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Ranking of fuzzy numbers is an important concept in the study of fuzzy set theory. In order to rank fuzzy numbers, one fuzzy number need to be compared with the others but often it is difficult to determine clearly which is larger or smaller. Numerous distance measures, similarity measures and uncertainty measures have been proposed in previous studies to rank fuzzy sets and extensions of fuzzy sets (type-2, Interval valued fuzzy sets, Intuitionistic fuzzy set (IFS) and generalisations) (Singh, 2013; Singh, 2014; Wei et al., 2011; Yang & Lin, 2009; Yu et al., 2019; Zeng & Guo, 2008). The applicability of different distance methods depends on various given concepts in various contexts. The concept of type-2 fuzzy set (T2FS) was introduced by Zadeh [3] as an extension of the type-1 fuzzy set (ordinary fuzzy set) (Zadeh, 1965). These sets are fuzzy sets whose membership grades themselves are as type-1 fuzzy sets which are characterized by primary, secondary membership functions and foot print of uncertainty(FOU); they are useful in situations where there is uncertainty in the membership function of a fuzzy set; hence they are useful in incorporating linguistic uncertainties (Zadeh, 1975). Mizumoto and Tanaka defined some basic properties of T2FS (1976). Equivalently overview of T2FS was presented by Mendel (2001). In theories and applications T2FS were used; but in most aspects due to complex and immense burdensome operations of the T2FS, the special cases of T2FS interval type-2 fuzzy sets (IT2FS) were used which contains a membership value from zero to one. A membership grade of a fuzzy set is a number from unit interval that assigns each element in the universe set to specify the proportion of belongingness to the set (Klir & Yuan, 1995). The proportion of non-belongingness is just automatically the complement of membership grade; unless the decision maker does not express the corresponding degree of non-membership grade (Kumar & Kaur, 2013). Thus, Atanassov introduced Intuitionistic fuzzy set (IF set) which is characterized by both membership function and non-membership function respectively (Attanassov, 1986). This idea which is a generalization of ordinary fuzzy set is useful when modelling real-life situations (Kumar & Kaur, 2013).
Decision making is a cognitive process generally used in industries, economy, innovation, medical, sustainable development and so on (Li & Liu, 2020; Samantra, 2012). Decision making involves the analysis of a finite set of alternatives described in terms of some evaluation criteria. However, it is difficult to assess the corresponding characteristics of a problem with precision and certainty due to the vagueness and complexity that exist in real life. Some researchers have used fuzzy sets, intuitionistic fuzzy (IF) sets, interval-valued IF sets, hesitant fuzzy information, to express evaluation information (Yu et al., 2019). Zadeh (1965) introduced fuzzy sets contributing to the field of Multi criteria decision making (MCDM) and later called Fuzzy multi criteria decision making (FMCDM) approach (Abdullah, 2013). Various researchers have applied the theory of T2FS, IFS (Wei et al., 2019), IVIFS (Wei et al., 2020) and IT2FS to the field of decision making problems (Jing, 2017; Kilic & Kaya, 2015; Lazim Abdullah, 2018; Li et al., 2020), ranking interval type-2 fuzzy set (Chen et al., 2012; Syafadhli et al., 2015), ranking Intuitionistic Fuzzy sets (Deng, 2010; Nehi, 2010), interval type-2 TOPSIS method (Chen & Lee, 2010; Lee & Chen, 2008), OWA operator(Zhou et al., 2008; Zhou et al., 2010), similarity and distance measures and several others (Wu & Mendel, 2009) but a very few studies are observed in decision making under T2IFS.