Correspondence theorem for fuzzy ideals

Kumbhojkar, H. V.; Bapat, M. S.

doi:10.1016/0165-0114(91)90225-f

Cited by 30 publications

(6 citation statements)

References 11 publications

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“…Dixit et al [6] depicted the notion of level subgroup in 1990. Kumbhojkar and Bapat [7] studied correspondence theorem for fuzzy ideals. Gupta and Kantroo [8] defined the relation between intrinsic product and fuzzy subring.…”

Section: Introductionmentioning

confidence: 99%

Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings

Gulzar¹,

Mateen²,

Chu³

et al. 2021

IJCIS

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The objective of this article is to present the notion of direct product of two complex intuitionistic fuzzy subrings. We show that the direct product of two complex intuitionistic fuzzy subrings is also complex intuitionistic fuzzy subring and discuss its various algebraic aspects. We also define the level subsets of the direct product of two complex intuitionistic fuzzy subsets and prove that the level subset of the direct product of two complex intuitionistic fuzzy subring is subring and prove some fundamental result of this phenomena. We show that the homomorphic image (preimage) of the direct product of complex intuitionistic fuzzy subrings is a complex intuitionistic fuzzy subring by using the notion of classical homomorphism.

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Section: Introductionmentioning

confidence: 99%

Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings

Gulzar¹,

Mateen²,

Chu³

et al. 2021

IJCIS

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“…Following Liu, Mukherjee and Sen [6] defined and examined the fuzzy prime ideals of a ring. Kumbhojkar and Bapat [1] defined and studied the ring R/J of the cosets of the fuzzy ideal J. In particular, Kuraoka and Kuroki [4] defined fuzzy quotient rings and gave homomorphism theorems and isomorphism theorems as to fuzzy ideals.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we introduce the notion of a fuzzy polynomial ideal α x of a polynomial ring R[x] induced by a fuzzy ideal α of a ring R, and obtain an isomorphism 1 theorem of a ring of fuzzy cosets of α x . It is shown that a fuzzy ideal α of a ring is fuzzy prime if and only if α x is a fuzzy prime ideal of R [x].…”

Section: Introductionmentioning

confidence: 99%

On the fuzzy polynomial ideals

Kim

2014

Journal of Intelligent &Amp; Fuzzy Systems

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In this paper we introduce the notion of a fuzzy polynomial ideal α x of a polynomial ring R[x] induced by a fuzzy ideal α of a ring R, and obtain an isomorphism theorem of a ring of fuzzy cosets of α x . It is shown that a fuzzy ideal α of a ring is fuzzy prime if and only if α x is a fuzzy prime ideal of R [x]. Moreover, we show that if α x is a fuzzy maximal ideal of R[x], then α is a fuzzy maximal ideal of R.

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“…Several attempts have been made to fuzzify the concepts of prime ideals/k-ideals/h-ideals of a semiring [1][2][3][4][5][6][7], prime ideals of a ring [8][9][10][11][12][13][14][15], and prime ideals of a semigroup [16][17][18]. We have discussed elsewhere [6], in detail, the deficiencies in the definition of a prime fuzzy h-ideal proposed in [7].…”

Section: Introductionmentioning

confidence: 99%

Proper Fuzzification of Prime Ideals of a Hemiring

Kumbhojkar¹

2012

Advances in Fuzzy Systems

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Prime fuzzy ideals, prime fuzzyk-ideals, and prime fuzzyh-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 fuzzyk-ideal (resp., anh-ideal) is proved to be a fuzzyk-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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Correspondence theorem for fuzzy ideals

Cited by 30 publications

References 11 publications

Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings

Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings

On the fuzzy polynomial ideals

Proper Fuzzification of Prime Ideals of a Hemiring

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