In this book the authors introduce and study the following notions: Neutrosophic Crisp Points, Neutrosophic Crisp Relations, Neutrosophic Crisp Sets, Neutrosophic Set Generated by (Characteristic Function), alpha-cut Level for Neutrosophic Sets, Neutrosophic Crisp Continuous Function, Neutrosophic Crisp Compact Spaces, Neutrosophic Crisp Nearly Open Sets, Neutrosophic Crisp Ideals, Neutrosophic Crisp Filter, Neutrosophic Crisp Local Functions, Neutrosophic Crisp Sets via (...) class='Hi'>Neutrosophic Crisp Ideals, Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity, Neutrosophic Topological Region, Neutrosophic Closed Set and Neutrosophic Continuous Function, etc. They compute the distances between neutrosophic sets and extend it to Neutrosophic Hesitancy Degree. The authors also generalize the Crisp Topological Space and Intuitionistic Topological Space to the notion of Neutrosophic Crisp Topological Space. At the end, they present applications to Neutrosophic Database, and show a security scheme based on Public Key Infrastructure (PKI) using Neutrosophic Logic Manipulation. The authors utilize neutrosophic sets in order to analyze social networks data conducted through learning activities, and for the Geographical Information Systems (GIS) they employ fundamental concepts and properties of a Neutrosophic Spatial Region. Keywords: Neutrosophic Crisp Points; Neutrosophic Crisp Relations; Neutrosophic Crisp Sets; Neutrosophic Crisp Continuous Function; Neutrosophic Crisp Compact Spaces; Neutrosophic Crisp Nearly Open Sets; Neutrosophic Crisp Ideals; Neutrosophic Crisp Filter; Neutrosophic Crisp Local Functions; Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals; Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity; Neutrosophic Topological Region; Neutrosophic Closed Set and Neutrosophic Continuous Function; Neutrosophic Hesitancy Degree; Neutrosophic Crisp Topological Space; Neutrosophic Database; Neutrosophic Logic Manipulation; Neutrosophic Spatial Region. (shrink)

The neutrosophic sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these the concepts to define a new types of neutrosophic crisp closed sets and limit points in neutrosophic crisp topological space, namly [neutrosophic crisp Gem sets and neutrosophic crisp Turig points] respactvely, we stady their properties in details and join it with topological concepts. Finally we used [ (...) class='Hi'>neutrosophic crisp Gem sets and neutrosophic crisp Turig points] to introduce of topological concepts as: neutrosophic crisp closed (open) sets, neutrosophic crisp closure, neutrosophic crisp interior, neutrosophic crisp extrior and neutrosophic crisp boundary which are fundamental for further reserch on neutrosophic crisp topology and will setrengthen the foundations of theory of neutrosophic topological spaces. (shrink)

In this paper, we generalize the crisp topological spaces to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology.

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the (...) neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Indeterminacy is different from randomness. Indeterminacy can be caused by physical space, materials and type of construction, by items involved in the space, or by other factors. In 1965 [51], Zadeh generalized the concept of crisp set by introducing the concept of fuzzy set, corresponding to the situation in which there is no precisely defined set;there are increasing applications in various fields, including probability, artificial intelligence, control systems, biology and economics. Thus, developments in abstract mathematics using the idea of fuzzy sets possess sound footing. In accordance, fuzzy topological spaces were introduced by Chang [12] and Lowen [33]. After the development of fuzzy sets, much attention has been paid to the generalization of basic concepts of classical topology to fuzzy sets and accordingly developing a theory of fuzzy topology [1-58]. In 1983, the intuitionistic fuzzy set was introduced by K. Atanassov [55, 56, 57] as a generalization of the fuzzy set, beyond the degree of membership and the degree of non-membership of each element. In 1999 and 2002, Smarandache [71, 72, 73, 74] defined the notion of Neutrosophic Sets, which is a generalization of Zadeh’s fuzzy set and Atanassov's intuitionistic fuzzy set. Some neutrosophic concepts have been investigated by Salama et al. [61-70]. Forwarding the study of neutrosophic sets, this book consists of seven chapters, targeting to:  generalize the previous studies in [1-59], and[91-94] so to define the neutrosopic crisp set and neutrosophic set concepts;  discuss their main properties; A. A. Salama & Florentin Smarandache  introduce and study some concepts of neutrosophic crisp and neutrosophic topological spaces and deduce their properties;  deduce many types of functions and give the relationships between different neutrosophic topological spaces, which helps to build new properties of neutrosophic topological spaces;  stress once more the importance of Neutrosophic Ideal as a nontrivial extension of neutrosophic set and neutrosophic logic [71, 72, 73, 74];  propose applications on computer sciences by using neutrosophic sets. (shrink)

