An improved ranking method for comparing trapezoidal intuitionistic fuzzy numbers and its applications to multicriteria decision making

Problems with qualitative, quantitative and uncertain information can be modelled better using trapezoidal intutionistic fuzzy numbers (TrIFNs) than fuzzy numbers. Due to the partial ordering of TrIFNs, many ranking methods are available in the literature for comparing fuzzy and intuitionistic fuzzy numbers (Li in Comput Math Appl 60:1557–1570, 2010; Li and Yang in Math Comput Appl 20(1):25–38, 2015; De and Das in 12th international conference on intelligent systems design and applications (ISDA), Kochi, India, 27–29 Nov, IEEE, 2012; Dubey and Mehara in Proceedings of the seventh conference of the European society for fuzzy logic and technology, pp 563–569, 2011; Nehi in Int J Fuzzy Syst 12:80–86, 2010; Fangwei and Xu in Soft Comput, 2016. doi:10.​1007/​s00500-015-1932-x; Jun in Expert Syst Appl 38:11730–11734, 2011, Int J Gen Syst 41(7):729–739, 2009, Group Decis Negot 21:519–530, 2012; Nayagam and Geetha in Appl Soft Comput 11(4):3368–3372, 2011; Nayagam et al. in Expert Syst Appl 38(3):1464–1467, 2011, Soft Comput, 2016. doi:10.​1007/​s00500-016-2249-0; Sahin in Soft Comput 20(7):2557–2563, 2016; Shu-Ping and Dong in Appl Soft Comput 29:153–168, 2015; Zeng et al. in Sci World J 1–8, 2014; Ye in Expert Syst Appl 36:6899–6902, 2009; Zhang and Yu in Knowl Based Syst 30:115–120, 2012). In order to overcome the shortcomings and limitations of the existing methods, a new method for comparing TrIFNs based on the concept of improved value index and improved ambiguity index is introduced, and the significance of the proposed method is illustrated using numerical examples. Further to show the applicability of the proposed method, a new algorithm for solving multicriteria decision-making problem is established.