MODULARITY OF AJMAL FOR THE LATTICES OF FUZZY IDEALS OF A RING

Document Type : Research Paper

Author

DEPARTMENT OF MATHEMATICS, RAMJAS COLLEGE, UNIVERSITY OF DELHI, NEW DELHI , INDIA

Abstract

In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set theoretic proof of the fact that the lattice  $\vartheta$(R) of all fuzzy ideals of a ring R is modular.

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References

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Iranian Journal of Fuzzy Systems
Volume 5, Issue 2 - Serial Number 2
May and June 2008
Pages 71-78

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