Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are (...) discussed. Using the notion of Inf-hesitant fuzzy ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established. (shrink)

Given i, j, k ∈ {1,2,3,4}, the notion of -length neutrosophic subalgebras in BCK=BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.

The notions of a commutative (∈, ∈)-neutrosophic ideal and a commutative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of a commutative (∈, ∈)-neutrosophic ideal are obtained. Relations between commutative (∈, ∈)-neutrosophic ideal and (∈, ∈)-neutrosophic ideal are discussed. Conditions for an (∈, ∈)-neutrosophic ideal to be a commutative (∈, ∈)-neutrosophic ideal are established. Relations between commutative (∈, ∈)-neutrosophic ideal, falling neutrosophic ideal and commutative falling neutrosophic ideal are considered. Conditions for a falling neutrosophic ideal to be (...) commutative are provided. (shrink)

The notions of a C-energetic subset and permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal.

As a generation of fuzzy set, the notion of complex fuzzy set which is an innovative concept is introduced by Ramot, Milo, Friedman and Kandel. The purpose of this article is to apply complex fuzzy set to BCK/BCI-algebras. The notions of a complex subalgebra and a complex left reduced ideal in a BCK/BCI- algebra are introduced, and related properties are investigated. Characterizations of a complex subalgebra are provided, and the homomorphic image of a complex subalgebra and a complex left reduced (...) ideal. (shrink)

The notion of int-soft ideal in a pseudo MV -algebra is introduced, and related properties are investigated. Conditions for a soft set to be an int-soft ideal are provided. Characterizations of int-soft ideal are considered. The extension property for implicative int-soft ideal is established.

The notions of a hyper MV-deductive system, a -hyper MV-deductive system, a - hyper MV-deductive system, a -hyper MV-deductive system, a -hyper MV-deductive system and a -hyper MV-deductive system are introduced, and then their relations are investigated.

Molodtsov introduced 1999 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. In this paper we apply the notion of soft sets by Molodtsov to ordered semigroups. The notions of soft ordered semigroup, soft ordered subsemigroup, soft left ideal, and left idealistic soft ordered semigroup are introduced, and various related properties are investigated.

Characterizations of an (∈, ∈)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (∈, ∈)-neutrosophic ideal. The relation between (∈, ∈)-neutrosophic ideal and (∈, ∈)-neutrosophic subalgebra in a BCK-algebra is discussed. Conditions for an (∈, ∈)-neutrosophic subalgebra to be a (∈, ∈)-neutrosophic ideal are provided. Using a collection of ideals in a BCK/BCI-algebra, an (∈, ∈)-neutrosophic ideal is established. Equivalence relations on the family of all (∈, ∈)-neutrosophic ideals are introduced, and (...) related properties are investigated. (shrink)

In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of \((\in, \in)\) and \((\in, \in\! \vee \, {q})\)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of \((\alpha,\beta)\)-fuzzy subalgebras and \((\alpha,\beta)\)-fuzzy ideals on equality algebras. (...) Also, by using the notion of \((\in, \in)\)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of \(X\), and we proved that the set of all classes of \(X\) by these order is a poset. (shrink)

The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filer are displayed.

The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filter are displayed.

Rough set theory is an excellent mathematical tool for the analysis of a vague description of actions in decision problems. Now, in this paper by considering the notion of an equality algebra, the notion of the lower and the upper approximations are introduced and some properties of them are given. Moreover, it is proved that the lower and the upper approximations define an interior operator and a closure operator, respectively. Also, using D-lower and D-upper approximation, conditions for a nonempty subset (...) to be definable are provided and investigated that under which condition D-lower and D-upper approximation can be filter. (shrink)

More general form of -neutrosophic ideal is introduced, and their properties are investigated. Relations between -neutrosophic ideal and )-neutrosophic ideal are discussed. Characterizations of )-neutrosophic ideal are discussed, and conditions for a neutrosophic set to be an )-neutrosophic ideal are displayed.

The notions of soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.

The notions of soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.

Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra, is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.

In this article, we apply the notion of interval neutrosophic sets to ideal theory in BCK/BCI-algebras.

