Indoor environmental quality assessment based on Interval-Valued Intuitionistic Fuzzy Linguistic Term Set TOPSIS method

Abstract

Established linguistic term sets (LTSs) can express only decision-maker membership, not hesitation and non-membership. In this paper, we propose an interval-valued intuitionistic fuzzy linguistic term set (IVIFLTS) in combination with an interval-valued intuitionistic fuzzy set (IVIFS), which uses interval-valued linguistic elements to represent the degree of membership and hesitation. We define a new score function for comparing two or more different IVIFLTS, along with the proof of the algorithm and properties of IVIFLTS. During the aggregation process, the IVIFLTS geometric weighted average operator is proposed, and the definition of the IVIFLTS distance metric is given considering the structure and characteristics of IVIFLTS. Based on this, we combine IVIFLTS with the TOPSIS method and present the specific calculation equation and implementation steps. Finally, we apply the IVIFLTS-TOPSIS method to evaluate the indoor environmental quality. Through practical case studies, we demonstrate that the IVIFLTS can flexibly address fuzzy information and accurately reflect decision-makers’ hesitation and non-membership thoughts.