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AIMS Mathematics

2022, Volume 7, Issue 7: 13278-13291. doi: 10.3934/math.2022733
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Research article

A study of fixed point sets based on Z-soft rough covering models

  • 1.
    Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan
  • 2.
    Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
  • 3.
    Department of Mathematics, Islamabad Model College for Girls, F-6/2, Islamabad, Pakistan
  • Received: 10 March 2022 Revised: 12 April 2022 Accepted: 22 April 2022 Published: 13 May 2022

  • MSC : 47H10, 54H25

  • Z-soft rough covering models are important generalizations of classical rough set theory to deal with uncertain, inexact and more complex real world problems. So far, the existing study describes various forms of approximation operators and their properties by means of soft neighborhoods. In this paper, we propose the notion of $ Z $-soft rough covering fixed point set (briefly, $\mathcal{Z}$-$\mathcal{SRCFP}$-set) induced by covering soft set. We study the conditions that the family of $ \mathcal{Z} $-$ \mathcal{SRCFP} $-sets become lattice structure. For any covering soft set, the $ \mathcal{Z} $-$ \mathcal{SRCFP} $-set is a complete and distributive lattice, and at the same time, it is also a double p-algebra. Furthermore, when soft neighborhood forms a partition of the universe, then $ \mathcal{Z} $-$ \mathcal{SRCFP} $-set is both a boolean lattice and a double stone algebra. Some main theoretical results are obtained and investigated with the help of examples.

    Citation: Imran Shahzad Khan, Choonkil Park, Abdullah Shoaib, Nasir Shah. A study of fixed point sets based on Z-soft rough covering models[J]. AIMS Mathematics, 2022, 7(7): 13278-13291. doi: 10.3934/math.2022733

    Related Papers:

  • Z-soft rough covering models are important generalizations of classical rough set theory to deal with uncertain, inexact and more complex real world problems. So far, the existing study describes various forms of approximation operators and their properties by means of soft neighborhoods. In this paper, we propose the notion of $ Z $-soft rough covering fixed point set (briefly, $\mathcal{Z}$-$\mathcal{SRCFP}$-set) induced by covering soft set. We study the conditions that the family of $ \mathcal{Z} $-$ \mathcal{SRCFP} $-sets become lattice structure. For any covering soft set, the $ \mathcal{Z} $-$ \mathcal{SRCFP} $-set is a complete and distributive lattice, and at the same time, it is also a double p-algebra. Furthermore, when soft neighborhood forms a partition of the universe, then $ \mathcal{Z} $-$ \mathcal{SRCFP} $-set is both a boolean lattice and a double stone algebra. Some main theoretical results are obtained and investigated with the help of examples.


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