This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying. It investigates topological notions defined by means of -open sets when these are planted into...This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying. It investigates topological notions defined by means of -open sets when these are planted into the frame-work of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying operations from P(X) to , where (X, τ) is a fuzzifying topological space. By making use of them we contract neighborhood structures, derived sets, closure operations and interior operations.展开更多
In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and t...In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.展开更多
Fuzzy C-means (FCM) is simple and widely used for complex data pattern recognition and image analyses. However, selecting an appropriate fuzzifier (m) is crucial in identifying an optimal number of patterns and achiev...Fuzzy C-means (FCM) is simple and widely used for complex data pattern recognition and image analyses. However, selecting an appropriate fuzzifier (m) is crucial in identifying an optimal number of patterns and achieving higher clustering accuracy, which few studies have investigated. Built upon two existing methods on selecting fuzzifier, we developed an integrated fuzzifier evaluation and selection algorithm and tested it using real datasets. Our findings indicate that the consistent optimal number of clusters can be learnt from testing different fuzzifiers for each dataset and the fuzzifier with the lowest value for this consistency should be selected for clustering. Our evaluation also shows that the fuzzifier impacts the clustering accuracy. For longitudinal data with missing values, m = 2 could be an empirical rule to start fuzzy clustering, and the best clustering accuracy was achieved for tested data, especially using our multiple-imputation based fuzzy clustering.展开更多
文摘This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying. It investigates topological notions defined by means of -open sets when these are planted into the frame-work of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying operations from P(X) to , where (X, τ) is a fuzzifying topological space. By making use of them we contract neighborhood structures, derived sets, closure operations and interior operations.
基金the National Natural Science Foundation of China (60274016)the Project of Scientific Research in Hight Education Bureau Liaoning Province (2023901018).
文摘In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.
文摘Fuzzy C-means (FCM) is simple and widely used for complex data pattern recognition and image analyses. However, selecting an appropriate fuzzifier (m) is crucial in identifying an optimal number of patterns and achieving higher clustering accuracy, which few studies have investigated. Built upon two existing methods on selecting fuzzifier, we developed an integrated fuzzifier evaluation and selection algorithm and tested it using real datasets. Our findings indicate that the consistent optimal number of clusters can be learnt from testing different fuzzifiers for each dataset and the fuzzifier with the lowest value for this consistency should be selected for clustering. Our evaluation also shows that the fuzzifier impacts the clustering accuracy. For longitudinal data with missing values, m = 2 could be an empirical rule to start fuzzy clustering, and the best clustering accuracy was achieved for tested data, especially using our multiple-imputation based fuzzy clustering.