The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations of positive implicative soju ideal are established. Finally, extension property for positive implicative soju ideal is constructed.

Two philosophical problems are thoroughly treated here: (1) how close the philosophical idea of Hong Tae-yong in eighteenth-century Korea is to the non-absolutist Weltanschauung of Chuang-tzu, and (2) how, by means of this non-absolutist idea, Hong was able to question the orthodox sinocentrism that most Korean Neo-Confucianists of the time stubbornly took for granted. Hong felt that Korean intellectuals had to look beyond sinocentrism for a consciousness of their own cultural identity. As a Confucian reformist, he highlights the realization of (...) this cultural identity as the imminently required move to accomplish social reform. (shrink)

How can people from diverse and different cultural backgrounds balance and reconcile their autonomous cultural identity with the universal dictates of the global age? My approach to this question is from an East Asian perspective, in particular by addressing the issue of 'Confucian cultural identity' under four broad topics: (1) the truth and falsehood of the discourse on 'Asian Values' and 'Confucian-style Capitalism'; (2) the spread of modern science and the tragic consequences of 'Instrumental Reason'; (3) criticism of instrumental reason (...) and its encounter with Confucian virtue ethics; and (4) a reassessment of the 'Anthropocosmic Moral Metaphysics' of (Neo-) Confucianism. In conclusion, on the impending demand to cope with the crisis of our cultural identity in the age of globalisation, our project to strive for the viability of Confucian humanism in the age of globalisation, I think, should mean no other than the invocation of care-ethics that takes care of our alienated neighbours on the one hand and a thrust of an eco-friendly world view to the anthropocentric hegemony over nature, which has been appreciated by 'modern' men since the Enlightenment, on the other hand. (shrink)

The purpose of this study is to gain a better understanding of the role of abstraction and idealization in Galileo’s scientific inquiries into the law of free falling motion, and their importance in the history of science. Because there is no consensus on the use of the terms “abstraction” and “idealization” in the literature, it is necessary to distinguish between them at the outset. This paper will argue for the importance of abstraction and idealization in physics and the theories and (...) laws of physics constructed with abduction from observations and that these theoretical laws of physics should be tested with deduction and induction thorough quasi-idealized entities rather than empirical results in the everyday world. Galileo’s work is linked to thought experiments in natural science. Galileo, using thought experiments based on idealization, persuaded others that what had been proven true for a ball on an inclined plane would be equally true for a ball falling through a vacuum. (shrink)

This study aims to understand scientific inference for the evolutionary procedure of Continental Drift based on abductive inference, which is important for creative inference and scientific discovery during problem solving. We present the following two research problems: (1) we suggest a scientific inference procedure as well as various strategies and a criterion for choosing hypotheses over other competing or previous hypotheses; aspects of this procedure include puzzling observation, abduction, retroduction, updating, deduction, induction, and recycle; and (2) we analyze the “theory (...) of continental drift” discovery, called the Earth science revolution, using our multistage inference procedure. Wegener’s Continental Drift hypothesis had an impact comparable to the revolution caused by Darwin’s theory of evolution in biology. Finally, the suggested inquiry inference model can provide us with a more consistent view of science and promote a deeper understanding of scientific concepts. (shrink)

The main objective of this book is to present the theory of general relativity in a direction that will be intelligible, informative, and interesting to the individual reader. Many of the texts about general relativity are either too thin on detail or too narrow in scope; this book was written with the aim of rectifying these shortcomings.

The objective of our study is to explore scientific creativity with a focus on intellectual (thinking) skills in the cognitive aspect by analyzing scientific theories, which are basically the creativity of historical great scientists, Galileo, Newton, Einstein While our study laid stress on the cognitive domain, exploration of the creativity of great scientists is also connected with affective characteristics (motives, task commitment, etc.) and their environmental factors (incubation period). Great scientists of the science history were aware of the discrepancy issue (...) among different fields of study and long searched for solutions, which they held in their minds. As a result, they created a certain hypothesis using the abstraction strategy in which they leave only the considerations suitable for the world view of the time. Then, they conducted a thought experiment that justified it. The reason why it was difficult for general people to understand was that there was a domain transition beyond materials obtained in the abstraction process. Furthermore, they all had strong motives for the future as well as task commitment. Knowledge is a product of natural selection, and the fusion of knowledge that does not presuppose the unity of knowledge is meaningless. (shrink)

