• Title/Summary/Keyword: (ordered) ideal

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ON TRIPOLAR FUZZY IDEALS IN ORDERED SEMIGROUPS

  • NUTTAPONG WATTANASIRIPONG;NAREUPANAT LEKKOKSUNG;SOMSAK LEKKOKSUNG
    • Journal of applied mathematics & informatics
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    • v.41 no.1
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    • pp.133-154
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    • 2023
  • In this paper, we introduce the concept of tripolar fuzzy sub-semigroups, tripolar fuzzy ideals, tripolar fuzzy quasi-ideals, and tripolar fuzzy bi-ideals of an ordered semigroup and study some algebraic properties of them. Moreover, we prove that tripolar fuzzy bi-ideals and quasi-ideals coincide only in a particular class of ordered semigroups. Finally, we prove that every tripolar fuzzy quasi-ideal is the intersection of a tripolar fuzzy left and a tripolar fuzzy right ideal.

Purities of Ordered Ideals of Ordered Semirings

  • Ayutthaya, Pakorn Palakawong na;Pibaljommee, Bundit
    • Kyungpook Mathematical Journal
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    • v.60 no.3
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    • pp.455-465
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    • 2020
  • We introduce the concepts of the left purity, right purity, quasi-purity, bipurity, left weak purity and right weak purity of ordered ideals of ordered semirings and use them to characterize regular ordered semirings, left weakly regular ordered semirings, right weakly regular ordered semirings and fully idempotent ordered semirings.

INTUITIONISTIC FUZZY IDEALS IN ORDERED SEMIGROUPS

  • Khan, Asghar;Khan, Madad;Hussain, Saqib
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.311-324
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    • 2010
  • We prove that a regular ordered semigroup S is left simple if and only if every intuitionistic fuzzy left ideal of S is a constant function. We also show that an ordered semigroup S is left (resp. right) regular if and only if for every intuitionistic fuzzy left(resp. right) ideal A = <$\mu_A$, $\gamma_A$> of S we have $\mu_A(a)\;=\;\mu_A(a^2)$, $\gamma_A(a)\;=\;\gamma_A(a^2)$ for every $a\;{\in}\;S$. Further, we characterize some semilattices of ordered semigroups in terms of intuitionistic fuzzy left(resp. right) ideals. In this respect, we prove that an ordered semigroup S is a semilattice of left (resp. right) simple semigroups if and only if for every intuitionistic fuzzy left (resp. right) ideal A = <$\mu_A$, $\gamma_A$> of S we have $\mu_A(a)\;=\;\mu_A(a^2)$, $\gamma_A(a)\;=\;\gamma_A(a^2)$ and $\mu_A(ab)\;=\;\mu_A(ba)$, $\gamma_A(ab)\;=\;\gamma_A(ba)$ for all a, $b\;{\in}\;S$.

COINCIDENCES OF DIFFERENT TYPES OF FUZZY IDEALS IN ORDERED Γ-SEMIGROUPS

  • Kanlaya, Arunothai;Iampan, Aiyared
    • Korean Journal of Mathematics
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    • v.22 no.2
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    • pp.367-381
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    • 2014
  • The notion of ${\Gamma}$-semigroups was introduced by Sen in 1981 and that of fuzzy sets by Zadeh in 1965. Any semigroup can be reduced to a ${\Gamma}$-semigroup but a ${\Gamma}$-semigroup does not necessarily reduce to a semigroup. In this paper, we study the coincidences of fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy ideals in regular, left regular, right regular, intra-regular, semisimple ordered ${\Gamma}$-semigroups.

ANTI-HYBRID INTERIOR IDEALS IN ORDERED SEMIGROUPS

  • LINESAWAT, KRITTIKA;LEKKOKSUNG, SOMSAK;LEKKOKSUNG, NAREUPANAT
    • Journal of applied mathematics & informatics
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    • v.40 no.3_4
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    • pp.769-784
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    • 2022
  • The main theme of this present paper is to study ordered semigroups in the context of anti-hybrid interior ideals. The notion of anti-hybrid interior ideals in ordered semigroups is introduced. We prove that the concepts of ideals and interior coincide in some particular classes of ordered semigroups; regular, intra-regular, and semisimple. Finally, the characterization of semisimple ordered semigroups in terms of anti-hybrid interior ideals is considered.

INTUITIONISTIC FUZZY SEMIPRIME IDEALS OF ORDERED SEMIGROUPS

  • Kim, Kyung Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.2
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    • pp.235-243
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    • 2009
  • In this paper, we introduce the notion of intuitionistic fuzzy semiprimality in an ordered semigroup, which is an extension of fuzzy semiprimality and investigate some properties of intuitionistic fuzzification of the concept of several ideals.

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CHARACTERIZING THE MINIMALITY AND MAXIMALITY OF ORDERED LATERAL IDEALS IN ORDERED TERNARY SEMIGROUPS

  • Iampan, Aiyared
    • Journal of the Korean Mathematical Society
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    • v.46 no.4
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    • pp.775-784
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    • 2009
  • In 1932, Lehmer [4] gave the definition of a ternary semigroup. We can see that any semigroup can be reduced to a ternary semigroup. In this paper, we give some auxiliary results which are also necessary for our considerations and characterize the relationship between the (0-)minimal and maximal ordered lateral ideals and the lateral simple and lateral 0-simple ordered ternary semigroups analogous to the characterizations of minimal and maximal left ideals in ordered semigroups considered by Cao and Xu [2].

THE STRUCTURE OF GALOIS CONNECTION IN FUZZY ORDERED SETS

  • Lee
    • Journal of applied mathematics & informatics
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    • v.6 no.1
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    • pp.247-252
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    • 1999
  • The purposed of this paper is to introduced some basic concepts of Galois connection between fuzzy ordered sets. And discuss its relations with the property of fuzzy ordered set.

INTUITIONISTIC FUZZY INTERIOR IDEALS IN ORDERED SEMIGROUPS

  • Shabir, Muhammad;Khan, A.
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1447-1457
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    • 2009
  • In this paper we define intuitionistic fuzzy interior ideals in ordered semigroups. We prove that in regular(resp. intra-regular and semisimple) ordered semigroups the concepts of intuitionistic fuzzy interior ideals and intuitionistic fuzzy ideals coincide. We prove that an ordered semi group is intuitionistic fuzzy simple if and only if every intutionistic fuzzy interior ideal is a constant function. We characterize intra-regular ordered semi groups in terms of interior (resp. intuitionistic fuzzy interior) ideals.

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