On Continuity of Complex Fuzzy Functions

In this paper, Some important theorems on fuzzy type I-continuous and II-continuous of complex fuzzy functions mapping generalized rectangular valued bounded closed complex complement normalized fuzzy numbers into itself are proved. Keywords: Fuzzy Complex Numbers, Fuzzy Complex Functions, Fuzzy Continuity

Heterogeneous neural networks: theory and applications

Aquest treball presenta una classe de funcions que serveixen de models neuronals generalitzats per ser usats en xarxes neuronals artificials. Es defineixen com una mesura de similitud que actúa com una definició flexible de neurona vista com un reconeixedor de patrons. La similitud proporciona una marc conceptual i serveix de cobertura unificadora de molts models neuronals de la literatura i d'exploració de noves instàncies de models de neurona. La visió basada en similitud porta amb naturalitat a integrar informació heterogènia, com ara quantitats contínues i discretes (nominals i ordinals), i difuses ó imprecises. Els valors perduts es tracten de manera explícita. Una neurona d'aquesta classe s'anomena neurona heterogènia i qualsevol arquitectura neuronal que en faci ús serà una Xarxa Neuronal Heterogènia.En aquest treball ens concentrem en xarxes neuronals endavant, com focus inicial d'estudi. Els algorismes d'aprenentatge són basats en algorisms evolutius, especialment extesos per treballar amb informació heterogènia. En aquesta tesi es descriu com una certa classe de neurones heterogènies porten a xarxes neuronals que mostren un rendiment molt satisfactori, comparable o superior al de xarxes neuronals tradicionals (com el perceptró multicapa ó la xarxa de base radial), molt especialment en presència d'informació heterogènia, usual en les bases de dades actuals.This work presents a class of functions serving as generalized neuron models to be used in artificial neural networks. They are cast into the common framework of computing a similarity function, a flexible definition of a neuron as a pattern recognizer. The similarity endows the model with a clear conceptual view and serves as a unification cover for many of the existing neural models, including those classically used for the MultiLayer Perceptron (MLP) and most of those used in Radial Basis Function Networks (RBF). These families of models are conceptually unified and their relation is clarified. The possibilities of deriving new instances are explored and several neuron models --representative of their families-- are proposed. The similarity view naturally leads to further extensions of the models to handle heterogeneous information, that is to say, information coming from sources radically different in character, including continuous and discrete (ordinal) numerical quantities, nominal (categorical) quantities, and fuzzy quantities. Missing data are also explicitly considered. A neuron of this class is called an heterogeneous neuron and any neural structure making use of them is an Heterogeneous Neural Network (HNN), regardless of the specific architecture or learning algorithm. Among them, in this work we concentrate on feed-forward networks, as the initial focus of study. The learning procedures may include a great variety of techniques, basically divided in derivative-based methods (such as the conjugate gradient)and evolutionary ones (such as variants of genetic algorithms).In this Thesis we also explore a number of directions towards the construction of better neuron models --within an integrant envelope-- more adapted to the problems they are meant to solve.It is described how a certain generic class of heterogeneous models leads to a satisfactory performance, comparable, and often better, to that of classical neural models, especially in the presence of heterogeneous information, imprecise or incomplete data, in a wide range of domains, most of them corresponding to real-world problems.Postprint (published version

