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Higher Type q-Rung Orthopair Fuzzy Sets: Interval Analysis

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q-Rung Orthopair Fuzzy Sets

Abstract

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.

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Authors and Affiliations

  1. Shanghai University, 99 Shangda Road, Baoshan District, Shanghai, 201900, China

    Yu-Dou Yang & Xue-Feng Ding

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  1. Yu-Dou Yang
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Correspondence to Xue-Feng Ding .

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  1. Thapar Institute of Engineering and Technology, Patiala, Punjab, India

    Harish Garg

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Yang, YD., Ding, XF. (2022). Higher Type q-Rung Orthopair Fuzzy Sets: Interval Analysis. In: Garg, H. (eds) q-Rung Orthopair Fuzzy Sets. Springer, Singapore. https://doi.org/10.1007/978-981-19-1449-2_7

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