Transformations and information granularity of knowledge structures in set-based granular computing

2021 ◽  
pp. 1-16
Author(s):  
Wen Sheng Du
Keyword(s):  
Granular Computing ◽  
Orthogonal Transformation ◽  
Knowledge Structure ◽  
Knowledge Structures ◽  
Equivalence Relations ◽  
Information Granularity ◽  
Special Cases ◽  
Definition Of ◽  
Definition Of Information ◽  
The Universe

Granular computing is a relatively new platform for constructing, describing and processing information or knowledge. For crisp information granulation, the universe is decomposed into granules by binary relations on the universe, say, preorder, tolerance and equivalence relations. A knowledge structure is composed of all information granules induced by a relation that corresponds to the granulation. This paper establishes a novel theoretical framework for the measurement of information granularity of knowledge structures. First, two new relations between knowledge structures are introduced through the use of their respective Boolean relation matrices, where the granular equality relation is defined based on an orthogonal transformation with the transformation matrix being a permutation matrix, and the granularly finer relation is presented by combining the classical finer relation and the orthogonal transformation. Then, it is demonstrated that the simplified knowledge structure base with the granularly finer relation is a partially ordered set, which can be represented by a Hasse diagram. Subsequently, an axiomatic definition of information granularity is proposed to satisfy the constraints regarding these two relations. Moreover, a general form of the information granularity is given, and some existing measures are proved to be its special cases. Finally, as an application of the proposed measure, the attribute significance measure is developed based on the information granularity.

Algebraic Properties of Rough Set on Two Universal Sets based on Multigranulation

2014 ◽  
Vol 1 (2) ◽  
pp. 49-61 ◽  
Author(s):  
Mary A. Geetha ◽  
D. P. Acharjya ◽  
N. Ch. S. N. Iyengar
Keyword(s):  
Information System ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Granular Computing ◽  
Real Life ◽  
Equivalence Relations ◽  
Life Problems ◽  
Algebraic Properties ◽  
The Universe

The rough set philosophy is based on the concept that there is some information associated with each object of the universe. The set of all objects of the universe under consideration for particular discussion is considered as a universal set. So, there is a need to classify objects of the universe based on the indiscernibility relation (equivalence relation) among them. In the view of granular computing, rough set model is researched by single granulation. The granulation in general is carried out based on the equivalence relation defined over a universal set. It has been extended to multi-granular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. But, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multi-granulation rough set on single universal set to multi-granulation rough set on two universal sets. In this paper, we define multi-granulation rough set for two universal sets U and V. We study the algebraic properties that are interesting in the theory of multi-granular rough sets. This helps in describing and solving real life problems more accurately.

scholarly journals Human Development VII: A Spiral Fractal Model of Fine Structure of Physical Energy Could Explain Central Aspects of Biological Information, Biological Organization and Biological Creativity

2006 ◽  
Vol 6 ◽  
pp. 1434-1440 ◽  
Author(s):  
Søren Ventegodt ◽  
Tyge Dahl Hermansen ◽  
Trine Flensborg-Madsen ◽  
Erik Rald ◽  
Maj Lyck Nielsen ◽  
...  
Keyword(s):  
Native American ◽  
Fractal Model ◽  
The Body ◽  
Biological Information ◽  
Biological Organization ◽  
Living Organisms ◽  
Definition Of ◽  
Definition Of Information ◽  
The Universe ◽  
Informational System

In this paper we have made a draft of a physical fractal essence of the universe, a sketch of a new cosmology, which we believe to lay at the root of our new holistic biological paradigm. We present the fractal roomy spiraled structures and the energy-rich dancing “infinite strings” or lines of the universe that our hypothesis is based upon. The geometric language of this cosmology is symbolic and both pre-mathematical and pre-philosophical. The symbols are both text and figures, and using these we step by step explain the new model that at least to some extent is able to explain the complex informational system behind morphogenesis, ontogenesis, regeneration and healing. We suggest that it is from this highly dynamic spiraled structure that organization of cells, organs, and the wholeness of the human being including consciousness emerge. The model of ““dancing fractal spirals” carries many similarities to premodern cultures descriptions of the energy of the life and universe. Examples are the Native American shamanistic descriptions of their perception of energy and the old Indian Yogis descriptions of the life-energy within the body and outside. Similar ideas of energy and matter are found in the modern superstring theories. The model of the informational system of the organism gives new meaning to Bateson’s definition of information: “A difference that makes a difference”, and indicates how information-directed self-organization can exist on high structural levels in living organisms, giving birth to their subjectivity and consciousness.

