Generalized operations in soft set theory via relaxed conditions on parameters

Abbas, Mujahid; Ali, Muhammad Irfan; Romaguera, Salvador

doi:10.2298/fil1719955a

Cited by 23 publications

(28 citation statements)

References 13 publications

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“…The ease of the definition of soft set made it more active to apply in many situations arising in information sciences, decision making, forecasting, demand analysis, mathematics and many other related disciplines as well. We refer reader for more studies on soft sets to ( [1,2,4,20,28,29,30]).…”

Section: Introductionmentioning

confidence: 99%

On Soft Ordered Maps

Al-shami¹,

El-Shafei²,

Abo-Elhamayel³

2018

(GLM)

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In the current work, we define soft λ-continuous, soft λ-open, soft λ-closed and soft λ-homeomorphism maps via soft topological ordered spaces, where λ ∈ {I, D, B}. The relationships among these soft maps are shown with the help of examples and their main properties are studied. In this regard, the equivalent conditions for each one of these soft maps are investigated, and an enough condition for the equivalent between soft λ-open and soft λ-closed maps is given for each λ. Also, we discuss the interrelations between these soft maps and their counterparts on topological ordered spaces and clarify a significant role of extended soft topologies in this point. In the end, we point out under what conditions the initiated soft maps preserve some soft ordered separation axioms, and conclude the behaviors of these soft maps under some compositions.

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Section: Introductionmentioning

confidence: 99%

On Soft Ordered Maps

Al-shami¹,

El-Shafei²,

Abo-Elhamayel³

2018

(GLM)

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“…(ii) (G, A) is an upper soft equal to (F, B), denoted by (G, A) ≈ s (F, B), provided that G(k) = X for each k ∈ A\B, F(k) = X for each k ∈ B\A, and G(k) = F(k) for each k ∈ A B. Generalized soft subset and generalized soft equality relations were studied in [2] under the names of -soft subset and -soft equality.…”

Section: Definition 212 ([3])mentioning

confidence: 99%

“…In [2], the authors mentioned the following two incorrect results which were numbered as Proposition 4.3 and Theorem 4.4, respectively. We give the following example to illustrate that the above two results need not be true in general.…”

Section: Proposition 38 Let (Fmentioning

confidence: 99%

“…With a view to preserve some classical set-theoretic laws true for soft sets, Abbas et al [1] gave the notions of -null soft set, -absolute soft set, -soft subset and -soft equality with illustrative examples. In order to avoid a shortcoming of non existence of a -soft union of two soft sets, Abbas et al [2] proposed the concepts of f -soft subset and f -soft equality. Then they defined f -soft union and f -soft intersection of two soft sets and discussed main properties.…”

Section: Introductionmentioning

confidence: 99%

“…To elucidate this matter, we give a counterexample. In [2], the authors obtained two results related to extended soft intersection and f -soft intersection of two soft sets. However, we observe that these results do not hold true.…”

Section: Introductionmentioning

confidence: 99%

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Investigation and corrigendum to some results related to g-soft equality and gf -soft equality relations

Al-shami

2019

Filomat

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Since Molodtsov defined the concept of soft sets, many types of soft equality relations between two soft sets were discussed. Among these types are-soft equality and f-soft equality relations introduced in [1] and [2], respectively. In this paper, we first aim to show that some results obtained in [1, 2] need not be true, by giving two counterexamples. Second, we investigate under what conditions these results are correct. Finally, we define and study the concepts of f-soft union and f-soft intersection for arbitrary family of soft sets.

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Insight into soft binary piecewise lambda operation: a new operation for soft sets

Sezgin,

Yavuz,

Özlü

2024

J.Umm Al-Qura Univ. Appll. Sci.

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The notion of soft set operations is one of the key concept for soft set theory as the theory has been progressing, both theoretically and practically, based on this notion. As proposing new soft set operations, deriving their algebraic properties, and studying the algebraic structure of soft sets from the perspective of soft set operations offer a comprehensive understanding of their applications as well as the appreciation of how soft set algebra can be applied to classical and nonclassical logic, in this study, a new soft set operation, called the “soft binary piecewise lambda operation" is proposed. Since one of the the main objective of abstract algebra is to analyze the properties of the operations defined on a set to classify the algebraic structures, the operation’s full properties and its distributions over other soft set operations are investigated to reveal which algebraic structures the operation forms individually, and together with other soft set operations in the collection of soft sets over the universe. It is showed that the operation forms a noncommutative semigroup and a right-left system, besides semi-rings and near-semi-rings together with certain types of soft set operations under certain conditions in the collection of soft sets over the universe. Since such in-depth analyses advance our knowledge of the applications of soft sets over a range of field, this novel operation may serve as an inspiration to create new perspectives for addressing issues related to parametric data, soft set-based cryptography, or decision-making techniques in practical settings, business, and technology.

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Generalized operations in soft set theory via relaxed conditions on parameters

Cited by 23 publications

References 13 publications

On Soft Ordered Maps

On Soft Ordered Maps

Investigation and corrigendum to some results related to g-soft equality and gf -soft equality relations

Insight into soft binary piecewise lambda operation: a new operation for soft sets

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