Model

Minglin Jiang

Abstract


Intuitionistic entropy measure is an important information measure to model the uncertain degree of an intuitionistic fuzzy set. The aim of this paper is to construct a new entropy measure of intuitionistic fuzzy sets,whichdevelops a new decision making method for intuitionistic fuzzy multiple attribute decision making(MADM) problems on the basis of compromise ratio method.Compromise ratio method simultaneously considers that the best alternative should be as close as possible to the positive ideal solution and as far away as possible from the negative ideal solution simultaneously,while the decision maker's subjective attitude is also included in the consideration. When the information of attribute weights is completely unknown or partly known, two weighting methods are developed on the basis of the new entropy measure. Finally, two application examples are given to illustrate the effectiveness and practicability of proposed method.


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References


AtanassovK.T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets & Systems, 20(1), 87-96.

AtanassovK.T. (1999). Intuitionistic Fuzzy Sets. New York: Physica-Verlag, Heidelberg.

BoranF.E., Akay D. (2014). A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition, Information Sciences, 255(28), 45–57.

Burillo P., Bustince H. (2001). Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems, 118(3), 305-316.

Bustince H., Burillo P. (1996). Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems, 79(3), 403-405.

Cheng H.D., Chen Y.H., Sun Y. (1999). A novel fuzzy entropy approach to image enhancement and thresholding. Signal Processing, 75(3), 277-301.

Chen S.M., Tan J.M. (1994).Handing multicriteria fuzzy decision-making problems based vague set theory. Fuzzy Sets and Systems, 67(2), 163-172.

De S.K., Sana S.S. (2015). Backlogging EOQ model for promotional effort and selling price sensitive demand- an intuitionistic fuzzy approach, Annals of Operations Research, 233(1),57-76.

GauW.L., BuehrerD.J. (1993). Vague sets. Systems IEEE Transactions on systems, Man & Cybernetics, 23(2), 610-614.

Herrera F., Herrera-Viedma E. (2000). Linguistic decision analysis: steps for solving decision problems under linguistic information, Fuzzy Sets & Systems, 115(1):67-82.

Joshi D., Kumar S. (2014). Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making, Egyptian Informatics Journal, 15(2),97-104.

Lee H.M., Chen C.M., Chen J.M., JouY.L. (2001). An efficient fuzzy classifier with feature selection based on fuzzy entropy. IEEE Transactions on Systems Man & Cybernetics Part B Cybernetics A Publication of the IEEE Systems Man & Cybernetics Society, 31(3),426-32.

Li D.F.(2005). Multiattribute decision making models and methods using intuitionistic fuzzy sets, Journal of Computer and System Sciences, 70(1), 73-85.

Li D.F., Ren H.P. (2015). Multi-attribute decision making method considering the amount and reliability of intuitionistic fuzzy information, Journal of Intelligent & Fuzzy Systems, 28(4),1877-1883.

Li H., Xie X. (2015). Gear fault pattern recognition based on kernel feature fuzzy clustering and fuzzy association entropy, Chinese Journal of Scientific Instrument, 36(4), 848-855.

Liang X., Wei C. (2013). An Atanassov’s intuitionistic fuzzy multi-attribute group decision making method based on entropy and similarity measure. International Journal of Machine Learning & Cybernetics, 5(3), 435-444.

Liu M.F., Ren H.P. (2015). A study of multi-attribute decision making based on a new intuitionistic fuzzy entropy measure, System Engineering Theory and Practice 35(11), 2909-2916.

Li Q., Zhao X., Lin R., Chen B.(2014). Relative entropy method for fuzzy multiple attribute decision making and its application to software quality evaluation, Journal of Intelligent & Fuzzy Systems, 26(4),1687-1693.

Liu M.F., Ren H.P. (2014). A new intuitionistic fuzzy entropy and application in multi-attribute decision making, Information, 5(4),587-601.

Mardani A., Jusoh A., ZavadskasE.K.(2015). Fuzzy multiple criteria decision-making techniques and applications-Two decades review from 1994 to 2014, Expert Systems with Applications, 42(8), 4126-4148.

Onar S.C., Oztaysi B., Kahraman C.(2014). Strategic decision selection using hesitant fuzzy TOPSIS and interval type-2 fuzzy AHP: A case study, International Journal of Computational Intelligence Systems, 7(5),1002-1021.

Shemshadi A., Shirazi H.,Toreihi M., TarokhM.J. (2011). A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting, Expert Systems with Applications, 38(10), 12160-12167.

Verma R., Sharma B.D. (2013). Exponential entropy on intuitionistic fuzzy sets, Kybernetika, 49(1),114-127.

Wei C.P., GaoZ.H., GuoT.T. (2012). An intuitionistic fuzzy entropy measure based on trigonometric function, Control and Decision, 27(4), 571-574.

Wu D., Mendel J.M.(2010). Computing with words for hierarchical decision making applied to evaluating a weapon system, IEEE Transactions on Fuzzy Systems, 18(3), 441-460.

Wu H.Y., TzengG.H., Chen Y.H. (2009). A fuzzy MCDM approach for evaluating bankingperformance based on Balanced Scorecard, Expert Systems with Applications, 36(6),10135–10147.

Wu J.Z., Zhang Q. (2011). Multicriteria decision making method based on intuitionistic fuzzy weighted entropy, Expert Systems with Applications, 38(1), 916-922.

Xu Z.S. (2007). Multi-person multi-attribute decision making models under intuitionistic fuzzy environment, Fuzzy Optimization Decision Making, 6(3), 221-236.

Xu Z.S. (2007). Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making, Fuzzy Optimization & Decision Making, 6(2),109-121.

Xu Z.S., Chen J. (2008). An overview of distance and similarity measures of intuitionistic fuzzy sets International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16(4), 529-555.

Xu Z.S., Liao H.C. (2014). Intuitionistic fuzzy analytic hierarchy process, IEEE Transactions on Fuzzy Systems, 22(4),749-761.

XuZ.S., Yager R.R.(2006). Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General Systems, 2006, 35(4):417-433.

Ye J. (2010). Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. European Journal of Operational Research, 205(1),202-204.

Ye J. (2010).Two effective measures of intuitionistic fuzzy ertropy, Computing, 87(1/2), 55-62.

Zadeh L.A. (1968). Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications, 23, 421–427.

Zhang Q.S., Jiang S.Y.(2008). A note on information entropy measure for vague sets. Information Sciences, 178, (21), 4184–4191.

Zhang X., Liu P., Wang Y. (2015). Multiple attribute group decision making methods based on intuitionistic fuzzy frank power aggregation operators, Journal of Intelligent & Fuzzy Systems, 29(5), 2235-2246.

Zhou T., Zhou Y. (2015). Fuzzy comprehensive evaluation of urban regeneration decision-making based on entropy weight method: Case study of yuzhong peninsula, China, Journal of Intelligent & Fuzzy Systems, 29(6), 2661-2668.

Zou X. (2012). Pattern recognition of surface electromyography signal based on multi-scale fuzzy entropy, Journal of Biomedical Engineering,29(29), 1184-1188.


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