Geometric lattice structure of covering-based rough sets through matroids

Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Geometric lattice has widely used in diverse fields, especially search algorithm design which plays important role in covering reductions. In this paper, we construct four geometric lattice structures of covering-based rough sets through matroids, and compare their relationships. First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by the covering, and its characteristics including atoms, modular elements and modular pairs are studied. We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets. Second, sufficient and necessary conditions for three types of covering upper approximation operators to be closure operators of matroids are presented. We exhibit three types of matroids through closure axioms, and then obtain three geometric lattice structures of covering-based rough sets. Third, these four geometric lattice structures are compared. Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely geometric lattice, to study covering-based rough sets

Transformation Paradox: A Framework for the Analysis of Politics in Enterprise Transformations

The purpose of this research is to develop a theoretical framework for the analysis of politics in enterprise transformations using a dialectical analysis approach (Hegel, 1989; Heraclitus, 1979; Pinkard, 1988; Skinner, 1978a, 1978b) and conduct an evaluation of the framework validity. The framework is constructed using a dialectical analysis of concepts stemming from the work of Alford and Friedland (1992) and considers four theoretical perspectives: autocratic, bureaucratic, pluralistic, and cognitive. The framework is then validated by means of qualitative metrics and adherence to critical ideology. This research addresses the problem that there is no holistic theoretical framework for the analysis of politics across the systemic, situational, and structural contexts found in enterprise transformations. Politics occurs at multiple levels in the enterprise making it difficult to identify the salient issues that need to be addressed in support of transformation. Transformations can be paradoxical as enterprises revert to the dominant paradigm that affirms present realities rather than developing a critical posture to break the constraining paradigm. The dialectical approach used embraces the power of multiple theoretical perspectives in the transformation process, asserting that theories have power over actions, behaviors, and language. The theoretical framework allows for the simultaneous existence of shifting states of cooperation, frustration, and paradigmatic hegemony over systemic, situational, and structural contexts that embody politics in enterprise transformations. Rough set theory is used to demonstrate the ability of the framework to be adaptive and to evolve based on the inclusion of new data. I conclude that the deployment of an evolving framework of this magnitude may have a significant impact on the management of transformation efforts and suggest new areas of research to further the work

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe

Metaphor and mathematics

Traditionally, mathematics and metaphor have been thought of as disparate: the former rigorous, objective, universal, eternal, and fundamental; the latter imprecise, derivative, nearly - if not patently - false, and therefore of merely aesthetic value, at best. A growing amount of contemporary scholarship argues that both of these characterizations are flawed. This dissertation shows that there are important connexions between mathematics and metaphor that benefit our understanding of both. A historically structured overview of traditional theories of metaphor reveals it to be a notion that is complicated, controversial, and inadequately understood; this motivates a non-traditional approach. Paradigmatically shifting the locus of metaphor from the linguistic to the conceptual - as George Lakoff, Mark Johnson, and many other contemporary metaphor scholars do - overcomes problems plaguing traditional theories and promisingly advances our understanding of both metaphor and of concepts. It is argued that conceptual metaphor plays a key role in explaining how mathematics is grounded, and simultaneously provides a mechanism for reconciling and integrating the strengths of traditional theories of mathematics usually understood as mutually incompatible. Conversely, it is shown that metaphor can be usefully and consistently understood in terms of mathematics. However, instead of developing a rigorous mathematical model of metaphor, the unorthodox approach of applying mathematical concepts metaphorically is defended

Being mathematical : an exploration of epistemological implications of embodied cognition