In this article, I examine Leibniz’s criticism of Spinoza’s notion of priority by nature based on the first proposition in Spinoza’s Ethics. Leibniz provides two counterexamples: first, the number 10’s being 6+3+1 is prior by nature to its being 6+4; second, a triangle’s property that two internal angles are equal to the exterior angle of the third is prior by nature to its property that the three internal angles equal two right angles. Leibniz argues that Spinoza’s notion cannot capture these (...) priority relations. Although this text has received some scholarly attention, Leibniz’s objection in this text has not been fully explained yet. I argue that evaluating Leibniz’s objection relies on how to understand Spinoza’s notion of conception: first, whether conception is co-extensive with inherence and causation; second, whether conception is mental. (shrink)

Using an analogy in science and everyday life is a double-edged sword because they are accompanied by alternative ideas, in addition to scientific concepts. Schools and public education explain global warming by making a common analogy between this phenomenon and greenhouse effects. Unfortunately, this analogy sometimes produces various incorrect explanatory mental models. To construct a correct understanding of global warming, it is necessary: first, to investigate the attributes of analogical reasoning; second, to understand these features by restructuring the greenhouse analogy; (...) and third, to explore the problems and benefits of the greenhouse analogy. The characteristics of relations, rather than objects, must be mapped according to the principle of systematicity, but the public tends to preserve the attributes of the base domain, which is mapped relatively easily. In conclusion, certain facets of the prevailing greenhouse analogy cause a distorted public view of climate change. We must use the greenhouse analogy and yet simultaneously emphasize the relations and attributes highlighted and hidden in the analogy during evaluation. (shrink)

How are pictures to be individuated from other kinds of representations, such as linguistic representations? The traditional view is that a picture represents what it represents because it resembles it. Thus, the so-called “resemblance” theory has been the dominant view in understanding pictorial representation. More recently, however, the basis of this view has been brought into question; several philosophers have tried to provide the right theory of pictorial (or iconic) representations. Flint Schier is one of them. He tries to explain (...) pictorial representations in terms of what he calls “natural generativity” in his book, Deeper Into Pictures. In this paper, I will raise a new problem that has never been debated before. Specifically, I will argue that Flint Schier’s individuation of iconic systems is problematic. I will show a counterexample to his method of individuation and argue that he cannot avoid the problem without abandoning one of the core claims of his theory. (shrink)

Role-based database management systems are most widely used for information storage and analysis but are known as vulnerable to insider attacks. The core of intrusion detection lies in an adaptive system, where an insider attack can be judged if it is different from the predicted role by performing classification on the user’s queries accessing the database and comparing it with the authorized role. In order to handle the high similarity of user queries for misclassified roles, this paper proposes a deep (...) metric neural network with strategic sampling algorithm that properly extracts salient features and directly learns a quantitative measure of similarity. A strategic sampling method of heuristically generating and learning training pairs through Monte Carlo search is proposed to select a training pair that can represent the entire dataset. With the TPC-E–based benchmark data trained with 11,000 queries for 11 roles, the proposed model produces the classification accuracy of 95.41%, which is the highest compared with the previous models. The results are verified through comparison of quantitative and qualitative evaluations, and the feature space modelled in the neural network is analysed by t-SNE algorithm. (shrink)

This article discusses three policy ideas that address the limitations of the traditional welfare state: universal basic income (UBI), universal basic services (UBS), and the social economy. As a lens from which to evaluate these policy alternatives, we develop a concept of active citizenship as an interactive and recursive process between people’s equal political influence and the institutional conditions in which they are placed. While the social policy discourse on active citizenship has centred on the debate between increasing individual responsibilities (...) or enhancing people’s capabilities, our conception recentres the political dimension of active citizenship as people’s capacity, not only to exercise individual self-determination, but also collective self-determination over shared conditions. We conclude that, in addition to the conditions for security and autonomy, opportunities for organised social cooperation are necessary to achieve a virtuous cycle between people’s political influence and the institutions that support it. (shrink)

In this paper, we introduce the notions of -fuzzy filters and -fuzzy Boolean filters in R0-algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that a fuzzy set in R0-algebras is an -fuzzy Boolean filter if and only if it is an -fuzzy implicative filter. Finally, we consider the concepts of implication-based fuzzy Boolean filters of R0-algebras.

