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Although smooth groups and smooth rings were presented, however the important method that smooth ring acts on smooth group has not been seen in report. In order to solve the problem, this paper defines smooth modulus, smooth homomorphism and smooth quotient modulus by the action. In order to compare two smooth modulus, this paper proves the fundamental theorem of smooth homomorphism of smooth modulus...
Aimed at that available application of smooth homomorphism is around the comparison of two smooth modulus with each other and any of its application to construct new smooth modulus has not been seen, this paper applies smooth homomorphism and modulus to construct smooth projective modulus and proves three theorems:1. the theorem that lifts some examples of smooth projective modulus. 2. the sufficient...
Different from available Rosenfeld fuzzy groups and YUAN fuzzy groups, smooth groups are a new kind of fuzzy group structure. However, smooth groups possess one kind of binary operations. In order to solve the problem, this paper forwards smooth rings which possess two kinds of binary operations, presents and proves two theorems: 1. smooth kernel of smooth homomorphism sigma is two-sided ideal. The...
A vague set uses a truth grade of membership and a false grade of membership to indicate the positive evidence and the negative evidence, respectively. A vague set can overcome the problem that the grade of membership of a fuzzy set can not distinguish the two evidences from each other. However, the algebraic structures of vague sets are still not obtained. To solve the problem, this paper fuses vague...
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