Higher Type q-Rung Orthopair Fuzzy Sets: Interval Analysis

As a crucial extension of q-rung orthopair fuzzy sets, in recent years, the exploration of q-rung interval-valued orthopair fuzzy set (q-RIVOFS) is necessary and meaningful for portraying complex decision-making systems. The objective of this chapter is to review several basic concepts of q-RIVOFS, propose some novel measures for q-RIVOFS and present its linkages with the applied areas by establishing a novel q-RIVOFS-TODIM decision-making model. In this chapter, at the beginning, several theoretical knowledge of q-RIVOFSs including basic definition, score and accuracy function, comparison laws, and fundamental operation rules are reviewed. Subsequently, some q-RIVOF cross-entropy and Hausdorff distance are formulated to measure specific divergence degree between two q-RIVOFSs. In addition, an integrated q-RIVOFS-TODIM approach is constructed to display the valid applications of q-RIVOFSs in MADM areas. After that, a medical waste disposal method selection illustrative example is conducted to demonstrate the advantages of q-RIVOFSs and the practicability of the proposed q-RIVOFS-TODIM approach. Finally, sensitivity analysis and comparative analysis are further performed to show the superiority and robustness of the proposed approach. The experimental results reveal that q-RIVOFSs as a fuzzy language possess far-ranging application space; the proposed q-RIVOFS-TODIM approach has an ability to reflect on the risk aversion psychological behaviors of decision-makers; and compared to methods based on the closeness of each alternative to ideal solutions, the proposed approach is able to circumvent the occurrence of inverse sequence.