Abstract
AbstractIn this chapter, the notion of interval complex q-rung orthopair fuzzy sets (IVC q-ROFSs) and its related interval complex q-rung orthopair fuzzy numbers (IVC q-ROFNs) are introduced to solve multi-attribute decision-making (MADM) problems. The IVC-q-ROFSs are formed by combining interval complex fuzzy sets (IVCFSs) and q-rung orthopair fuzzy sets (q-ROFSs) and these can be viewed as an extension of fuzzy sets (FSs), intuitionistic fuzzy sets (IFSs), interval-valued fuzzy sets (IVFSs), interval-valued intuitionistic fuzzy sets (IVIFSs), Pythagorean fuzzy sets (PFSs), q-ROFSs, complex Pythagorean fuzzy sets (CPFSs), complex q-ROFSs, etc. So, the IVC-q-ROFS is a hybrid structure that gives high flexibility and becomes more functional in various types of uncertain problems that are time-periodic by default. We also study some fundamental properties and aggregation operators based on IVC q-ROFNs. In some practical applications, due to the increase of complex uncertainty in fuzzy environments, there exist some issues where the decision-makers face challenges to express the incomplete knowledge precisely by a single complex-valued membership degree and a single complex-valued non-membership degree. Such problems arise because the data provided to the decision-makers need another superior environment than the existing environments where it is enabled to answer those questions where the complex-valued membership grade and the complex-valued non-membership grade are not precise, i.e., they represent uncertainty. So, to remove such uncertainty, there is a demand for another superior environment that is capable of accommodating such information. This leads to the invention of IVC q-ROFSs and, under this environment, we can solve MADM problems by an exact methodology. Moreover, we propose score function, accuracy function, and various aggregate operators by using IVC q-ROFSs. Based on aggregate operators, we propose weight operators on the set of attributes. Finally, we give a numerical example to illustrate the feasibility and validity of the proposed method in a practical scenario.KeywordsPythagorean fuzzy setq-rung orthopair fuzzy setInterval complex q-rung orthopair fuzzy setMADM
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