The symmetrical interval intuitionistic uncertain linguistic operators and their application to decision making

• We point out the issues of the operational laws on IIULSs in the reference.
• We define some new operational laws that eliminate the existing issues.
• The expected and accuracy functions are defined to rank IIULSs.
• Two operators on IIULSs are defined, and optimal models are established.
• An approach is developed, and the associated example is offered.

Interval intuitionistic uncertain linguistic sets are an important generalization of fuzzy sets, which well cope with the experts’ qualitative preferences as well as reflect the interval membership and non-membership degrees of the uncertain linguistic term. This paper first points out the issues of the operational laws on interval intuitionistic uncertain linguistic numbers in the literature, and then defines some alternative ones. To consider the relationship between interval intuitionistic uncertain linguistic sets, the expectation and accuracy functions are defined. To study the application of interval intuitionistic uncertain linguistic sets, two symmetrical interval intuitionistic uncertain linguistic hybrid aggregation operators are defined. Meanwhile, models for the optimal weight vectors are established, by which the optimal weighting vector can be obtained. As a series of development, an approach to multi-attribute decision making under interval intuitionistic uncertain linguistic environment is developed, and the associated example is provided to demonstrate the effectivity and practicality of the procedure.