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AIMS Mathematics

2023, Volume 8, Issue 6: 14850-14866. doi: 10.3934/math.2023759
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The connection between ordinary and soft $ \sigma $-algebras with applications to information structures

  • 1.
    Department of Mathematics, Sana'a University, P.O. Box 1247 Sana'a, Yemen
  • 2.
    Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq
  • 3.
    Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh 16273, Saudi Arabia
  • Received: 13 February 2023 Revised: 05 April 2023 Accepted: 17 April 2023 Published: 21 April 2023

  • MSC : 06D72, 08A65

  • The paper presents a novel analysis of interrelations between ordinary (crisp) $ \sigma $-algebras and soft $ \sigma $-algebras. It is known that each soft $ \sigma $-algebra produces a system of crisp (parameterized) $ \sigma $-algebras. The other way round is also possible. That is to say, one can generate a soft $ \sigma $-algebra from a system of crisp $ \sigma $-algebras. Different methods of producing soft $ \sigma $-algebras are discussed by implementing two formulas. It is demonstrated how these formulas can be used in practice with the aid of some examples. Furthermore, we study the fundamental properties of soft $ \sigma $-algebras. Lastly, we show that elements of a soft $ \sigma $-algebra contain information about a specific event.

    Citation: Tareq M. Al-shami, Zanyar A. Ameen, Abdelwaheb Mhemdi. The connection between ordinary and soft $ \sigma $-algebras with applications to information structures[J]. AIMS Mathematics, 2023, 8(6): 14850-14866. doi: 10.3934/math.2023759

    Related Papers:

  • The paper presents a novel analysis of interrelations between ordinary (crisp) $ \sigma $-algebras and soft $ \sigma $-algebras. It is known that each soft $ \sigma $-algebra produces a system of crisp (parameterized) $ \sigma $-algebras. The other way round is also possible. That is to say, one can generate a soft $ \sigma $-algebra from a system of crisp $ \sigma $-algebras. Different methods of producing soft $ \sigma $-algebras are discussed by implementing two formulas. It is demonstrated how these formulas can be used in practice with the aid of some examples. Furthermore, we study the fundamental properties of soft $ \sigma $-algebras. Lastly, we show that elements of a soft $ \sigma $-algebra contain information about a specific event.


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