Proper Fuzzification of Prime Ideals of a Hemiring. (20th November 2012)

• Record Type: Journal Article
• Authors: Kumbhojkar, H. V.
• Other Names: Xu Sendren Sheng-Dong Academic Editor.
• Is Part Of: Advances in fuzzy systems. Volume 2012(2012)
• Publication Date: 2012-11-20
• Subjects: Fuzzy systems -- Periodicals; Systèmes flous; Fuzzy systems; Periodicals; 511.313
• DOI: 10.1155/2012/801650
• Languages: English
• ISSNs: 1687-7101

Abstract

Abstract : 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.