Triangular Norm Based Measures And Games With Fuzzy Coalitions
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Triangular Norm Based Measures And Games With Fuzzy Coalitions
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Author : D. Butnariu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Triangular Norm Based Measures And Games With Fuzzy Coalitions written by D. Butnariu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Business & Economics categories.
This book aims to present, in a unified approach, a series of mathematical results con cerning triangular norm-based measures and a class of cooperative games with Juzzy coalitions. Our approach intends to emphasize that triangular norm-based measures are powerful tools in exploring the coalitional behaviour in 'such games. They not and simplify some technical aspects of the already classical axiomatic the only unify ory of Aumann-Shapley values, but also provide new perspectives and insights into these results. Moreover, this machinery allows us to obtain, in the game theoretical context, new and heuristically meaningful information, which has a significant impact on balancedness and equilibria analysis in a cooperative environment. From a formal point of view, triangular norm-based measures are valuations on subsets of a unit cube [0, 1]X which preserve dual binary operations induced by trian gular norms on the unit interval [0, 1]. Triangular norms (and their dual conorms) are algebraic operations on [0,1] which were suggested by MENGER [1942] and which proved to be useful in the theory of probabilistic metric spaces (see also [WALD 1943]). The idea of a triangular norm-based measure was implicitly used under various names: vector integrals [DVORETZKY, WALD & WOLFOWITZ 1951], prob abilities oj Juzzy events [ZADEH 1968], and measures on ideal sets [AUMANN & SHAPLEY 1974, p. 152].
Triangular Norm Based Measures And Games With Fuzzy Coalitions
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Author : D. Butnariu
language : en
Publisher:
Release Date : 2014-01-15
Triangular Norm Based Measures And Games With Fuzzy Coalitions written by D. Butnariu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Triangular Norms
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Author : Erich Peter Klement
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Triangular Norms written by Erich Peter Klement and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Philosophy categories.
The history of triangular norms started with the paper "Statistical metrics" [Menger 1942]. The main idea of Karl Menger was to construct metric spaces where probability distributions rather than numbers are used in order to de scribe the distance between two elements of the space in question. Triangular norms (t-norms for short) naturally came into the picture in the course of the generalization of the classical triangle inequality to this more general set ting. The original set of axioms for t-norms was considerably weaker, including among others also the functions which are known today as triangular conorms. Consequently, the first field where t-norms played a major role was the theory of probabilistic metric spaces ( as statistical metric spaces were called after 1964). Berthold Schweizer and Abe Sklar in [Schweizer & Sklar 1958, 1960, 1961] provided the axioms oft-norms, as they are used today, and a redefinition of statistical metric spaces given in [Serstnev 1962]led to a rapid development of the field. Many results concerning t-norms were obtained in the course of this development, most of which are summarized in the monograph [Schweizer & Sklar 1983]. Mathematically speaking, the theory of (continuous) t-norms has two rather independent roots, namely, the field of (specific) functional equations and the theory of (special topological) semigroups.
Quantitative Logic And Soft Computing
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Author : Bing-Yuan Cao
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-14
Quantitative Logic And Soft Computing written by Bing-Yuan Cao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-14 with Technology & Engineering categories.
Admittedly, the notion “intelligence or intelligent computing” has been around us for several decades, implicitly indicating any non-conventional methods of solving complex system problems such as expert systems and intelligent control techniques that mimic human skill and replace human operators for automation. Various kinds of intelligent methods have been suggested, phenomenological or ontological, and we have been witnessing quite successful applications. On the other hand, “Soft Computing Techniques” is the concept coined by Lot? Zadeh, referring to “a set of approaches of computing which parallels the remarkable ability of the human mind to reason and learn in an environment of uncertainty, imprecision and partial truth. ” Such a notion is well contrasted with the conventionalbinary logic based hard c- puting and has been effectively utilized with the guiding principle of “exploiting the tolerance for uncertainty,imprecision and partial truth to achieve tractability, - bustness and low solution cost. ” The soft computing techniques are often employed as the technical entities in a tool box with tools being FL, ANN, Rough Set, GA etc. Based on one’s intuition and experience, an engineer can build and realize hum- like systems by smartly mixing proper technical tools effectivelyand ef?ciently in a wide range of ?elds. For some time, the soft computing techniques are also referred to as intelligent computing tools.
