Entropy for Vague sets based on convex simplex

Wei, Bo; Peng, Junhuan; Yang, Hong-Lei

doi:10.1109/iccrd.2011.5763897

Cited by 2 publications

(1 citation statement)

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“…In many researches of transforming vague sets into fuzzy sets (Lin et al 2004;Fanet al 2006;Xu 2013;Wei 2012;Zhou and Yu 2011;Wang et al 2013;Wang and Liu 2023), the core problem is the influence of vague set hesitation (neutral degree) 𝜋 𝐴 (𝑥) = 1 − 𝑡 𝐴 (𝑥) − 𝑓 𝐴 (𝑥) on true membership and false membership and what proportion of hesitancy degree tends to true or false membership degree respectively. From different angles and using different methods, many scholars have proposed a number of methods for transforming vague sets with different characteristics into fuzzy sets (Huang and He 2007;Lin et al 2004;Fan et al 2006;Xu 2013;Wei et al 2012;Zhou and Yu 2011;Wang et al2013;Wang et al 2003 ). Such methods as mean value method and scale method (Li et al 2003), fractional scale method (Lin et al 2004), difference correction method (Xu 2013), static hesitancy transformation method (Fan et al 2006), dynamic hesitancy transformation method (Lian 2021), and improvements and extensions of the above methods.…”

Section: Introductionmentioning

confidence: 99%

Method, model and application of transforming Vague set into Fuzzy set for Water conservancy system evaluation

Zhao,

Wang,

Zhao

et al. 2024

Preprint

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The complexity, multilevel nature, and fuzziness of water conservancy, hydrology, and water resources systems have led to the widespread use of fuzzy set theory and vague set theory in system evaluation, recognition, and decision making. In this study, we propose a model transforming vague sets into fuzzy sets realizing the organic combination of the two theories for better describing nonlinear mapping relationships within a system and handling fuzzy uncertain information. Analyzing vague set and fuzzy set's definition and geometric meaning, a mathematical model of transforming vague set into fuzzy set is established with the principle and method of hesitancy degree allocation. Then, under three different relation situations between true membership \({t}_{A}\left(x\right)\) and false membership\({f}_{A}\left(x\right)\), the mathematical proof and derivation of the model above are carried out, and the physical and geometric meanings of the transformation model are clarified, as well as, comparing and analyzing the results of different situations, the established model is verified by examples. Finally, taking the safety evaluation of Jinan urban flood control system as an example, the model is transformed and applied to verify the effectiveness and reliability of the proposed model. This study provides an effective approach to address the limitations of fuzzy sets in considering uncertain information as well as linear similarity measurement models between vague sets and advances its application in the future system management.

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