In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.

In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.

In this paper, we introduce the concept of ""neutrosophic crisp neighborhoods system for the neutrosophic crisp point ". Added to, we introduce and study the concept of neutrosophic crisp local function, and construct a new type of neutrosophic crisp topological space via neutrosophic crisp ideals. Possible application to GIS topology rules are touched upon.

In this paper, we introduce and study the concept of" neutrosophic closed set" and" neutrosophic continuous function". Possible application to GIS topology rules are touched upon.

In this paper, multi attribute decision making problem based on grey relational analysis in neutrosophic cubic set environment is investigated. In the decision making situation, the attribute weights are considered as single valued neutrosophic sets. The neutrosophic weights are converted into crisp weights. Both positve and negative GRA coefficients, and weighted GRA coefficients are determined. Hamming distances for weighted GRA coefficients and standard (ideal) GRA coefficients are determined. The relative closeness coefficients are derived in order to (...) rank the alternatives. The relative closeness coefficients are designed in ascending order. Finally, a numerical example is solved to demonstrate the applicability of the proposed approach. (shrink)

The purpose of this paper is to introduce new types of neutrosophic crisp sets with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties, and discussed the relationship between neutrosophic crisp sets and others. Also, we introduce and study the neutrosophic crisp point and neutrosophic crisp relations. Possible applications to database are touched upon.

The n-th PowerSet is used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. Neutrosophic set has been derived from (...) a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. This first volume collects original research and applications from different perspectives covering different areas of neutrosophic studies, such as decision-making, neutroalgebra, neutro metric, and some theoretical papers. (shrink)

In this paper, we presented antoher concept of neutrosophic open sets called neutrosophic semi-α-open sets and studied their fundamental poperties in neutrosophic topological spaces. We also present neutrospohic semi-α-interior and neutrosophic semi-α-closure and study some of their fundamental properties.

The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.

In this paper, we defined (I,T) − standard neutrosophic rough sets based on an implicator I and a t-norm T on I; lower and upper approximations of standard neutrosophic sets in a standard neutrosophic approximation are defined. Some properties of (I,T) − standard neutrosophic rough sets are investigated. We consider the case when the neutrosophic components (truth, indeterminacy, and falsehood) are totally dependent, single-valued, and hence their sum is ≤ 1.

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and (...) for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined be-tween each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. (shrink)

In this paper we introduce the concept of interval valued neutrosophic soft topological space together with interval valued neutrosophic soft finer and interval valued neutrosophic soft coarser topology. We also define interval valued neutrosophic interior and closer of an interval valued neutrosophic soft set. Some theorems and examples are cites. Interval valued neutrosophic soft subspace topology are studied. Some examples and theorems regarding this concept are presented.

The concept of neutrosophic locally compact and neutrosophic compact open topology are introduced and some interesting propositions are discussed.

Enterprise resource planning (ERP) has a significant impact on modern businesses by enhancing productivity, automation, and streamlining of business processes, even accounting. Manufacturers can assure proper functioning and timely client demand using ERP software. Coordination, procurement control, inventory control, and dispatch of commodities are all features of supply chain management.

