As is well known, any preorder R on a set U induces an Alexandrov topology on U. In some interesting cases related to data mining an Alexandrov topology can be transformed into different types of logico-algebraic models. In some cases, (pre)topological operators provided by Pointless Topology may define a topological space on U even if R is not a preorder. If this is the case, then we call R a crypto-preorder. The paper studies the conditions under which a relation R (...) is a crypto-preorder and how to transform a crypto-preorder into a proper preorder. (shrink)

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)

Both neutrosophic sets theory and rough sets theory are emerging as powerful tool for managing uncertainty, indeterminate, incomplete and imprecise information .In this paper we develop an hybrid structure called “ rough neutrosophic sets” and studied their properties.

In writing papers, students confront two obstacles. First, they may not know what philosophical writing is, mistaking an extended statement of their opinion for a philosophy paper. Second, some students lack certain key writing skills and so have difficulty organizing and conveying their view on a philosophical issue. In addition to reading good philosophical works, students need practice writing, editing, and revising their work and so rough drafts become a key component in teaching philosophical writing. This paper outlines the traditional (...) procedure for rough drafts, highlights some difficulties with this approach, and then details an alternative approach that is advantageous in several ways. In addition, an example classroom handout is provided that introduces this alternative procedure. (shrink)

There are various recent efforts to broaden applications of ontologies with vague knowledge, motivated in particular by applications of bio(medical)-ontologies, as well as to enhance rough set information systems with a knowledge representation layer by giving more attention to the intension of a rough set. This requires not only representation of vague knowledge but, moreover, reasoning over it to make it interesting for both ontology engineering and rough set information systems. We propose a minor extension to OWL 2 DL, called (...) rOWL, and define the novel notions of rough subsumption reasoning and classification for rough concepts and their approximations. (shrink)

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.

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

Recently, big data analytics have gained significant attention in healthcare industry due to generation of massive quantities of data in various forms such as electronic health records, sensors, medical imaging, and pharmaceutical details. However, the data gathered from various sources are intrinsically uncertain owing to noise, incompleteness, and inconsistency. The analysis of such huge data necessitates advanced analytical techniques using machine learning and computational intelligence for effective decision making. To handle data uncertainty in healthcare sector, this article presents a novel (...) metaheuristic rough set-based feature selection with rule-based medical data classification technique on MapReduce framework. The proposed MRSFS-RMDC technique designs a butterfly optimization algorithm for minimal rough set selection. In addition, Hadoop MapReduce is applied to process massive quantity of data. Moreover, a rule-based classification approach named Repeated Incremental Pruning for Error Reduction is used with the inclusion of a set of conditional rules. The RIPPER will scale in a linear way with the number of training records utilized and is suitable to build models with data uncertainty. The proposed MRSFS-RMDC technique is validated using benchmark dataset and the results are inspected under varying aspects. The experimental results highlighted the supremacy of the MRSFS-RMDC technique over the recent state of art methods in terms of different performance measures. The proposed methodology has achieved a higher F-score of 96.49%. (shrink)

Back to the Rough Ground is a philosophical investigation of practical knowledge, with major import for professional practice and the ethical life in modern society. Its purpose is to clarify the kind of knowledge that informs good practice in a range of disciplines such as education, psychotherapy, medicine, management, and law. Through reflection on key modern thinkers who have revived cardinal insights of Aristotle, and a sustained engagement with the Philosopher himself, it presents a radical challenge to the scientistic assumptions (...) that have dominated how these professional domains have been conceived, practiced, and institutionalized. (shrink)

Informal justice often is castigated as rough justice, procedurally unauthorized and substantively unrationalized and prone to error. Yet those same features are present, to some extent, in formal justice as well: they do not form the basis for any sharp categorical contrast between formal and informal justice. Furthermore, some roughness in justice may be no bad thing. Certain of those elements of roughness in formal justice are inextricably bound up with other features of formal justice that are rightly (...) deemed morally important. And rough informal justice can sometimes be used to change formal justice in more just directions. (shrink)

