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The promotion of law of excluded middle - generalized excluded middle and the mathematical representation

Does not belong to a large extent , the two can coexist , but the two are proportional stratified . Mathematical language that is : given the domain of u ( the set of all things ), a fuzzy set A ( the ambiguity of things under discussion ) is that for any M ∈, are assigned a number (M) ∈ [0,1 ] (called M on the membership degree ), mapping :> [0,1] M -> (M) ∈ [0,1] with a mathematical formula can be expressed as : (M) V (M) ≤ 1 when (M) the range is { 0,1 } , the fuzzy set A to set off into the ordinary , so ordinary collection is a special case of fuzzy sets ; excluded middle is the general law of excluded middle is a special case . 7 Conclusions generalized excluded middle only inherited form of logic and mathematical logic in the rational part of the law of excluded middle , but also to avoid the formation of the defects of a dialectical perspective and with a reasonable and logical thinking. The logical thinking and the Relativism, sophistry is essentially different . For this reason, the generalized law of excluded middle way of thinking in modern science to take an active role and a wide range of application. It is not only natural sciences ( such as: mathematics, topology , control theory, fuzzy math library , artificial intelligence , artificial neural network, etc.) but also for the social sciences ( such as: economic management, psychology, education, medicine , etc.) A powerful way of thinking of cognition ,tn requin pas cher, allowing computers to mimic human brain to identify complex systems discrimination, and improve the automation level. With the further development of science and technology , in particular, fuzzy , gray mathematics, artificial intelligence and artificial neural networks, the further development of science , general law of excluded middle will play an increasingly important role.