Let κ and λ be infinite cardinals, F a filter on κ, and G a set of functions from κ to κ. The filter F is generated by G if F consists of those subsets of κ which contain the range of some element of G. The set G is $ -closed if it is closed in the $ -topology on κ κ. (In general, the $ -topology on IA has basic open sets all Π i∈ I U (...) i such that, for all $i \in I, U_i \subseteq A$ and $|\{i \in I: U_i \neq A\}| .) The primary question considered in this paper asks "Is there a uniform ultrafilter on κ which is generated by a closed set of functions?" (Closed means $ -closed.) We also establish the independence of two related questions. One is due to Carlson: "Does there exist a regular cardinal κ and a subtree T of $^{ such that the set of branches of T generates a uniform ultrafilter on κ?"; and the other is due to Pouzet: "For all regular cardinals κ, is it true that no uniform ultrafilter on κ is analytic?" We show that if κ is a singular, strong limit cardinal, then there is a uniform ultrafilter on κ which is generated by a closed set of increasing functions. Also, from the consistency of an almost huge cardinal, we get the consistency of CH + "There is a uniform ultrafilter on ℵ 1 which is generated by a closed set of increasing functions". In contrast with the above results, we show that if κ is any cardinal, λ is a regular cardinal less than or equal to κ and P is the forcing notion for adding at least $(\kappa^{ generic subsets of λ, then in V P , no uniform ultrafilter on κ is generated by a closed set of functions. (shrink)

We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

In this paper we introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies in [9,11] , the important topological neutrosophic ideals has been given in [4]. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to fiind new neutrosophic topology from the original one in [8]. The basic structure, especially a basis (...) for such generated neutrosophic topologies and several relations between different topological neutrosophic ideals and neutrosophic topologies are also studied here. Possible application to GIS topology rules are touched upon. -/- . (shrink)

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements (...) are characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets. (shrink)

We show that the set of points of an overt closed subspace of a metric completion of a Bishop-locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop-compact. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

In this paper, we introduce and investigate a new class of sets and functions between topological space called neutrosophic semi-supra open set and neutrosophic semi-supra open continuous functions respectively.

A rough fuzzy set is the result of the approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets and standard neutrosophic information system, and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets.

If there is a homeomorphic embedding of one set into another, the sets are said to be topologically comparable. Friedman and Hirst have shown that the topological comparability of countable closed subsets of the reals is equivalent to the subsystem of second order arithmetic denoted byATR 0. Here, this result is extended to countable closed locally compact subsets of arbitrary complete separable metric spaces. The extension uses an analogue of the one point compactification of ℝ.

Aristotle's Nicomachean Ethics, based on lectures that he gave in Athens in the fourth century BCE, is one of the most significant works in moral philosophy, and has profoundly influenced the whole course of subsequent philosophical endeavour. It is soundly located within a philosophical tradition, but its argument differs markedly from those of Plato and Socrates in its emphasis on the exercise - as opposed to the mere possession - of virtue as the key to human happiness, offering seminal discussions (...) of ethical issues that are practical in their intent. Topics covered include the role of luck in human wellbeing, moral education, responsibility, courage, justice, moral weakness, friendship and pleasure. This accessible new translation by Roger Crisp follows the Greek text closely and also provides a non-Greek-reader with the flavour of the original. The volume also includes a historical and philosophical introduction and notes on further reading. (shrink)

In his recent paper on Aristotelian dialectic, Professor Hamlyn claims that ‘what may be important for Aristotle's purposes is not the truth but the acceptance of the truth’ . Dialectic is protreptic, and not strictly philosophical, spadework: ‘[t]he appeal to endoxa is, as it were, a setting of the scene, providing the context for argument out of which, it is hoped, will emerge the insights from which demonstration and thus further understanding can follow’.