Information is considered to be the major part of an organization. With the enhancement of technology, the knowledge level is increasing with the passage of time. This increase of information is in volume, velocity, and variety. Extracting meaningful insights is the dire need of an individual from such information and knowledge. Visualization is a key tool and has become one of the most significant platforms for interpreting, extracting, and communicating information. The current study is an endeavour toward data modelling and (...) user knowledge by using a rough set approach for extracting meaningful insights. The technique has used different rough set algorithms such as K-nearest neighbours, decision rules, decomposition tree, and local transfer function classifier for an experimental setup. The approach has found its accuracy for the optimal use of data modelling and user knowledge. The experimental setup of the proposed method is validated by using the dataset available in the UCI web repository. Results of the proposed study show that the model is effective and efficient with an accuracy of 96% for KNN, 87% for decision rules, 91% for decision trees, 85.04% for cross validation architecture, and 94.3% for local transfer function classifier. The validity of the proposed classification algorithms is tested using different performance metrics such as F-score, precision, accuracy, recall, specificity, and misclassification rates. For all these performance metrics, the KNN classifier outperformed, and this high performance shows the applicability of the KNN classifier in the proposed problem. (shrink)

David Carr; Roughing Out the Ground Rules: reason and experience in practical deliberation, Journal of Philosophy of Education, Volume 29, Issue 1, 30 May 2006.

Rough polyadic modal logics, introduced in the paper, contain modal operators of many arguments with a relational semantics, based on the Pawlak's rough set theory. Rough set approach is developed as an alternative to the fuzzy set philosophy, and has many applications in different branches in Artificial Intelligence and theoretical computer science.

This Paper combines interval- valued neutrouphic sets and rough sets. It studies roughness in interval- valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower and upper approximations of interval valued neutrosophic sets.

The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (indiscernibility) relation R U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the "elementary" (...) sets are not mutually disjoint, but all the theory of generalized rough sets can be developed in analogy with the standard Pawlak approach. On the power set of the universe, the algebraic structure of the quasi fuzzy-intuitionistic "classical" (BZ) lattice is introduced and the sets of all "closed" and of all "open" definable sets with the associated complete (in general nondistributive) ortholattice structures are singled out. (shrink)

The present paper deals with the problem of evaluating empirical evidence for therapeutic decisions in medicine. The article discusses the views of Nancy Cartwright and John Worrall on the function that randomization plays in ascertaining causal relations with reference to the therapies applied. The main purpose of the paper is to present a general idea of alternative method of evaluating empirical evidence. The method builds on data analysis that makes use of rough set theory. The first attempts to apply the (...) method show that it is an interesting alternative to randomized controlled trials. (shrink)

In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix). With the strong semantics, where only the value t is (...) treated as designated, the above logic is a “common denominator” for Kleene and Łukasiewicz 3-valued logics, which represent its two different “determinizations”. In turn, the weak semantics—where both t and u are treated as designated—represents such a “common denominator” for two major 3-valued paraconsistent logics. We give sound and complete, cut-free sequent calculi for both versions of the logic generated by the rough set Nmatrix. Then we derive from these calculi sequent calculi with the same properties for the various “determinizations” of those two versions of the logic (including Łukasiewicz 3-valued logic). Finally, we show how to embed the four above-mentioned determinizations in extensions of the basic rough set logics obtained by adding to those logics a special two-valued “definedness” or “crispness” operator. (shrink)

This paper considers Pindar's diverse appropriations of elements of the sacred topography of Aegina for different purposes in epinikia composed for Aeginetan victors. It focuses on poems likely performed in the vicinity of the Aiakeion for their different mobilizations of a monument that we know from Pausanias stood beside the Aiakeion—the tomb of Phokos, an earth mound topped with the “rough stone” that killed him. The more speculative final part of the paper suggests that it may also be possible to (...) track a coherent ideology attached to the island's sacred topography across several Aeginetan odes, thereby detecting a broader structural unity that accompanies and frames the different individual appropriations of different poems. This part starts from Pausanias’ mythic narrative of the exemplary justice of Aiakos banishing his own son Telamon as the aetiology for a distinctive Aeginetan justice system inscribed in a whole set of man-made monuments that ring the island with concentric circles of rough stones. (shrink)

