Abstract
Extending of the T-operators on hesitant fuzzy sets (HFSs) is important in the theory and applications. In this paper, we used two comparative operators for expressing monotonicity of the T-operators on hesitant fuzzy elements (HFEs). Hence, properties of some T-operators for Xu-Xia partial order (≤ℍ(m)) and Xia-Xu order (⪯) are studied on typical hesitant fuzzy elements (THFEs). Finally, an application of T-operators on HFEs has been explained in fuzzy rule-based systems for a practical problem in economics. Also, for a conceptual comparison, a benchmark data under a hesitant fuzzy information environment has been used.
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