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Advances in Fuzzy Systems
Volume 2012 (2012), Article ID 801650, 8 pages
Research Article

Proper Fuzzification of Prime Ideals of a Hemiring

403 Poorvarang Apartments, 13th Lane, Kolhapur 416008, Maharashtra, India

Received 26 April 2012; Accepted 8 October 2012

Academic Editor: Sendren Sheng-Dong Xu

Copyright © 2012 H. V. Kumbhojkar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Prime fuzzy ideals, prime fuzzy k-ideals, and prime fuzzy h-ideals are roped in one condition. It is shown that this way better fuzzification is achieved. Other major results of the paper are: every fuzzy ideal (resp., k-ideal, h-ideal) is contained in a prime fuzzy ideal (resp., k-ideal, h-ideal). Prime radicals and nil radicals of a fuzzy ideal are defined; their relationship is established. The nil radical of a fuzzy k-ideal (resp., an h-ideal) is proved to be a fuzzy k-ideal (resp., h-ideal). The correspondence theorems for different types of fuzzy ideals of hemirings are established. The concept of primary fuzzy ideal is introduced. Minimum imperative for proper fuzzification is suggested and it is shown that the fuzzifications introduced in this paper are proper fuzzifications.