Interval Shadowed Set Model Based On Fuzzy Entropy And Its Application

Shadowed set theory is an approximate computing model which combines fuzzy sets and three-way decision theory,and can effectively describe inaccurate or uncertain information.As an extension of the fuzzy set,shadowed set transforms multi-valued logic of fuzzy set into three-valued logic,which significantly reduces the information redundancy of fuzzy set in the practical application background.And its three-valued logic is also more accord with human cognitive habits than fuzzy sets.However,from the perspective of uncertainty measure,classical shadowed set model still suffer from a large loss of information.Therefore,in this thesis,the theory of shadowed set and its extended model are deeply studied,and the method of uncertainty measure for shadowed sets is proposed.Then,a more semantically explanatory shadowed set model is constructed.Subsequently,the model is applied to the field of clustering analysis to construct a new three-way clustering algorithm.Finally,the algorithm is successfully applied to steel production.The main works of this thesis are shown as the follows.(1)Based on the entropy measure methods of fuzzy sets,the concept of interval fuzzy entropy is defined and used to measure the uncertainty of shadowed sets.Then,based on interval fuzzy entropy,an interval shadowed set model with less uncertainty lose is proposed.By solving a problem of minimizing the loss of fuzzy entropy,the optimal thresholds are obtained.After that,discussions under two hypothetical extreme thresholds show that the interval shadowed set model not only has good decision-making ability,but also provides a reasonable semantic explanation in theory.Finally,the validity of the interval shadowed set model is verified by instences analysis and experimental results.(2)Based on the peak density clustering algorithm,a new peak density clustering algorithm based on interval shadowed sets is proposed.Compared with the peak density clustering algorithm,this algorithm not only retains its advantage of not requiring iteration,but also avoids the problem that the given truncation distance affects the noise detection strategy.The experimental results show that the proposed algorithm can distribute objects to corresponding clusters more reasonably,and has strong robustness for noisy data.And the three-way clustering structure also conforms to human cognitive habits.(3)There are massive production data in the actual industrial production process,and manual comparison analysis is inefficient and error-prone.Clustering analysis is the optimal solution to sovle these problems.Therefore,the peak density clustering algorithm based on interval shadowed sets algorithm proposed in this thesis is applied to steel-making data set to solve the difficulties in industrial production and improve the quality and efficiency of industrial production.And the experimental results show that the classification results of the algorithm not only can effectively distinguish different types of steel,but also can effectively detect the quality of steel.