• 대한수학회보
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• 제50권6호
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• pp.1937-1956
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• 2013

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are introduced, and related properties and relations are investigated. Conditions for a union-soft ideal to be closed are provided. Conditions for a union-soft ideal to be a union-soft commutative ideal are also provided. Characterizations of (closed) union-soft ideals and union-soft commutative ideals are established. Extension property for a union-soft commutative ideal is established.

• Korean Journal of Mathematics
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• 제30권2호
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• pp.263-281
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• 2022

The main aim of this paper is to discuss two different types of soft hemirings, soft intersection and soft union. We discuss applications and results related to soft intersection hemirings or soft intersection k-ideals and soft union hemirings or soft union k-ideals. The deep concept of k-closure, intersection and union of soft sets, ∧-product and ∨-product among soft sets, upper 𝛽-inclusion and lower 𝛽-inclusion of soft sets is discussed here. Many applications related to soft intersection-union sum and soft intersection-union product of sets are investigated in this paper. We characterize k-hemiregular hemirings by the soft intersection k-ideals and soft union k-ideals.

• Korean Journal of Mathematics
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• 제28권1호
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• pp.89-104
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• 2020

In this paper, we connect (α, β) union soft sets and their ideal related properties with KU-algebras. In particular, we will study (α, β)-union soft sets, (α, β)-union soft ideals, (α, β)-union soft commutative ideals and ideal relations in KU-algebras. Finally, a characterization of ideals in KU-algebras in terms of (α, β)-union soft sets have been provided.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.671-686
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• 2015

The notion of soft α-ideals and α-idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft α-ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and α-idealistic soft BCI-algebras are being related. The restricted intersection, union, restricted union, restricted difference and "AND" operation of soft α-ideals and α-idealistic soft BCI-algebras are established. The characterizations of (fuzzy) α-ideals in BCI-algebras are given by using the concept of soft sets. Relations between fuzzy α-ideals and α-idealistic soft BCI-algebras are discussed.

• 대한장애인치과학회지
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• 제7권1호
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• pp.38-43
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• 2011

Treatment of the mandibular fracture consists of reduction and fixation. Primary wire & Arch bar are perhaps the ideal method for intermaxillary fixation. But, daily feeding, swallowing, speech, and in some instances, respiration is difficult to maintain during the period of intermaxillary fixation, owing to muscle weakness, emotional disorder and poor oral hygiene in a position of the long-term bed disabled patient with multiple injuries. Therefore, Intermaxillary fixation is not applied in the disabled bed patient, the alternative methods must be obtained. In the case of the mandibular fracture, because of the absence of weight bearing, osseous union may eventually occur even without immobilization if the patient is maintained without wound infection on a controlled soft diet. For the purpose of the prevention of the wound infection, the establishment of an drainage on the oral lacerated wound is necessary for the removal of the hematoma & seroma in the fracture site. This is the report of a case that was managed conservatively without the intermaxillary fixation in the long-term disabled bed patient with a mandibular compound fracture.