Interval type-2 fuzzy Hamy mean operators and their application in multiple criteria decision making

Abstract

Interval type-2 fuzzy set (IT2FS) is a widely used tool for handling vagueness and imprecision in real-world problems. To aggregate the interval type-2 fuzzy information, some useful aggregation operators have been developed such as IT2-OWA, IT2-FWA, and IT2-Frank operators. In particular, some aggregation operators which can capture and reflect and interrelationships among aggregated arguments are intensively studied, among which Hamy mean (HM) is an important alternative. However, the traditional HM does not focus on fusion of fuzzy information and the weighted vector of the aggregated arguments. In this study, we extend the HM to accommodate interval type-2 fuzzy environment and show its application to multiple criteria decision making (MADM). In order to simplify the computing, we first define the concept of symmetric triangular interval type-2 fuzzy set and propose some operational laws. Motivated by the idea of HM operator, we develop the symmetric triangular interval type-2 fuzzy Hamy mean (STIT2FHM) operator for aggregating the interval type-2 fuzzy information. Some useful properties such as monotonicity, boundedness, and idempotency are studied in detail. Furthermore, we discuss some special cases with respect to different parameter values of the STIT2FHM operator. For the situations where the input arguments have different importance, we further develop the weighted symmetric triangular interval type-2 fuzzy Hamy mean (WSTIT2FHM) operator to aggregate interval type-2 fuzzy information. Based on it, an approach to MCDM problems with symmetric triangular interval type-2 fuzzy information is developed. Finally, a real-world example concerning tourism recommender system is provided to illustrate the practicality and effectiveness of the proposed method.