In this paper, we introduce the notions of -fuzzy filters and -fuzzy Boolean filters in R0-algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that a fuzzy set in R0-algebras is an -fuzzy Boolean filter if and only if it is an -fuzzy implicative filter. Finally, we consider the concepts of implication-based fuzzy Boolean filters of R0-algebras.

ObjectivesHostile attribution bias is reportedly common from non-clinical population to those with serious mental illness, such as schizophrenia, and is known to be closely related to theory of mind. This study aimed to investigate whether ToM skills mediate the relationship among neurocognitive ability, personality traits, and attribution bias.MethodsA total of 198 non-clinical youths were recruited. To assess their neurocognitive ability and ToM skills, the participants were asked to complete Raven’s Standard Progressive Matrices and the Korean version of the Reading the (...) Mind in Eyes Test. To determine their personality traits, the Eysenck Personality Questionnaire and interpersonal reactivity index were used. To evaluate hostile attribution bias, the Ambiguous Intentions Hostility Questionnaire was administered. Path analysis and bias-corrected percentile bootstrap methods were used to estimate model fit and the parameters of the mediating effects.ResultsBased on model comparison, the best model characterized two direct pathways from psychoticism and the K-RMET to hostility attribution bias and three indirect pathways, wherein SPM, perspective taking, and psychoticism influenced hostile attribution bias through K-RMET. The final model fit indices were good [x2/df = 1.126; comparative fit index = 0.996; root mean square error of approximation = 0.026; standard root mean square residual = 0.026 and Akaike information criterion = 28.251] and the K-RMET fully mediated the association between SPM, perspective taking, psychoticism, and hostile attribution bias.ConclusionThe main findings suggested that ToM skills, such as the RMET, play an important role in explaining the relationship among neurocognitive ability, personality traits, and hostile attribution bias. ToM skills and a remediation strategy may need to be developed to balance the enhanced hostility bias that underlies the paranoia. (shrink)

Purpose The debate about the end-of-life care decision is becoming a serious ethical and legal concern in the Far-Eastern countries of Korea, China and Japan. However, the issues regarding end-of-life care will reflect the cultural background, current medical practices and socioeconomic conditions of the countries, which are different from Western countries and between each other. Understanding the genuine thoughts of patients who are critically ill is the first step in confronting the issues, and a comparative descriptive study of these perspectives (...) was conducted by collaboration between researchers in all three countries. Methods Surveys using self-reporting paper questionnaire forms were conducted from December 2008 to April 2009 in Korea (six hospitals in two regions), China (five hospitals in four regions) and Japan (nine hospitals in one region). The subjects were patients who were critically ill who had been diagnosed as having cancer. A total of 235 participants (Korea, 91; China, 62; Japan, 52) were eventually recruited and statistically analysed. Results Most respondents had sometimes or often thought of their own death, mostly fear of ‘separation from loved ones’. They wanted to hear the news regarding their own condition directly and frankly from the physician. A quarter of them preferred making end-of-life care decisions by themselves, while many respondents favoured a ‘joint decision’ with their family members. The most favoured proxy decision maker was the spouse, followed by the children. Most admitted the necessity of ‘advance directives’ and agreed with artificial ventilation withdrawal in irreversible conditions. The most common reason was ‘artificial prolongation of life is unnecessary’. Most respondents agreed with the concept of active euthanasia; however, significant differences were sometimes observed in the responses according to variables such as patient's country of origin, age, gender and education level. Conclusion Patients in Far-Eastern countries gave various responses regarding end-of-life care decisions. Although familial input is still influential, most patients think of themselves as the major decision maker and accept the necessity of advance directives with Westernization of the society. Artificial ventilation withdrawal and even active euthanasia may be acceptable to them. (shrink)