Chakraborty and Banerjee have introduced a rough consequence logic based on the modal logic S5. This paper shows that rough consequence logics, with many of the same properties, can be based on modal logics as weak as K, with a simpler formulation than that of Chakraborty and Banerjee. Also provided are decision procedures for the rough consequence logics and equivalences and independence relations between various systems S and the rough consequence logics, based on them. It also shows that each logic, (...) based on such an S, is theorem equivalent, but not necessarily equivalent, to the modal logic M-S. The paper also shows that rough consequence logic, which was designed to handle rough equality, is somewhat limited for that purpose. (shrink)

In the paper, we study connections between rough concept lattices and domains. The main result is representation theorems of complete lattices and algebraic lattices by concepts based on Rough Set Theory. It is shown that there is a deep relationship between Rough Set Theory and Domain Theory.

Labels provide a quick and effective solution to obtain people interesting content from large-scale social network information. The current interest label extraction method based on the subgraph stream proves the feasibility of the subgraph stream for user label extraction. However, it is extremely time-consuming for constructing subgraphs. As an effective mathematical method to deal with fuzzy and uncertain information, rough set-based representations for subgraph stream construction are capable of capturing the uncertainties of the social network. Therefore, we propose an effective (...) approach called RS_UNITE_SS, which is suitable for large-scale social network user interest label extraction. Specifically, we first propose the subgraph division algorithm to construct a subgraph stream by incorporating a rough set. Then, the algorithm for user real-time interest label extraction based on upper approximation is proposed by using sequentially characteristics of the subgraph. Empirically, we evaluate RS_UNITE_SS over real-world datasets, and experimental results demonstrate that our proposed approach is more computationally efficient than existing methods while achieving higher precision value and MRR value. (shrink)

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.

What exactly is a “wicked problem”? It is a social or economic problem that is so complex and so interconnected with other issues that it is extraordinarily difficult or impossible to resolve. This is because all proposed resolutions generate equally complex, equally wicked problems. In this essay, I argue that precision medicine, especially in the context of the U.S. healthcare system, generates numerous wicked problems related to distributive justice. Further, I argue that there are no easy solutions to these wicked (...) problems. The need for trade-offs is inescapable. Rough justice is the best outcome we can hope for, and that outcome requires a commitment to processes of public reason that are fair and inclusive. (shrink)

In this paper, we present a modality-free pre-rough algebra. Łukasiewicz Moisil algebra and Wajsberg algebra are equivalent under a transformation. A similar type of equivalence exists in our proposed definition and standard definition of pre-rough algebra. We obtain a few modality-free algebras weaker than pre-rough algebra. Furthermore, it is also established that modality-free versions for other analogous structures weaker than pre-rough algebra do not exist. Both Hilbert-type axiomatization and sequent calculi for all proposed algebras are presented.

When it comes to making decisions in vague problems, rough is one of the best tools to help analyzers. So based on rough and hoop concepts, two kinds of approximations (Lower and Upper) for filters in hoops are defined, and then some properties of them are investigated by us. We prove that these approximations- lower and upper- are interior and closure operators, respectively. Also after defining a hyper operation in hoops, we show that by using this hyper operation, set of (...) all rough filters is monoid. For more study, we define the implicative operation on the set of all rough filters and prove that this set with implication and intersection is made a hoop. (shrink)

In this paper, we first defined soft intervalvalued neutrosophic rough sets(SIVN- rough sets for short) which combines interval valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of soft interval valued intuitionistic fuzzy rough sets( SIVIF- rough sets). Finally an illustartive example is given to verfy the developped algorithm and to demonstrate its practicality and effectiveness.