Definition of Information Core for Documents Classification

2018 ◽  
Vol 50 (4) ◽  
pp. 25-34 ◽  
Author(s):  
Eduard A. Manziuk ◽  
Alexander V. Barmak ◽  
Yuriy V. Krak ◽  
Veda S. Kasianiuk
Keyword(s):  
Definition Of ◽  
Definition Of Information

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

Fundamental relations and identities of fuzzy hyperalgebras

2021 ◽  
pp. 1-10
Author(s):  
Narjes Firouzkouhi ◽  
Abbas Amini ◽  
Chun Cheng ◽  
Mehdi Soleymani ◽  
Bijan Davvaz
Keyword(s):  
Universal Algebra ◽  
Equivalence Relation ◽  
Polynomial Function ◽  
Equivalence Relations ◽  
Fundamental Relation ◽  
Term Function ◽  
Biological Phenomena ◽  
Definition Of

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

scholarly journals L2-BETTI NUMBERS OF DISCRETE MEASURED GROUPOIDS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1169-1188 ◽  
Author(s):  
ROMAN SAUER
Keyword(s):  
Probability Space ◽  
Betti Numbers ◽  
Free Action ◽  
Countable Group ◽  
Equivalence Relations ◽  
Dimension Theory ◽  
Discrete Groups ◽  
Type Ii ◽  
Orbit Equivalent ◽  
Definition Of

There are notions of L2-Betti numbers for discrete groups (Cheeger–Gromov, Lück), for type II1-factors (recent work of Connes-Shlyakhtenko) and for countable standard equivalence relations (Gaboriau). Whereas the first two are algebraically defined using Lück's dimension theory, Gaboriau's definition of the latter is inspired by the work of Cheeger and Gromov. In this work we give a definition of L2-Betti numbers of discrete measured groupoids that is based on Lück's dimension theory, thereby encompassing the cases of groups, equivalence relations and holonomy groupoids with an invariant measure for a complete transversal. We show that with our definition, like with Gaboriau's, the L2-Betti numbers [Formula: see text] of a countable group G coincide with the L2-Betti numbers [Formula: see text] of the orbit equivalence relation [Formula: see text] of a free action of G on a probability space. This yields a new proof of the fact the L2-Betti numbers of groups with orbit equivalent actions coincide.

Symbolic Macroconcept of the Universe in the Aspect of the First Cognitive Sign in Russian Linguoculture

2021 ◽  
Vol 16 (1) ◽  
pp. 92-101
Author(s):  
Marina V. Pimenova ◽  
◽  
Aigul A. Bakirova ◽  
Keyword(s):  
Middle Part ◽  
Russian Language ◽  
The World ◽  
Symbolic Meanings ◽  
New Type ◽  
Human World ◽  
Internal Volume ◽  
Definition Of ◽  
Universe Structure ◽  
The Universe

The article analyzes the cognitive signs of the macroconcept universe in Russian linguoculture. The relevance of the research is determined by the prospect of studying a new type of mental structures - symbolic macroconcepts. The purpose of the article is to describe the specifics of the macroconcept universe structure formation from the standpoint of the definition of syncretic primordial signs. The main methods in the work are the historical and etymological analysis of the studied macroconcept representative, descriptive and interpretive methods. During the study, seven motivating signs of the macroconcept universe were noted: 'earth', 'live', ‘world’，‘inhabit’，‘inhabited’，‘settlement’，‘light’. All identified motivating signs are syncretic symbolic primordial signs 'house' (conceptum, according to V. V. Kolesov). Motivating signs express two main symbolic meanings of Russian linguoculture: home is a place where people live, settle; home is the world of people and all living beings, this world-light (unlike that world-light where the souls of the dead go: that world-light is located in the sky), it is built on earth. The macroconcept universe is objectified by erased metaphors of a closed space (in particular, the metaphor of a key), which has an internal volume, center-middle, limits, parts, edges, corners, people live in this house, they live and exist in it, it is inhabited and settle down in Russian linguoculture. The model of the universe in the Russian language picture of the world is three-parted: the middle part in it represents the human world, in which the principle of anthropocentrism is manifested - a person measures space and chooses himself as a reference point. The syncretic primary sign ‘house’ unites in itself all the motivating signs of the studied macroconcept, keeping their relevance to our days. Keywords: macroconcept, motivating signs, first sign, language picture of the world, linguoculture, comparative studies

Definition of information and entropy in the absence of noise

2020 ◽  
pp. 1-33
Author(s):  
Roman V. Belavkin ◽  
Panos M. Pardalos ◽  
Jose C. Principe ◽  
Ruslan L. Stratonovich
Keyword(s):  
Definition Of ◽  
Definition Of Information

scholarly journals Safeguarding information as an asset: Do we need a redefinition in the knowledge economy and beyond?

