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

Jindong Qin
2017 Granular Computing  
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. Keywords Multiple criteria analysis · Symmetric triangular interval type-2 fuzzy set · Hamy mean · Symmetric triangular interval type-2 fuzzy Hamy mean operator · Weighted symmetric triangular interval type-2 fuzzy Hamy mean operator · Tourism recommender system Lai et al. 1994; Opricovic and Tzeng 2004;
more » ... aty 1986; Srinivasan and Shocker 1973) , the criteria value take the form of numeric, however, in many actual situations, due to the various complex factors, such as time pressure, lack of knowledge, and the experts' limited expertise about the problem domain, it is difficult for decision maker to express their preference by crisp number. To deal with this issue, a suitable approach is to use fuzzy number instead of numerical value to represent the decision maker's preference. Since Zadeh (1965) introduced the type-1 fuzzy set (T1FS) theory, the TIFS theory is widely used in management science, artificial intelligence, applied mathematics, mainly in decision making, many type-1 fuzzy techniques for dealing with MCDM problems have been developed during the last Abstract Interval type-2 fuzzy set (IT2FS) is a widely used tool for handling vagueness and imprecision in realworld 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
doi:10.1007/s41066-017-0041-x fatcat:da34fklgurd6nfsu4bf46h53ma