Research article

Int-soft ideals over the soft sets in ordered semigroups

  • Received: 30 November 2019 Accepted: 14 February 2020 Published: 05 March 2020
  • MSC : 06F05, 06D72, 20M12

  • In this paper, the notions of int-soft left (right) ideals, int-soft interior ideals and int-soft bi-ideals over the soft sets are introduced and several related properties of these notions are investigated. Characterizations of int-soft ideals over the soft sets are considered. Moreover, for any soft set $(\eta, U)$ over $S$, the notion of a soft set over the soft sets $(\chi_{\eta(u)}, V)$ is introduced. It is prove that a soft set $(\eta, S)$ is a soft left ideal (resp. right ideal, interior ideal, bi-ideal) over $S$ if and only if $(\chi_{\eta(x)}, S)$ is an int-soft left ideal (resp. right ideal, interior ideal, bi-ideal) over the soft sets.

    Citation: G. Muhiuddin, Ahsan Mahboob. Int-soft ideals over the soft sets in ordered semigroups[J]. AIMS Mathematics, 2020, 5(3): 2412-2423. doi: 10.3934/math.2020159

    Related Papers:

  • In this paper, the notions of int-soft left (right) ideals, int-soft interior ideals and int-soft bi-ideals over the soft sets are introduced and several related properties of these notions are investigated. Characterizations of int-soft ideals over the soft sets are considered. Moreover, for any soft set $(\eta, U)$ over $S$, the notion of a soft set over the soft sets $(\chi_{\eta(u)}, V)$ is introduced. It is prove that a soft set $(\eta, S)$ is a soft left ideal (resp. right ideal, interior ideal, bi-ideal) over $S$ if and only if $(\chi_{\eta(x)}, S)$ is an int-soft left ideal (resp. right ideal, interior ideal, bi-ideal) over the soft sets.


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