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Top1. Introduction
The concept of fuzzy set was introduced by Zadeh (Zadeh, 1965) and it dealt with imprecision, vagueness in real life situations. In the year 1970, Bellman and Zadeh (Bellman & Zadeh, 1970) introduced the concept of decision making problems involving uncertainty. The concept of intuitionistic fuzzy sets (IFSs) was introduced by Atanassov (Atanassov, 1986) in1986 by describing the objective world from three aspects of support, opposition and neutrality, respectively and thus have been widely studied and applied by many researchers (Fei et al., 2018; Zhang et al., 2018). Also, many researchers have given more attention to interval valued fuzzy sets (IVFSs) (Turksen, 1986; Gorzalczany, 1987), interval valued intuitionistic fuzzy sets (IVIFSs) (Atanassov & Gargov, 1987; Wei et al., 2019), which are all the generalization of the fuzzy set proposed by Zadeh (Zadeh, 1965) and applied them in several decision making problems. However, the fuzzy set takes only a membership function and the degree of non-membership function which is just a compliment of the degree of membership function. There may be a situation where the sum of the membership function and non-membership function is greater than one. Thus orthopair fuzzy sets have been introduced in which the membership grades of an element
are pairs of values in the unit interval,
, one of which indicates support of membership in the fuzzy set and other indicates support against membership in the fuzzy set. For example, Atanassov’s classical intuitionistic fuzzy sets (Atanassov, 1986; Atanassov, 2012; Atanassov et al., 2013) and Atanassov’s second kind of intuitionistic fuzzy sets (Atanassov, 1983; Atanassov, 2016). Recently, Yager (Yager, 2013; Yager, 2014) introduced another orthopair of fuzzy set, known as Pythagorean fuzzy set (PFS), where the square sum of the support of membership and support against membership value is equal to or less than one. Also, many researchers have paid great attention to interval valued Pythagorean fuzzy sets (IVPFSs) (Garg, 2017; Garg, 2018), which is the generalization of the Pythagorean fuzzy sets (PFSs) set proposed by Yager and applied them in several decision making problems. PFSs and IVPFSs have attracted the attention of many researchers within a short period of time. There are several methods in the field of PFS to solve real-life multi-criteria, decision-making problems viz. extension of TOPSIS (Zhang & Xu, 2014), similarity measure (Zhang, 2016), alternative queuing method (Gou et al., 2016), extended TODIM methods (Geng et al., 2017), Bonferroni mean (Jing et al., 2017), improved score function (Garg, 2017; Geng et al., 2017) and many others. Several researchers have also proposed real-life applications under Pythagorean fuzzy environment. For more details one may mention the works of Li et al. (Li et al., 2018), Zhou et al. (Zhou et al., 2018), Bolturk (Boltruk, 2018), Qin (Qin, 2018), Wan et al. (Wan et al., 2018), Lin et al. (Lin et al., 2018) and Chen (Chen, 2018). But, if orthopair fuzzy set as <0.9, 0.6>, where 0.9 is the support of the membership of certain criteria of a parameter and 0.6 is the support against membership then it does not follow the condition of IFS as well as PFS. However, the cubic sum of the support of membership and support against membership degrees is equal to or less than one. And in this situation Senapati and Yager (Senapati & Yager, 2019; Senapati & Yager, 2020) very recently introduced Fermatean Fuzzy set (FFS). They also showed that FFSs have more uncertain than IFSs and PFSs and are capable of handling higher level of uncertainties (Senapati & Yager, 2019) and solved MCDM problem. MCDM (Ye, 2009; Yu et al., 2018) is a branch of Operations Research (OR) having a comparatively short history of near about five decades. It is being successfully used in the field of information science, banking sector, industries etc. it is also be applied for making decision in our daily life problems like selection a flat/house to purchase, buying a new car or buying electronic gadgets such as smart phone, laptop, smart watch etc., selection of a bride and/or groom and many others.