2016 ◽  
Vol 18 (1) ◽  
Author(s):  
Adeniji K. Adesemowo ◽  
Rossouw Von Solms ◽  
Reinhard A. Botha
Keyword(s):  
Internal Control ◽  
Knowledge Economy ◽  
Large Body ◽  
Research Approach ◽  
Significant Finding ◽  
Information Risk ◽  
Starting Point ◽  
Information Assets ◽  
Definition Of ◽  
Definition Of Information

Background: With the evolution of data, via information into knowledge and beyond, intangible information assets (seen as an integral part of IT assets in this article) increasingly come to fore. A contemporary issue facing organisations in the knowledge economy and beyond is how best to safeguard and derive optimum value from their evolving information assets. A well-known fact is that risk exists because there is the possibility of threats to an asset. Likewise, no assets equals no risk. Although a large body of work is addressing threat models, the nature of the assets of the knowledge economy and beyond has not been well researched.Objectives: To investigate the definition of information assets across a number of financial, risk and information technology standards, frameworks and regulations, in order to ascertain whether a coherent definition exists across the board. If there is none (or limited), then propose a workable definition that is apt for the knowledge economy and beyond.Method: Qualitative thematic content analysis and a comparative study based on four main themes (Assets, Types of Asset, Information, and Information Assets). This then serves as a basis for argumentation schemes that lead to a proposed re-definition. The qualitative research approach assists us to address the concern of the incoherent definition of information and information assets across the board.Results: Contrary to expectations, the research study found the current definition to be incoherent. When the asset to be controlled is not properly defined and understood, it stands the risk of not being identified properly. This implies that the effectiveness, efficiency, reliability of internal control, and compliance with the applicable legislation and regulations would not be appropriate. This article highlights the need for a fundamental shift in how information assets (valuable, but unvalued organisational intangible assets) are being viewed and treated, especially with regard to information risk and internal controls.Conclusion: This article has identified a major defect in most standards, frameworks, and regulations dealing with regard to the safeguarding and management of information assets (and IT assets). It has established from the review carried out that information assets have not been properly defined across the board. Beyond this significant finding, it was further shown that the principle of risk (assessment) across the board requires the identification of the asset that needs to be controlled. A starting point, then, is a coherent definition (as proposed) for the information asset in itself. Therefore, proper definition across the board might assists in proper identification that could result in appropriate control and graceful handling of the end-of-life disposal.Keywords: infonomics; information asset; information risk; internal control; reputation loss

What has Natural Information to do with Intentional Representation?

2001 ◽  
Vol 49 ◽  
pp. 105-125 ◽  
Author(s):  
Ruth Garrett Millikan
Keyword(s):  
Informational Semantics ◽  
Original Definition ◽  
Natural Information ◽  
The One ◽  
Definition Of ◽  
Definition Of Information ◽  
Flow Of Information

‘According to informational semantics, if it's necessary that a creature can't distinguish Xs from Ys, it follows that the creature can't have a concept that applies to Xs but not Ys.’ (Fodor, 1994, p. 32)There is, indeed, a form of informational semantics that has this verificationist implication. The original definition of information given in Dretske'sKnowledge and the Flow of Information(1981, hereafter KFI), when employed as a base for a theory of intentional representation or ‘content,’ has this implication. I will argue that, in fact, most of what an animal needs to know about its environment is not available as natural information of this kind. It is true, I believe, that there is one fundamental kind of perception that depends on this kind of natural information, but more sophisticated forms of inner representation do not. It is unclear, however, exactly what ‘natural information’ is supposed to mean, certainly in Fodor's, and even in Dretske's writing. In many places, Dretske seems to employ a softer notion than the one he originally defines. I will propose a softer view of natural information that is, I believe, at least hinted at by Dretske, and show that it does not have verificationist consequences. According to this soft informational semantics, a creature can perfectly well have a representation of Xs without being able to discriminate Xs from Ys.

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