Integrative Levels of Knowing

Diese Dissertation beschäftigt sich mit einer systematischen Organisation der epistemologischen Dimension des menschlichen Wissens in Bezug auf Perspektiven und Methoden. Insbesondere wird untersucht inwieweit das bekannte Organisationsprinzip der integrativen Ebenen, das eine Hierarchie zunehmender Komplexität und Integration beschreibt, geeignet ist für eine grundlegende Klassifikation von Perspektiven bzw. epistemischen Bezugsrahmen. Die zentrale These dieser Dissertation geht davon aus, dass eine angemessene Analyse solcher epistemischen Kontexte in der Lage sein sollte, unterschiedliche oder gar konfligierende Bezugsrahmen anhand von kontextübergreifenden Standards und Kriterien vergleichen und bewerten zu können. Diese Aufgabe erfordert theoretische und methodologische Grundlagen, welche die Beschränkungen eines radikalen Kontextualismus vermeiden, insbesondere die ihm innewohnende Gefahr einer Fragmentierung des Wissens aufgrund der angeblichen Inkommensurabilität epistemischer Kontexte. Basierend auf Jürgen Habermas‘ Theorie des kommunikativen Handelns und seiner Methodologie des hermeneutischen Rekonstruktionismus, wird argumentiert, dass epistemischer Pluralismus nicht zwangsläufig zu epistemischem Relativismus führen muss und dass eine systematische Organisation der Perspektivenvielfalt von bereits existierenden Modellen zur kognitiven Entwicklung profitieren kann, wie sie etwa in der Psychologie oder den Sozial- und Kulturwissenschaften rekonstruiert werden. Der vorgestellte Ansatz versteht sich als ein Beitrag zur multi-perspektivischen Wissensorganisation, der sowohl neue analytische Werkzeuge für kulturvergleichende Betrachtungen von Wissensorganisationssystemen bereitstellt als auch neue Organisationsprinzipien vorstellt für eine Kontexterschließung, die dazu beitragen kann die Ausdrucksstärke bereits vorhandener Dokumentationssprachen zu erhöhen. Zudem enthält der Anhang eine umfangreiche Zusammenstellung von Modellen integrativer Wissensebenen.This dissertation is concerned with a systematic organization of the epistemological dimension of human knowledge in terms of viewpoints and methods. In particular, it will be explored to what extent the well-known organizing principle of integrative levels that presents a developmental hierarchy of complexity and integration can be applied for a basic classification of viewpoints or epistemic outlooks. The central thesis pursued in this investigation is that an adequate analysis of such epistemic contexts requires tools that allow to compare and evaluate divergent or even conflicting frames of reference according to context-transcending standards and criteria. This task demands a theoretical and methodological foundation that avoids the limitation of radical contextualism and its inherent threat of a fragmentation of knowledge due to the alleged incommensurability of the underlying frames of reference. Based on Jürgen Habermas’s Theory of Communicative Action and his methodology of hermeneutic reconstructionism, it will be argued that epistemic pluralism does not necessarily imply epistemic relativism and that a systematic organization of the multiplicity of perspectives can benefit from already existing models of cognitive development as reconstructed in research fields like psychology, social sciences, and humanities. The proposed cognitive-developmental approach to knowledge organization aims to contribute to a multi-perspective knowledge organization by offering both analytical tools for cross-cultural comparisons of knowledge organization systems (e.g., Seven Epitomes and Dewey Decimal Classification) and organizing principles for context representation that help to improve the expressiveness of existing documentary languages (e.g., Integrative Levels Classification). Additionally, the appendix includes an extensive compilation of conceptions and models of Integrative Levels of Knowing from a broad multidisciplinary field

New Trends in Neutrosophic Theory and Applications Volume II

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 was 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. Single valued neutrosophic sets have found their way into several hybrid systems, such as neutrosophic soft set, rough neutrosophic set, neutrosophic bipolar set, neutrosophic expert set, rough bipolar neutrosophic set, neutrosophic hesitant fuzzy set, etc. Successful applications of single valued neutrosophic sets have been developed in multiple criteria and multiple attribute decision making. This second volume collects original research and application papers from different perspectives covering different areas of neutrosophic studies, such as decision making, graph theory, image processing, probability theory, topology, and some theoretical papers. This volume contains four sections: DECISION MAKING, NEUTROSOPHIC GRAPH THEORY, IMAGE PROCESSING, ALGEBRA AND OTHER PAPERS. First paper (Pu Ji, Peng-fei Cheng, Hongyu Zhang, Jianqiang Wang. Interval valued neutrosophic Bonferroni mean operators and the application in the selection of renewable energy) aims to construct selection approaches for renewable energy considering the interrelationships among criteria. To do that, Bonferroni mean (BM) and geometric BM (GBM) are employed