The work broadens – to a considerable extent – Z. Pawlak’s original method (1982, 1992) of approximation of sets. The approximation of sets included in a universum U goes on in the contextual approximation space CAS which consists of: 1) a sequence of Pawlak’s approximation spaces (U,Ci), where indexes i from set I are linearly ordered degrees of contexts (I, <), and Ci is the universum partition U, 2) a sequence of binary relations on sets included in U, relations called (...) context relations indexed with degrees of contexts. The introduction of relations of contexts of sets was inspired by the work of W. Ziarnko (1993). Intuitively, set X is the context of set Y to the degree i, when on the basis of knowledge of the elements of set X we can obtain knowledge about the belonging of these elements to set Y to the degree i which is a degree of uncertainty or ambiguity, or inaccuracy. The operations of approximation of sets Ci-, BNi, Ci+, called lower approximation of the degree i, boundary of the degree i, upper approximation of the degree i, are formulated in a way which is analogous with the systems of Pawlak’s approximation, by expanding their formulas accordingly. In the next part of the work, it is shown (in an analogous way to Bryniarski’s work (1989)) that one can define the following operations on contextual rough sets: the union of contextual rough sets, the intersection of contextual rough sets and the complement of contextual rough set. It is proved that the algebra of contextual rough sets is a ditributive lattice with a unit and with a zero. On the basis of the results presented above the problem of defining operations on contextual rough sets by membership relations (Bryniarski 1989) may be formulated analogously to the classical operations on sets. (shrink)

Alstin, Zac Conventional wisdom teaches that prohibition is counter-productive. We are all familiar with the idea that making something illegal - whether it be drug abuse, alcohol consumption, or abortion - merely 'drives it underground'. Abortion is indeed one of the most potent examples, with the spectre of 'backyard abortion' haunting any talk of restricting abortion access. On a global scale the term 'unsafe abortion' serves the same purpose - reinforcing the idea that unless abortion is made safe, legal, and (...) easy to access, women will resort to abortion practices that are intrinsically unsafe. (shrink)

Rough Sets were introduced by Z. Pawlak in the year 1982 with the intention to address knowledge representation and data processing from the angle of computation and decision making. The main idea...

In qualitative research into emotions, researchers and participants share emotion-laden interactions. Few demonstrate how the analytic value of emotions may be harnessed. In this article we provide an account of our emotional experiences conducting research with two groups: adults living with cystic fibrosis and spouse caregivers of cancer patients. We describe our emotion work during research interviews, and discuss its methodological and theoretical implications. Reflections depict competing emotion norms in qualitative research. Experiences of vulnerability and involuntary “emotional callusing” illustrate the (...) insight into participants’ experiences afforded to us through emotion work. This prompted us to extend Hochschild’s theory to incorporate unconscious activity mediated through habitus, allowing us to demonstrate how the “emotional” nature of emotions research can galvanize analytic insight. (shrink)

The rough set theory has interesting properties such as that a rough set is considered as distinct sets in distinct knowledge bases, and that distinct rough sets are considered as one same set in a certain knowledge base. This leads to a significant philosophical interpretation: a concept (or phenomenon) may be understood as different ones in different philosophical perspectives, while different concepts (or phenomena) may be understood as a same one in a certain philosophical perspective. Such properties of rough set (...) theory produce a mathematical model to support critical realism and the theory ladenness of observation in the philosophy of science. (shrink)

Rough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It is additionally shown that (...) co-granular or point-wise approximations defined by σ-ideals/filters (for an arbitrary relation σ) fit easily into the entire scheme. Concepts of the rationality of objects (vague or crisp) and their types are introduced and are shown to be applicable to most general rough sets by the present author. Surprising results on these are proved on these by her in this part of the research paper. The present paper is the first of a three part study on the topic. (shrink)

In this article I explore how cosmopolitanism can be a challenge for ordinary language philosophy. I also explore cosmopolitan aspects of Stanley Cavell’s ordinary language philosophy. Beginning by considering the moral aspects of cosmopolitanism and some examples of discussions of cosmopolitanism in philosophy of education, I turn to the scene of instruction in Wittgenstein and to Stanley Cavell’s emphasis on the role of autobiography in philosophy. The turn to the autobiographical dimension of ordinary language philosophy, especially its use of “I” (...) and “We”, becomes a way to work on the tension between the particular and the universal claims of cosmopolitanism. I show that the autobiographical aspects of philosophy and the philosophical significance of autobiographical writing in ordinary language philosophy can be seen as a test of representativeness—a test of the ground upon which one stands when saying “I”, “We” and “You.”. (shrink)