This paper is a discussion of Jonathan Dancy's book Ethics Without Principles (2004). Holism about reasons is distinguished into a weak version, which allows for invariant reasons, and a strong, which doesn't. Four problems with Dancy's arguments for strong holism are identified. (1) A plausible particularism based on it will be close to generalism. (2) Dancy rests his case on common-sense morality, without justifying it. (3) His examples are of non-ultimate reasons. (4) There are certain universal principles it is hard (...) not to see as invariant, such as that the fact that some action causes of suffering to a non-rational being always counts against it. The main difficulty with weak holism is that justification can be seen as analogous to explanation, which will give us an atomistic and generalist conception of a normative reason. Key Words: Dancy • generalism • holism • particularism • reasons. (shrink)

We consider interpretable topological spaces and topological groups in a p-adically closed field K. We identify a special class of “admissible topologies” with topological tameness properties like generic continuity, similar to the topology on definable subsets of Kn. We show that every interpretable set has at least one admissible topology, and that every interpretable group has a unique admissible group topology. We then consider definable compactness (in the sense of Fornasiero) on interpretable groups. We show that an interpretable group (...) is definably compact if and only if it has finitely satisfiable generics (fsg), generalizing an earlier result on definable groups. As a consequence, we see that fsg is a definable property in definable families of interpretable groups, and that any fsg interpretable group defined over Qp is definably isomorphic to a definable group. (shrink)

Someone once told me that the average number of readers of a philosophy article is about six. That is a particularly depressing thought when one takes into account the huge influence of certain articles. When I think of, say, Gettier's article on knowledge, or Quine's ‘Two Dogmas’, I begin to wonder whether anyone is ever likely to read anything I write. Usually the arguments of these very influential articles have been subjected to widespread analysis and interpretation. The case of Elizabeth (...) Anscombe's ‘Modern Moral Philosophy’, published in 1958, is something of an exception. That article has played a significant part in the development of so-called ‘virtue ethics’, which has burgeoned over the last three decades in particular. But there has been less close attention to its arguments than one might have expected. (shrink)

This paper concerns the relation between goodness, or value, and practical reasons, and in particular the so-called ‘buck-passing’ account (BPA) of that relation recently offered by T. M. Scanlon, according to which goodness is not reason-providing but merely the higher-order property of possessing lower-order properties that provide reasons to respond in certain ways. The paper begins by briefly describing BPA and the motivation for it, noting that Scanlon now accepts that the lower-order properties in question may be evaluative. He also (...) insists that the BPA is not biconditional (wisely, since otherwise goodness becomes a ‘Cambridge property’), which leaves him with the task of explaining why goodness arises only in a sub-set of cases in which lower-order properties ground reasons. Having rejected two attempts to do this, based on elucidation of the responses and of the reasons, I suggest that Scanlon may claim that goodness arises in, and only in, cases where the lower-order properties are evaluative and that goodness itself provides us with a way of distinguishing the evaluative from the non-evaluative. In other words, he should retain the negative component of BPA, according to which being good is not itself reason-providing, while surrendering the positive, according to which the property of goodness is merely the higher-order property of having lower-order properties that provide reasons to respond. CiteULike Connotea Del.icio.us What's this? (shrink)

We consider semi‐algebraic sets and properties of these sets that are expressible by sentences in first‐order logic over the reals. We are interested in first‐order properties that are invariant under topological transformations of the ambient space. Two semi‐algebraic sets are called topologically elementarily equivalent if they cannot be distinguished by such topological first‐order sentences. So far, only semi‐algebraic sets in one and two‐dimensional space have been considered in this context. Our contribution is a natural characterisation of topological elementary equivalence of (...) regular closed semi‐algebraic sets in three‐dimensional space, extending a known characterisation for the two‐dimensional case. Our characterisation is based on the local topological behaviour of semi‐algebraic sets and the key observation that topologically elementarily equivalent sets can be transformed into each other by means of geometric transformations, each of them mapping a set to a first‐order indistinguishable one. (shrink)