Matter-Antimatter : An Accentuation-Attrition Model

A system of matter dissipating antimatter and parallel system of antimatter that contribute to the dissipation of the velocity of production of matter is investigated. It is shown that the time independence of the contributions portrays another system by itself and constitutes the equilibrium solution of the original time independent system. With the methodology reinforced with the explanations, we write the governing equations with the nomenclature for the systems in the foregoing, by concatenation process, ipso facto. We discuss following systems in all its predicational anteriorities, character consonations, ontological consonances, primordial exactitude, accolytish representation, differential relations, and concomitant contiguous similarities. (1) Antimatter as an integral part of the electromagnetic phenomena. (2) Electricity consists of the flow of electrons and positrons in opposite directions along a conductor (not only of electrons, as current accepted knowledge describes), induced by the crossing of a magnetic field through the conductor. (3) When a charged particle passes through matter at rest it will cause the production of electron pairs, that is, electrons and positrons, but if nothing separates them by force, they will reunite after the passing of the charged particle, nullifying each other, and the atoms of matter will be back at rest. (4) In order to preserve the law of conservation of energy, the amount of energy required to break free the electron and the positron from a bielectron (a theoretical dual particle containing an electron and a positron) must be equal to the amount of energy released by a matter-antimatter encounter of the same particles. (5) When a conductor is at rest all the bielectrons are located at their respective orbits in the conductor's atoms, generating no electric charge. (6) When a conductor is placed under a moving magnetic field, its otherwise stable bielectrons will break apart into electrons and positrons, which will flow in opposite directions along the conductor. At the closing of the circuit, electrons and positrons, attracted to each other by their opposite charge, reunite into bielectrons releasing an equal amount of energy as initially required to separate them. (7) Matter gormandizes antimatter (Antimatter has to pre-exist to be able to appear in a collision of particles. We are not creating antimatter; antimatter is there, intermingled with matter. Particle collisions do not “produce” antimatter; they separate antimatter from the particles of which it is part). (8) We assume that should there be another force in physics: the force of attraction between matter and antimatter and give a model. We shall call it Bundeswehr (German for "Federal Defense"). So Bundeswehr binds matter and antimatter. (9) At the closing of the circuit the free electrons and positrons, pushed forward by their own “pressure”, are irresistibly pulled by the attraction of their antimatter counterpart. It is this process of mutual attraction and continuous reunification into bielectrons which causes the flow of electrons and positrons along the conductors. Paper answers, not wholly or in full measure, but substantially the relationship between dark matter and antimatter and speculates in epiphenomena and phenomenological form the circumspective jurisprudence of consideration of the antimatter as dark matter. This also answers the long standing question in cosmology that why matter is prevalent in the universe in contrast to antimatter. The paper seems to confirm antimatter as an intrinsic constituent of ordinary matter; antimatter as an integral part of the electromagnetic phenomena; the existence of a new particle namely bielectron, consisting of an electron and a positron joined together within the atom; that matter and antimatter preceded the big-bang and their violent encounter may have been the actual cause of the big-bang itself; that matter and antimatter have a pacific coexistence in today’s universe, after the big-bang; the possible existence of a new force in physics namely Bundeswehr, which would recombine and keep matter and antimatter particles together. Keywords: matter-antimatter, where antimatter is, dark-matter, theory of electricity, bielectron, Big-Bang, origin of the Universe

