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

Abstract

Abstract 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.