Research On The Model And Application Of Algebraic Granular Computing

Granular computing provides a new perspective for solving complex problems by imitating human thinking mode.An in-depth study of granular computing theory can promote the machine solution to complex problems and expand the application of artificial intelligence technology.The algebraic structure is a commonly used data structure in the field of computer science,and the quotient space theory describes the problem with the topological structure,which brings inspiration for solving algebraic structure problems.Therefore,on the basis of the algebraic system and granular computing theory,this thesis establishes an algebraic granular computing model based on quotient space and studies its structure and application.First,in order to solve algebraic problems by applying the granular computing method,this thesis introduces algebraic structure,gives a formal definition of the algebraic granular computing model,and demonstrates the necessity of congruence relation as a granulation criterion to construct congruence granularity.Discussing the structural completeness of the model lays a foundation for the theory of algebraic granular computing.Secondly,the focus is on the granularity conversion method of algebraic granular computing,and the upper and lower approximation congruence of the equivalent granularity is solved by the decomposition method and the merging method respectively.Under the guidance of topological quotient space theory,the synthesis technique of quotient space and the principle of fidelity and false preservation of algebraic granule computing are given,and the consistency of algebraic and topological quotient spaces in direct granulation and chain granulation is demonstrated,which is an algebraic.The granularity transformation of granular computing provides a theoretical basis.Finally,algebraic granular computing is applied to image segmentation.When using the clustering method to segment the image,in order to overcome the shortcomings of the mean clustering algorithm,such as sensitivity to the initial cluster center and poor noise resistance,this thesis establishes the congruence granularity for granulation by comparing the similarity of the objects and selects the cluster median.The number is used as the new cluster center to replace the mean to ensure the robustness of the new algorithm.The experimental results show that the new algorithm can accurately find the cluster centers,improve the clustering accuracy,and has a better recognition effect when applied to image segmentation.In this thesis,an algebraic granular computing model based on quotient space theory is established,and its theoretical framework and solution methods are deeply studied.The model is combined with a clustering algorithm and applied to image segmentation,which broadens the scope of application of the model and strengthens algebra.The effectiveness of granular computing applications further enriches and expands the theoretical system of granular computing.