Towards a classification of continuity and on the emergence of generality

This dissertation has for its primary task the investigation, articulation, and comparison of a variety of concepts of continuity, as developed throughout the history of philosophy and a part of mathematics. It also motivates and aims to better understand some of the conceptual and historical connections between characterizations of the continuous, on the one hand, and ideas and commitments about what makes for generality (and universality), on the other. Many thinkers of the past have acknowledged the need for advanced science and philosophy to pass through the “labyrinth of the continuum” and to develop a sufficiently rich and precise model or description of the continuous; but it has been far less widely appreciated how the resulting description informs our ideas and commitments regarding how (and whether) things become general (or how we think about universality). The introduction provides some motivation for the project and gives some overview of the chapters. The first two chapters are devoted to Aristotle, as Aristotle’s Physics is arguably the foundational book on continuity. The first two chapters show that Aristotle\u27s efforts to understand and formulate a rich and demanding concept of the continuous reached across many of his investigations; in particular, these two chapters aim to better situate certain structural similarities and conceptual overlaps between his Posterior Analytics and his Physics, further revealing connections between the structure of demonstration or proof (the subject of logic and the sciences) and the structure of bodies in motion (the subject of physics and study of nature). This chapter also contributes to the larger narrative about continuity, where Aristotle emerges as one of the more articulate and influential early proponents of an account that aligns continuity with closeness or relations of nearness. Chapter 3 is devoted to Duns Scotus and Nicolas Oresme, and more generally, to the Medieval debate surrounding the “latitude of forms” or the “intension and remission of forms,” in which concerted efforts were made to re-focus attention onto the type of continuous motions mostly ignored by the tradition that followed in the wake of Aristotelian physics. In this context, the traditional appropriation of Aristotle’s thoughts on unity, contrariety, genera, forms, quantity and quality, and continuity is challenged in a number of important ways, reclaiming some of the largely overlooked insights of Aristotle into the intimate connections between continua and genera. By realizing certain of Scotus’s ideas concerning the intension and remission of qualities, Oresme initiates a radical transformation in the concept of continuity, and this chapter argues that Oresme’s efforts are best understood as an early attempt at freeing the concept of continuity from its ancient connection to closeness. Chapters 4 and 5 are devoted to unpacking and re-interpreting Spinoza’s powerful theory of what makes for the ‘oneness’ of a body in general and how ‘ones’ can compose to form ever more composite ‘ones’ (all the way up to Nature as a whole). Much of Spinoza reads like an elaboration on Oresme’s new model of continuity; however, the legacy of the Cartesian emphasis on local motion makes it difficult for Spinoza to give up on closeness altogether. Chapter 4 is dedicated to a closer look at some subtleties and arguments surrounding Descartes’ definition of local motion and ‘one body’, and Chapter 5 builds on this to develop Spinoza’s ideas about how the concept of ‘one body’ scales, in which context a number of far-reaching connections between continuity and generality are also unpacked. Chapter 6 leaves the realm of philosophy and is dedicated to the contributions to the continuitygenerality connection from one field of contemporary mathematics: sheaf theory (and, more generally, category theory). The aim of this chapter is to present something like a “tour” of the main philosophical contributions made by the idea of a sheaf to the specification of the concept of continuity (with particular regard for its connections to universality). The concluding chapter steps back and discusses a number of distinct characterizations of continuity in more abstract and synthetic terms, while touching on some of the corresponding representations of generality to which each such model gives rise. This chapter ends with a brief discussion of some of the arguments that have been deployed in the past to claim that continuity (or discreteness) is “better.

Development of a model of machine hand eye coordination and program specifications for a topological machine vision system

A unified approach to computer vision and manipulation is developed which is called choreographic vision. In the model, objects to be viewed by a projected robot in the Viking missions to Mars are seen as objects to be manipulated within choreographic contexts controlled by a multimoded remote, supervisory control system on Earth. A new theory of context relations is introduced as a basis for choreographic programming languages. A topological vision model is developed for recognizing objects by shape and contour. This model is integrated with a projected vision system consisting of a multiaperture image dissector TV camera and a ranging laser system. System program specifications integrate eye-hand coordination and topological vision functions and an aerospace multiprocessor implementation is described

Cities Made of Boundaries: Mapping Social Life in Urban Form

Cities Made of Boundaries presents the theoretical foundation and concepts for a new social scientific urban morphological mapping method, Boundary Line Type (BLT) Mapping. Its vantage is a plea to establish a frame of reference for radically comparative urban studies positioned between geography and archaeology. Based in multidisciplinary social and spatial theory, a critical realist understanding of the boundaries that compose built space is operationalised by a mapping practice utilising Geographical Information Systems (GIS). Benjamin N. Vis gives a precise account of how BLT Mapping can be applied to detailed historical, reconstructed, contemporary, and archaeological urban plans, exemplified by sixteenth to twenty-first century Winchester (UK) and Classic Maya Chunchucmil (Mexico). This account demonstrates how the functional and experiential difference between compact western and tropical dispersed cities can be explored. The methodological development of Cities Made of Boundaries will appeal to readers interested in the comparative social analysis of built environments, and those seeking to expand the evidence-base of design options to structure urban life and development

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches