Measuring associations is an important scientific task. A novel measurement method maximal information coefficient (MIC) was proposed to identify a broad class of associations. As foreseen by its authors, MIC implementation algorithm ApproxMaxMI is not always convergent to real MIC values. An algorithm called SG (Simulated annealing and Genetic) was developed to facilitate the optimal calculation of MIC, and the convergence of SG was proved based on Markov theory. When run on fruit fly data set including 1,000,000 pairs of gene expression profiles, the mean squared difference between SG and the exhaustive algorithm is 0.00075499, compared with 0.1834 in the case of ApproxMaxMI. The software SGMIC and its manual are freely available at http://lxy.depart.hebust.edu.cn/SGMIC/SGMIC.htm.

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Let L be a commutative unital quantale. For every L-fuzzy relation E on a nonempty set X, we define an upper rough approximation operator on L X , which is a fuzzy extension of the classical Pawlak upper rough approximation operator. We show that this operator has close relation with the subsethood operator on X. Conversely, by an L-fuzzy closure operator on X, we can easily get an L-fuzzy relation. We show that this relation can be characterized by more smooth ways. Without the help of the lower approximation operator, L-fuzzy rough sets can still be studied by means of constructive and axiomatic approaches, and L-fuzzy similarities and L-fuzzy closure operators are one-to-one corresponding. We also show that, the L-topology induced by the upper rough approximation operator is stratified and Alexandrov.