The atonement is one of the central and defining doctrines of Christian theology. Yet the nature of the atonement – how it is that Christ's life and death on the cross actually atone for human sin – remains a theological conundrum. This article offers a new argument for an old theory of the atonement, namely, penal substitution. First, it sets out the theological context for the argument. This involves giving some account of alternative theories of the atonement in the tradition, (...) and why penal substitution might be thought a particularly appealing way of thinking about the atonement. The article then presents an argument for a version of penal substitution that involves the application of an idea found in some Augustinian accounts of the transmission of sin from Adam to his progeny. At the end of this exposition, it offers some brief comments on the metaphysics undergirding the theology of this argument. The final section discusses several theological and philosophical objections to this reasoning. (shrink)

The last few years have seen a remarkable revival of interest in the virtues, which have regained their central role in moral philosophy. This thought-provoking new collection is a much-needed survey of virtue ethics and virtue theory. The specially commissioned articles by an international team of philosophers represent the state of the art in this subject and will set the agenda for future work in the area. The contributors--including Lawrence Blum, John Cottingham, Julia Driver, Rosalind Hursthouse, Terence Irwin, Susan Moller (...) Okin, Onora O'Neill, Michael Slote, Michael Stocker, and David Wiggins--cover practical virtue ethics, ancient views of the virtues, impartiality and partiality, Kant, utilitarianism, human nature, natural and artificial virtues, virtue and the good life, the vices, emotions, politics, feminism, moral education, and community. (shrink)

Available from UMI in association with The British Library. Requires signed TDF. ;The thesis consists in the development and application of an ideal utilitarian moral theory. ;In chapter one, classical Mental State and modern Desire theories of prudential value are rejected. In chapter two, perfectionism is rejected and an alternative ideal utilitarian Objective List theory is set out. In chapter three, it is argued that prudential rationality requires maximization and temporal neutrality. The aggregation and incommensurability of values is discussed. In (...) chapter four, it is argued that value alone gives rise to grounding reasons for action; the only values are prudential values; we are required to be personally as well as temporally neutral; moral rationality is maximizing. A problem arising when a certain form of incommensurability is combined with the notion of maximizing expected utility is examined. In chapter five, an intrapersonally indirect form of moral theory is defended. ;In the second, practical part of the thesis, the theory developed in the first part is applied to two moral problems: vegetarianism and future generations. In chapter six, the conclusion is that utilitarianism requires us to eat non-intensively-reared meat and to abstain from intensively reared meat. In chapter seven, population problems arising from Derek Parfit's work are considered in the light of the theory. (shrink)

The concept of divine justice has been the subject of considerable scrutiny in recent philosophical theology, as it bears upon the notion of punishment with respect to the doctrine of eternal damnation. In this essay, I set out a version of the traditional retributive view of divine punishment and defend it against one of the most important and influential contemporary detractors from this position, Thomas Talbott. I will show that, contrary to Talbott’s argument, punishment may satisfy divine justice, and that (...) perfect justice is commensurate with retribution, rather than, as he suggests, reconciliation and restoration. (shrink)

Although there is now some recognition that sexual abuse, particularly that which occurs in religious settings, has spiritual implications for women who have been abused, the spiritual implications of sexual abuse which occurs beyond the confines of specific religious practices and beliefs tend not to be acknowledged. Taking a stance that all people, irrespective of their involvement in a formal religion, are inherently spiritual, this paper identifies the key concepts associated with spirituality as meaning, identity, connectedness, transformation and transcendence. Examples (...) as to how each of these may be issues following the experience of sexual abuse are provided. This approach challenges prevailing notions that sexual abuse only has spiritual implications for women who identify with a particular religious tradition. Instead it is argued that an experience of sexual abuse can be critical for the spiritual life of any woman who is subjected to abuse. (shrink)

