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The Approximation Operators on Rings and Semi-Rings

Author: MaLiZhen
Tutor: QinKeYun
School: Southwest Jiaotong University
Course: Applied Mathematics
Keywords: Approximation space Rough rings Rough Ideals Congruence relations K- ideal
CLC: O159
Type: Master's thesis
Year: 2010
Downloads: 20
Quote: 0
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Abstract


This article will be a combination of rough set theory and abstract algebra . On the basis of previous research work , with the congruence relation induced approximation operators , to form the corresponding approximation space , and then the ring and is semi- the ring approximation operators constructor and basic properties of a study . The specific results are as follows : Rough Ring Research , based on some form of ring congruence relations were established on the ring rough approximation operators approximation operators Structures and Related Properties . Are discussed under the ring homomorphism approximation set variation , the Rough rings , rough ideal homomorphism nature . In addition, in the ring direct product structure induced by fuzzy ideals of direct product of approximation operators , the nature of the approximation operators . Given on rough semi- ring research , intends full of ideals and intends to K - ideal concept , with the full from the total yoke closed ideal generated the same I relations induced by the regular semiring and contemplated is the half-ring on the approximation operator sub and discuss their basic properties . This is a rough set basic theoretical research , the results the Rough Ring findings supplement with the perfect combination of rough set theory and abstract algebra has a certain theoretical significance .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Fuzzy Mathematics
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