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With the gradual improvement of people’s living standards, more and more people buy houses for life in a certain city either for work or for education of children. But it is difficult for homebuyers to choose an appropriate house from the house resources by the real estate agents because they need to simultaneously consider factors such as price, value, size, and location. Some of the factors might be even contradictory. Therefore, house selection is a multi-criteria decision-making problem (MCDM).
MCDM approaches can be suitable tools to deal with the house selection problem. In the decades, researchers have proposed various methods regarding MCDM problems in fuzzy environments. For example, Prabhu and Ilangkumaran (2019) and Ahmet (2021) presented work on the analytic hierarchy process (AHP). Li (2010) and Li and Nan (2011) presented research on the technique for order preference by similarity to idea solution (TOPSIS). Other research was conducted on areas such as the relative ratio (RR) method (Li, 2009), fuzzy linear programming technique for multidimensional analysis of preference (FLINMAP) method (Li & Sun, 2007), linear programming (LP) (Yu et al., 2019), nonlinear programming approach (Li, 2011; Li & Liu, 2015), and game theory (Ye & Li, 2021; Liang et al., 2023).
The traditional AHP may not reflect the opinions of decision-makers. Therefore, new versions of AHP with fuzzy sets have been proposed. Zadeh (1965) proposed the fuzzy theory as an extension of the classical sets, and Atanassov (1986) proposed intuitionistic fuzzy sets (IFSs) as an extension of fuzzy sets. Atanassov (1989) also proposed interval-valued intuitionistic fuzzy sets (IVIFSs). However, the sum of the membership and non-membership of IVIFSs is equal to or less than one, and which may not be in line with people’s way of thinking. To address this problem, Yager (2013) proposed Pythagorean fuzzy sets (PFSs) as an extension of the IFSs. Because PFSs allows the sum of membership and non-membership to exceed one, and the sum of squares to not exceed one, Pythagorean fuzzy sets theory are more powerful and flexible in solving problems involving uncertainty. Interval-valued Pythagorean fuzzy sets (IVPFSs) (Zhang, 2016), a generalization of PFSs, emerged as an effective tool to model the uncertain and imprecise information in the real-life decision evaluation process, and this method can be considered when decision-makers fail to employ crisp values, but use interval values to express their evaluation information. In the proposed method, linguistic variables of interval-valued Pythagorean fuzzy numbers (IVPFNs) are used in the evaluations by the homebuyers and experts.
Hwang (1981) first proposed the TOPSIS method. Regarding the uncertainty in real situations, many studies on fuzzy extensions have been completed to enrich the theory of TOPSIS method. Different versions of TOPSIS based on fuzzy sets have been developed for considering uncertainties and vagueness in MCDM problems, such as the fuzzy TOPSIS (Dwivedi et al., 2018), the weighted fuzzy TOPSIS (Prabhu & Ilangkumaran, 2019), the intuitionistic fuzzy TOPSIS (Li & Nan, 2011), the interval-valued intuitionistic fuzzy TOPSIS (Li, 2010), and the Pythagorean fuzzy TOPSIS (Zhang & Xu, 2014). Although many studies state that methods of TOPSIS with different fuzzy sets have been applied widely in various fields, relatively little attention has been paid to the extended TOPSIS dealing with house selection problems under complex uncertainty based on IVPFSs. From the aforementioned studies, we were inspired to use weighted fuzzy TOPSIS (FTOPSIS) to rank the houses.