In this article I assess the coherence of Jonathan Edwards's doctrine of divine simplicity as an instance of an actus purus account of perfect-being theology. Edwards's view is an idiosyncratic version of this doctrine. This is due to a number of factors including his idealism and the Trinitarian context from which he developed his notion of simplicity. These complicating factors lead to a number of serious problems for his account, particularly with respect to the opera extra sunt indivisa principle. I (...) conclude that Edwards sets out an interesting and subtle version of the doctrine, but one which appears mired in difficulties from which he is unable to extract himself. (shrink)

In recent systematic theology versions of the Ransom account of the atonement have proliferated. Much of this work uses Gustav Aulén's Christus Victor as a point of departure. In this paper I first distinguish between models and theories of atonement. Then I discuss three recent theological perorations of the Ransom model as a prelude to setting out four interpretive strategies for understanding this view of atonement. I then offer some critical remarks on these strategies, concluding that the Ransom view as (...) set forth here does not provide a complete model of atonement. (shrink)

This paper argues against Martin Peterson in favour of the ‘standard view’ of rightness, according to which rightness does not come in degrees. It begins with a defence of the standard view against the charge that it is committed to ‘deontic leaps’. It goes on to claim that greater conceptual parsimony would allow Peterson to avoid certain problems involving equality and related matters that arise out of his conception of moral value, and that Peterson should take the same instrumentalist attitude (...) towards the norms of practical rationality as he does towards the norms of common-sense morality. The paper closes with some doubts about Peterson’s programme of consequentialization and its alleged advantages. (shrink)

In this paper, we propose a new technique for the enhancing images. It will work on removing the noise contained in the image as well as improving its contrast based on three different enhancing transforms, we commence by embedding the image into a neutrosophic domain; where the image will be mapped in three different levels, a level of trueness, a level of falseness and a level of indeterminacy. Hence, we act separately on each level using the enhancement transforms. Finally, (...) we introduce a new analysis in the field of analysis and processing of images using the neutrosophic crisp set theory via Mat lab program where has been obtained three images, which helps in a new analysis to improve and retrieve images. (shrink)

The traditional soft set is a mapping from a parameter set to family of all crisp subsets of a universe. Molodtsov introduced the soft set as a generalized tool for modelling complex systems involving uncertain or not clearly defined objects. In this paper, the notion of neutrosophic soft set is reanalysed. The novel theory is a combination of neutrosophic set theory and soft set theory. The complement, “and”, “or”, intersection and union operations are defined on the (...) class='Hi'>neutrosophic soft sets. The neutrosophic soft relations accompanied with their compositions are also defined. The basic properties of the neutrosophic soft sets, neutrosophic soft relations and neutrosophic soft compositions are also discussed. (shrink)

The purpose of this paper is to introduce and study the characteristic function of a neutrosophic set. After given the fundamental definitions of neutrosophic set operations generated by the characteristic function of a neutrosophic set ( Ng for short), we obtain several properties, and discussed the relationship between neutrosophic sets generated by Ng and others. Finally, we introduce the neutrosophic topological spaces generated by Ng . Possible application to GIS topology rules are touched upon.

“Neutrosophics Knowledge” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professional, in good English and Arabic, containing a brief review of a problem and obtained results. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope (...) of neutralities, as well as their interactions with different ideational spectra. (shrink)

Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indetermi nacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI al gebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts of neutrosophic regular filter, neutrosophic closed filter and fuzzy regular filter in pseudo-BCI algebras are introduced, and some basic (...) properties are discussed. Moreover, the relationships among neutrosophic regular filter, fuzzy filters and anti-grouped neutrosophic filters are prese nted, and the results are proved: a neutrosophic filter (fuzzy filter) is a neutrosophic regular filter (fuzzy regular filter), if and only if it is both a neutrosophic closed filter (fuzzy closed filter) and an anti-grouped neutrosophic filter (fuzzy anti-grouped filter). (shrink)