Soft near-semirings

Waheed Ahmad Khan; Abdul Rehman; Abdelghani Taouti; Waheed Ahmad Khan; Abdul Rehman; Abdelghani Taouti

doi:10.3934/math.2020417

AIMS Mathematics

2020, Volume 5, Issue 6: 6464-6478. doi: 10.3934/math.2020417

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Research article

Soft near-semirings

1.
Department of Mathematics, University of Education Lahore, Attock Campus, Pakistan
2.
ETS-Maths and NS Engineering Division, HCT, University City P. O. Box 7947, Sharjah, United Arab Emirates

Received: 01 July 2020 Accepted: 12 August 2020 Published: 19 August 2020
MSC : 16Y30, 03G25, 03E72

Soft set theory was introduced by Molodtsov to deal with uncertainty. In this manuscript, we commence with the notion of soft near-semirings based on soft set theory. Several associated concepts including soft subnear-semirings, idealistic soft near-semirings, soft near-semiring homomorphism and soft near-semiring anti-homomorphism are also introduced. Moreover, numerous related properties are discussed and illustrated by suitable examples. We also present the notion of chain condition along with its applications towards soft near-semirings. We conclude that applying different types of union operations on soft sets without further restrictions are possible as long as chain condition is satisfied. Few related characteristics of soft left (resp., right) near-semirings are also explored by using soft near-semiring homomorphism and soft near-semiring anti-homomorphism. Furthermore, we found that under soft near-semiring anti-homomorphism the image of soft right (left) near-semiring is a soft left (right) near-semiring. This study also bridging the link between classical near-semirings and soft sets theory.
- soft near-semirings,
- soft idealistic near-semirings,
- soft anti-homomorphism
Citation: Waheed Ahmad Khan, Abdul Rehman, Abdelghani Taouti. Soft near-semirings[J]. AIMS Mathematics, 2020, 5(6): 6464-6478. doi: 10.3934/math.2020417

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Abstract

Soft set theory was introduced by Molodtsov to deal with uncertainty. In this manuscript, we commence with the notion of soft near-semirings based on soft set theory. Several associated concepts including soft subnear-semirings, idealistic soft near-semirings, soft near-semiring homomorphism and soft near-semiring anti-homomorphism are also introduced. Moreover, numerous related properties are discussed and illustrated by suitable examples. We also present the notion of chain condition along with its applications towards soft near-semirings. We conclude that applying different types of union operations on soft sets without further restrictions are possible as long as chain condition is satisfied. Few related characteristics of soft left (resp., right) near-semirings are also explored by using soft near-semiring homomorphism and soft near-semiring anti-homomorphism. Furthermore, we found that under soft near-semiring anti-homomorphism the image of soft right (left) near-semiring is a soft left (right) near-semiring. This study also bridging the link between classical near-semirings and soft sets theory.

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