Special types of intuitionistic fuzzy left h-ideals of hemirings

Dudek, Wiesław A.

doi:10.1007/s00500-007-0169-8

Cited by 23 publications

(10 citation statements)

References 10 publications

(10 reference statements)

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“…Fuzzy k-ideals are studied in [21][22][23]. Fuzzy h-ideals of a hemiring are studied by many authors, for example [16][17][18][24][25][26][27]. In this paper we characterize hemirings in which each h-ideal is idempotent.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of hemirings by theirh-ideals

Dudek

Shabir

Anjum

2010

Computers & Mathematics with Applications

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a b s t r a c tIn this paper we characterize hemirings in which all h-ideals or all fuzzy h-ideals are idempotent. It is proved, among other results, that every h-ideal of a hemiring R is idempotent if and only if the lattice of fuzzy h-ideals of R is distributive under the sum and h-intrinsic product of fuzzy h-ideals or, equivalently, if and only if each fuzzy h-ideal of R is intersection of those prime fuzzy h-ideals of R which contain it. We also define two types of prime fuzzy h-ideals of R and prove that, a non-constant h-ideal of R is prime in the second sense if and only if each of its proper level set is a prime h-ideal of R.

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Section: Introductionmentioning

confidence: 99%

Characterizations of hemirings by theirh-ideals

Dudek

Shabir

Anjum

2010

Computers & Mathematics with Applications

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“…Several researchers established and investigated a fuzzy theory of semirings. They introduced the notions such as fuzzy semirings, fuzzy (prime) ideals, fuzzy k-ideals, fuzzy h-ideals and L-fuzzy ideals in semirings, and obtained many interesting results (see Ahsan et al 1993;Akram and Dudek 2008;Dudek 2008;Biswas 1994, 1995;Ghosh 1998;Glazek 2002;Golan 2003;Iwano and Steiglitz 1990;Jun et al 1996Jun et al , 1998Jun et al , 2004Kim and Park 1996;Kim 2000;Neggers et al 1999;Zhan and Dudek 2007). Kleene algebras (cf.…”

Section: Introductionmentioning

confidence: 99%

Inductive semimodules and the vector modules over them

Feng

Jun

2008

Soft Comput

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The notion of an inductive semimodule over an ordered *-semiring is introduced and some related properties are investigated. Inductive semimodules are extensions of several important algebraic structures such as Kleene modules, Kleene algebras and inductive *-semirings. We prove that an inductive semimodule over an ordered *-semiring K is a Kleene module if and only if K is a Kleene algebra. Moreover, we establish that the vector module of an inductive semimodule over an ordered Conway semiring is again an inductive semimodule over the matrix semiring. Consequently, in an inductive semimodule over an ordered Conway semiring, least solutions to linear inequation systems can be denoted by linear expressions, avoiding the least fixed point operator. In addition, we also introduce a related notion called weak inductive semimodules, and propose several open problems on them.

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“…In particular, Ma et al discussed the properties of generalized interval-valued fuzzy h-ideals of hemirings in [21]. On the other hand, Dudek et al [4][5][6] introduced the concepts of fuzzy ideals of fuzzy rings and (a, b)-fuzzy h-ideals of hemirings. Fruitful results have been obtained in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, the implication-based fuzzy h-bi-ideals (resp., h-quasi-ideals) of a hemiring were considered. The other important results related with fuzzy h-ideals of a hemiring were given in [4,5,27].…”

Section: Introductionmentioning

confidence: 99%