Proper Fuzzification of Prime Ideals of a Hemiring | Zendy

H.V. Kumbhojkar | Zendy

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Proper Fuzzification of Prime Ideals of a Hemiring

Author(s) -

H.V. Kumbhojkar

Publication year - 2012

Publication title -

advances in fuzzy systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.38

H-Index - 19

eISSN - 1687-711X

pISSN - 1687-7101

DOI - 10.1155/2012/801650

Subject(s) - ideal (ethics) , mathematics , prime (order theory) , prime ideal , radical of an ideal , fuzzy logic , associated prime , fuzzy set , discrete mathematics , minimal ideal , combinatorics , maximal ideal , computer science , artificial intelligence , principal ideal ring , philosophy , epistemology , commutative ring , commutative property

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

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