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<p>p, q, r-spherical fuzzy sets (p, q, r-SFSs) provide a flexible framework for modelling uncertainty beyond classical fuzzy systems. Similarity measures are essential for quantifying relationships in such environments; however, existing measures are often constrained by restrictive structural assumptions, limiting their applicability to generalized fuzzy models. To overcome these limitations, this study proposes a novel Divergence-Based Similarity (DBS) measure for p, q, r-SFSs by integrating Kullback–Leibler and Jensen–Shannon divergence principles. The proposed measure satisfies fundamental axiomatic properties, including boundedness, symmetry, and entropy preservation, while ensuring smooth parameter continuity. An algorithm for selecting optimal parameter values is also presented. The proposed DBS framework is highly generalized and reduces to similarity measures for several well-known fuzzy models under appropriate parameter settings. The effectiveness of the model is demonstrated through its applications to multi-criteria decision-making problems, including medical diagnosis and pattern recognition. Comparative results demonstrate that the proposed approach provides more reliable similarity evaluation and classification performance than existing methods, offering a unified and robust framework for decision-making under p, q, r-spherical fuzzy uncertainty.</p>

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A novel divergence-based similarity measure for p, q, r-spherical fuzzy sets and its application in multi-criteria decision-making

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Garima Bisht

摘要

p, q, r-spherical fuzzy sets (p, q, r-SFSs) provide a flexible framework for modelling uncertainty beyond classical fuzzy systems. Similarity measures are essential for quantifying relationships in such environments; however, existing measures are often constrained by restrictive structural assumptions, limiting their applicability to generalized fuzzy models. To overcome these limitations, this study proposes a novel Divergence-Based Similarity (DBS) measure for p, q, r-SFSs by integrating Kullback–Leibler and Jensen–Shannon divergence principles. The proposed measure satisfies fundamental axiomatic properties, including boundedness, symmetry, and entropy preservation, while ensuring smooth parameter continuity. An algorithm for selecting optimal parameter values is also presented. The proposed DBS framework is highly generalized and reduces to similarity measures for several well-known fuzzy models under appropriate parameter settings. The effectiveness of the model is demonstrated through its applications to multi-criteria decision-making problems, including medical diagnosis and pattern recognition. Comparative results demonstrate that the proposed approach provides more reliable similarity evaluation and classification performance than existing methods, offering a unified and robust framework for decision-making under p, q, r-spherical fuzzy uncertainty.