A Contribution to the Theory of Soft Sets via Generalized Relaxed Operations

Basit Ali; Naeem Saleem; Nozara Sundus; Sana Khaleeq; Muhammad Saeed; Reny George

doi:10.3390/math10152636

A Contribution to the Theory of Soft Sets via Generalized Relaxed Operations

Basit Ali, Naeem Saleem, Nozara Sundus, Sana Khaleeq, Muhammad Saeed, Reny George

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Soft set theory has evolved to provide a set of valuable tools for dealing with ambiguity and uncertainty in a variety of data structures related to real-world challenges. A soft set is characterized via a multivalued function of a set of parameters with certain conditions. In this study, we relax some conditions on the set of parameters and generalize some basic concepts in soft set theory. Specifically, we introduce generalized finite relaxed soft equality and generalized finite relaxed soft unions and intersections. The new operations offer a great improvement in the theory of soft sets in the sense of proper generalization and applicability.

Original language	English
Article number	2636
Journal	Mathematics
Volume	10
Issue number	15
DOIs	https://doi.org/10.3390/math10152636
State	Published - Aug 2022

Keywords

gf-soft equality
gf-soft intersection
gf-soft subset
gf-soft union
soft set

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10.3390/math10152636

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title = "A Contribution to the Theory of Soft Sets via Generalized Relaxed Operations",

abstract = "Soft set theory has evolved to provide a set of valuable tools for dealing with ambiguity and uncertainty in a variety of data structures related to real-world challenges. A soft set is characterized via a multivalued function of a set of parameters with certain conditions. In this study, we relax some conditions on the set of parameters and generalize some basic concepts in soft set theory. Specifically, we introduce generalized finite relaxed soft equality and generalized finite relaxed soft unions and intersections. The new operations offer a great improvement in the theory of soft sets in the sense of proper generalization and applicability.",

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author = "Basit Ali and Naeem Saleem and Nozara Sundus and Sana Khaleeq and Muhammad Saeed and Reny George",

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AU - Ali, Basit

AU - Saleem, Naeem

AU - Sundus, Nozara

AU - Khaleeq, Sana

AU - Saeed, Muhammad

AU - George, Reny

PY - 2022/8

Y1 - 2022/8

N2 - Soft set theory has evolved to provide a set of valuable tools for dealing with ambiguity and uncertainty in a variety of data structures related to real-world challenges. A soft set is characterized via a multivalued function of a set of parameters with certain conditions. In this study, we relax some conditions on the set of parameters and generalize some basic concepts in soft set theory. Specifically, we introduce generalized finite relaxed soft equality and generalized finite relaxed soft unions and intersections. The new operations offer a great improvement in the theory of soft sets in the sense of proper generalization and applicability.

AB - Soft set theory has evolved to provide a set of valuable tools for dealing with ambiguity and uncertainty in a variety of data structures related to real-world challenges. A soft set is characterized via a multivalued function of a set of parameters with certain conditions. In this study, we relax some conditions on the set of parameters and generalize some basic concepts in soft set theory. Specifically, we introduce generalized finite relaxed soft equality and generalized finite relaxed soft unions and intersections. The new operations offer a great improvement in the theory of soft sets in the sense of proper generalization and applicability.

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KW - gf-soft intersection

KW - gf-soft subset

KW - gf-soft union

KW - soft set

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VL - 10

JO - Mathematics

JF - Mathematics

IS - 15

M1 - 2636

ER -

A Contribution to the Theory of Soft Sets via Generalized Relaxed Operations

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Keywords

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