The new construction of knowledge measure on intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets

Chunfeng Suo; Yan Wang; Dan Mou; Chunfeng Suo; Yan Wang; Dan Mou

doi:10.3934/math.20231387

AIMS Mathematics

2023, Volume 8, Issue 11: 27113-27127. doi: 10.3934/math.20231387

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Research article

The new construction of knowledge measure on intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets

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

Received: 22 July 2023 Revised: 21 August 2023 Accepted: 31 August 2023 Published: 25 September 2023
MSC : 90B50, 91A35

As we all know, when describing knowledge measures in the context of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets, it is always considered as dual measures of entropy. However, information content and information clarity is closely related with the amount of knowledge. Motivated by this fact, in this study, we focus on a new axiomatic definition of knowledge measures for intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets. First, we present the formulas of the knowledge measures using different abstract functions, and we proved these functions satisfy the axioms. On the basis of mathematical analysis and numerical examples, we further analyze the characteristics of the suggested knowledge measure. Finally, in order to demonstrate how rational and useful the system we developed is, we provide medical diagnoses and specific multi-attribute decision problems.
- intuitionistic fuzzy set,
- interval-valued intuitionistic fuzzy set,
- knowledge measure,
- multi-attribute decision making
Citation: Chunfeng Suo, Yan Wang, Dan Mou. The new construction of knowledge measure on intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets[J]. AIMS Mathematics, 2023, 8(11): 27113-27127. doi: 10.3934/math.20231387

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Abstract

As we all know, when describing knowledge measures in the context of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets, it is always considered as dual measures of entropy. However, information content and information clarity is closely related with the amount of knowledge. Motivated by this fact, in this study, we focus on a new axiomatic definition of knowledge measures for intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets. First, we present the formulas of the knowledge measures using different abstract functions, and we proved these functions satisfy the axioms. On the basis of mathematical analysis and numerical examples, we further analyze the characteristics of the suggested knowledge measure. Finally, in order to demonstrate how rational and useful the system we developed is, we provide medical diagnoses and specific multi-attribute decision problems.

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