In this thesis I explore epistemological implications of embodied cognition in the hope of developing my apprehension of what it means to think mathematically. I allow my understanding of embodied cognition to emerge in stages, early in the piece laying contrasts against which it may be set, infolding elements to the purpose of qualitatively interpreting data as my thesis finds form. I use the language of autopoiesis to frame an understanding of change in the context of an individual’s learning and also within broader constructs, such as in mathematics classrooms. I recognise dualisms and set them aside in an attempt to reread what it means to think mathematically.Research from a variety of fields constitutes one part of my data, the second part being a selection of experiences drawn from mathematics classes I have taught. In balancing the two, I find that an embodied account contributes a means of interpreting mathematical experience wherein received boundaries, such as between you and me, and categories, such as "number", are not globally robust, and intentionality pervades and shapes the worlds we create.The perspective that embodiment affords my apprehension of mathematical thinking is consistent with a formulation in which judgements of what is good are aligned in part with a kind of aesthetic, whereby being moral is founded in innate dispositions. The question of what one is to do with an embodied epistemology is therefore focused on a consideration of how I am to orient myself to teaching mathematics.Throughout all of this, the locus of my attention remains within the classroom, fixed upon the goal of eliciting perspective and on developing skill in interpreting experience; on becoming a tactful teacher, sensitive to the tacit language of the body

From the Voice to the Violent Act: Language and Violence in Contemporary Drama

Aleks Sierz coined the phrase In-Yer-Face Theatre to categorize a new generation of plays written by a group of upstart playwrights in Britain and America. In addressing these plays, I draw upon recent contributions within the social sciences in order to understand better the interstices of language and violence in this drama. This interdisciplinary approach underscores the social considerations at the heart of these plays. Although frequently criticized for a perceived lack of social consciousness and a seemingly gratuitous use of profanity, prurient sexuality, and graphic violence, these writers in fact continue, and contribute to, a tradition of theater that is serious, ethically based, and socially aware. Specifically, the language represented in these plays is symptomatic of, and complicit in, the violence depicted on stage. I first argue that coercive institutional language subjects the characters in David Mamet\u27s 0leanna to systematic violence long before the infamous moment of violence that concludes the play. The reifying language of consumer capitalism in the plays of Patrick Marber and Mark Ravenhill precipitates violence by rewriting the cultural codes that inform subjectivity and the way that interpersonal relationships are conceived and experienced. Examining the work of David Harrower, Bryony Lavery, David Eldridge, and Tracy Letts, I identify examples of public language and show how they hamper intellectual development and maturity and disengage the cognitive mechanisms that allow individuals to regulate their behavior. I explore the allegiance on the part of those in subcultures of violence to the heavily gendered constructions of identity facilitated by their subcultural languages, and I address the linguistic mechanisms by which the characters in Rebecca Prichard\u27s Fair Game create the sense that violence is necessary. In addition, I interrogate the formal nature of hyper-masculine violence. Finally, in the plays of Martin McDonagh, Judy Upton, and Rebecca Prichard, I discuss the adoption of traditionally male forms of violence by women, focusing on language\u27s role in determining the likelihood and the nature of the violence committed both by and against women

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

Characterising and modeling the co-evolution of transportation networks and territories

The identification of structuring effects of transportation infrastructure on territorial dynamics remains an open research problem. This issue is one of the aspects of approaches on complexity of territorial dynamics, within which territories and networks would be co-evolving. The aim of this thesis is to challenge this view on interactions between networks and territories, both at the conceptual and empirical level, by integrating them in simulation models of territorial systems.Comment: Doctoral dissertation (2017), Universit\'e Paris 7 Denis Diderot. Translated from French. Several papers compose this PhD thesis; overlap with: arXiv:{1605.08888, 1608.00840, 1608.05266, 1612.08504, 1706.07467, 1706.09244, 1708.06743, 1709.08684, 1712.00805, 1803.11457, 1804.09416, 1804.09430, 1805.05195, 1808.07282, 1809.00861, 1811.04270, 1812.01473, 1812.06008, 1908.02034, 2012.13367, 2102.13501, 2106.11996

Proceedings of the 5th MIT/ONR Workshop on C[3] Systems, held at Naval Postgraduate School, Monterey, California, August 23 to 27, 1982

"December 1982."Includes bibliographies and index.Office of Naval Research Contract no. ONR/N00014-77-C-0532 NR041-519edited by Michael Athans ... [et al.]