A New Kind of Derivations in BCI-Algebras

Abstract A new kind of derivation in BCI-algebras is introduced, and related properties are investigated. For a self map d f q of a BCI-algebra X, conditions for the kernel of d f q to be both a subalgebra and an ideal of X are provided. Mathematics Subject Classification: 06F35, 03G25 Keywords: (p-semisimple, quasi associative) BCI-algebra, Inside (resp. outside) f q -derivation, Kernel of a self map d f q

Soft p-ideals of soft BCI-algebras

AbstractMolodtsov [D. Molodtsov, Soft set theory–First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Jun [Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413] applied first the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. In this paper we introduce the notion of soft p-ideals and p-idealistic soft BCI-algebras, and then investigate their basic properties. Using soft sets, we give characterizations of (fuzzy) p-ideals in BCI-algebras. We provide relations between fuzzy p-ideals and p-idealistic soft BCI-algebras

Generalizations of -Subalgebras in BCK/BCI-Algebras Based on Point -Structures

The aim of this article is to obtain more general forms than the papers of (Jun et al. (2010); Jun et al. (in press)). The notions of -subalgebras of types , and are introduced, and the concepts of -support and -support are also introduced. Several related properties are investigated. Characterizations of -subalgebra of type are discussed, and conditions for an -subalgebra of type to be an -subalgebra of type are considered

Coderivations of Ranked Bigroupoids

The notion of (co)derivations of ranked bigroupoids is discussed by Alshehri et al. (in press), and their generalized version is studied by Jun et al. (under review press). In particular, Jun et al. (under review press) studied coderivations of ranked bigroupoids. In this paper, the generalization of coderivations of ranked bigroupoids is discussed. The notion of generalized coderivations in ranked bigroupoids is introduced, and new generalized coderivations of ranked bigroupoids are obtained by combining a generalized self-coderivation with a rankomorphism. From the notion of (X,∗,&)-derivation, the existence of a rankomorphism of ranked bigroupoids is established

Graphs Based on BCK/BCI-Algebras

The associated graphs of BCK/BCI-algebras will be studied. To do so, the notions of (l-prime) quasi-ideals and zero divisors are first introduced and related properties are investigated. The concept of associative graph of a BCK/BCI-algebra is introduced, and several examples are displayed

Closed Int Soft -Ideals and Int Soft c--Ideals

The aim of this paper 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 notions of closed intersectional soft -ideals and intersectional soft commutative -ideals are introduced, and related properties are investigated. Conditions for an intersectional soft -ideal to be closed are provided. Characterizations of an intersectional soft commutative -ideal are established, and a new intersectional soft c--ideal from an old one is constructed

The Combination of Soft Sets and N-Structures with Applications

Using the notions of soft sets and N-structures, N-soft set theory is introduced. We apply it to both a decision making problem and a BCK/BCI algebra

Quasi-valuation maps based on positive implicative ideals in BCK-algebras

The notion of PI-quasi-valuation maps of a BCK-algebra is introduced, and related properties are investigated. The relationship between an I-quasi-valuation map and a PI-quasivaluation map is examined. Conditions for an I-quasi-valuation map to be a PI-quasi-valuation map are provided, and conditions for a real-valued function on a BCK-algebra to be a quasi-valuation map based on a positive implicative ideal are founded. The extension property for a PI-quasi-valuation map is established

Implicative Int-Soft Filters of R

The notion of implicative int-soft filters is introduced, and related properties are investigated. A relation between an int-soft filter and an implicative int-soft filter is discussed, and conditions for an int-soft filter to be an implicative int-soft filter are provided. Characterizations of an implicative int-soft filter are considered, and a new implicative int-soft filter from an old one is displayed. The extension property of an implicative int-soft filter is established

The development of a web-based app employing machine learning for delirium prevention in long-term care facilities in South Korea

Background Long-term care facilities (LCFs) in South Korea have limited knowledge of and capability to care for patients with delirium. They also often lack an electronic medical record system. These barriers hinder systematic approaches to delirium monitoring and intervention. Therefore, this study aims to develop a web-based app for delirium prevention in LCFs and analyse its feasibility and usability. Methods The app was developed based on the validity of the AI prediction model algorithm. A total of 173 participants were selected from LCFs to participate in a study to determine the predictive risk factors for delerium. The app was developed in five phases: (1) the identification of risk factors and preventive intervention strategies from a review of evidence-based literature, (2) the iterative design of the app and components of delirium prevention, (3) the development of a delirium prediction algorithm and cloud platform, (4) a pilot test and validation conducted with 33 patients living in a LCF, and (5) an evaluation of the usability and feasibility of the app, completed by nurses (Main users). Results A web-based app was developed to predict high risk of delirium and apply preventive interventions accordingly. Moreover, its validity, usability, and feasibility were confirmed after app development. By employing machine learning, the app can predict the degree of delirium risk and issue a warning alarm. Therefore, it can be used to support clinical decision-making, help initiate the assessment of delirium, and assist in applying preventive interventions. Conclusions This web-based app is evidence-based and can be easily mobilised to support care for patients with delirium in LCFs. This app can improve the recognition of delirium and predict the degree of delirium risk, thereby helping develop initiatives for delirium prevention and providing interventions. Moreover, this app can be extended to predict various risk factors of LCF and apply preventive interventions. Its use can ultimately improve patient safety and quality of care. © 2022, The Author(s).1