Novel information measures considering the closest crisp set on fuzzy multi-attribute decision making

Le Fu; Jingxuan Chen; Xuanchen Li; Chunfeng Suo; Le Fu; Jingxuan Chen; Xuanchen Li; Chunfeng Suo

doi:10.3934/math.2025138

AIMS Mathematics

2025, Volume 10, Issue 2: 2974-2997. doi: 10.3934/math.2025138

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Research article

Novel information measures considering the closest crisp set on fuzzy multi-attribute decision making

School of Mathematics and Statistics, Beihua University, Jilin, 132000, Jilin, China

Received: 28 November 2024 Revised: 06 January 2025 Accepted: 07 February 2025 Published: 17 February 2025
MSC : 90B50, 91A35

The information measure of interval-valued intuitionistic fuzzy sets holds extensive application value in decision-making and pattern recognition. The primary contribution of this paper lied in presenting a functional model for assessing the information content of interval-valued intuitionistic fuzzy sets. Initially, we introduced the concept of closest crisp set associated with interval-valued intuitionistic fuzzy set and explored its pertinent properties. Subsequently, taking into account the distance between interval-valued intuitionistic fuzzy set and its closest crisp set, we derived a comprehensive expression for functions pertaining to similarity measures, knowledge measures and entropy on interval-valued intuitionistic fuzzy set that adhered to specific criteria. Furthermore, we explored the interconversion between these three measures. The advantage of these functional expressions and transformation relationships lied in their ability to generate numerous formulas for defining information measures. Finally, we demonstrated the practical application of knowledge measure in investment case. The practicality of the proposed measures were corroborated through sensitivity analysis and comparative analysis.
- interval-valued intuitionistic fuzzy set,
- closest crisp set,
- knowledge measure,
- similarity measure,
- entropy
Citation: Le Fu, Jingxuan Chen, Xuanchen Li, Chunfeng Suo. Novel information measures considering the closest crisp set on fuzzy multi-attribute decision making[J]. AIMS Mathematics, 2025, 10(2): 2974-2997. doi: 10.3934/math.2025138

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Abstract

The information measure of interval-valued intuitionistic fuzzy sets holds extensive application value in decision-making and pattern recognition. The primary contribution of this paper lied in presenting a functional model for assessing the information content of interval-valued intuitionistic fuzzy sets. Initially, we introduced the concept of closest crisp set associated with interval-valued intuitionistic fuzzy set and explored its pertinent properties. Subsequently, taking into account the distance between interval-valued intuitionistic fuzzy set and its closest crisp set, we derived a comprehensive expression for functions pertaining to similarity measures, knowledge measures and entropy on interval-valued intuitionistic fuzzy set that adhered to specific criteria. Furthermore, we explored the interconversion between these three measures. The advantage of these functional expressions and transformation relationships lied in their ability to generate numerous formulas for defining information measures. Finally, we demonstrated the practical application of knowledge measure in investment case. The practicality of the proposed measures were corroborated through sensitivity analysis and comparative analysis.

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