Power Algebras Over Semirings
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Author : Jonathan S. Golan
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-07-31
Power Algebras Over Semirings written by Jonathan S. Golan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-31 with Computers categories.
This research monograph investigates sets of the form RA where R is a semiring, and A is a set with a certain structure. Such constructs generalise fuzzy and toll algebraic structures, which in recent years have shown themselves of importance in engineering and computer science, as well as in new mathematical disciplines like idempotent analysis. This volume puts much of the ad hoc work of the past decade on a firm mathematical foundation by creating a unified approach which has important implications in such diverse areas as formal language theory, discrete dynamical systems, models of optimal control, and many others. This book also seeks to address the fundamental question posed by Höhle and Sostak as to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory. Since the development of a new mathematical theory is basically inductive, this book begins with a large number of instances which appear in various mathematical contexts, and then develops a general abstract framework, with many examples which will encourage further study in greater depth. Audience: This work will be of interest to mathematicians whose work involves associative rings and algebras, ordered algebraic structures, optimal control, graph theory, fuzzy sets and fuzzy algebraic structures.
Granular Computing
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Author : Andrzej Bargiela
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Granular Computing written by Andrzej Bargiela and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
This book is about Granular Computing (GC) - an emerging conceptual and of information processing. As the name suggests, GC concerns computing paradigm processing of complex information entities - information granules. In essence, information granules arise in the process of abstraction of data and derivation of knowledge from information. Information granules are everywhere. We commonly use granules of time (seconds, months, years). We granulate images; millions of pixels manipulated individually by computers appear to us as granules representing physical objects. In natural language, we operate on the basis of word-granules that become crucial entities used to realize interaction and communication between humans. Intuitively, we sense that information granules are at the heart of all our perceptual activities. In the past, several formal frameworks and tools, geared for processing specific information granules, have been proposed. Interval analysis, rough sets, fuzzy sets have all played important role in knowledge representation and processing. Subsequently, information granulation and information granules arose in numerous application domains. Well-known ideas of rule-based systems dwell inherently on information granules. Qualitative modeling, being one of the leading threads of AI, operates on a level of information granules. Multi-tier architectures and hierarchical systems (such as those encountered in control engineering), planning and scheduling systems all exploit information granularity. We also utilize information granules when it comes to functionality granulation, reusability of information and efficient ways of developing underlying information infrastructures.
Semirings And Affine Equations Over Them
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Author : Jonathan S. Golan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Semirings And Affine Equations Over Them written by Jonathan S. Golan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.
Cardinalities Of Fuzzy Sets
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Author : Maciej Wygralak
language : en
Publisher: Springer
Release Date : 2012-12-06
Cardinalities Of Fuzzy Sets written by Maciej Wygralak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num bers: the natural numbers. That these complementary aspects of the counting pro cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.
Models In Cooperative Game Theory
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Author : Rodica Branzei
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-08
Models In Cooperative Game Theory written by Rodica Branzei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-08 with Business & Economics categories.
Cooperative game theory is a booming research area with many new developments in the last few years. So, our main purpose when prep- ing the second edition was to incorporate as much of these new dev- opments as possible without changing the structure of the book. First, this o?ered us the opportunity to enhance and expand the treatment of traditional cooperative games, called here crisp games, and, especially, that of multi-choice games, in the idea to make the three parts of the monograph more balanced. Second, we have used the opportunity of a secondeditiontoupdateandenlargethelistofreferencesregardingthe threemodels of cooperative games. Finally, we have bene?ted fromthis opportunity by removing typos and a few less important results from the ?rst edition of the book, and by slightly polishing the English style and the punctuation, for the sake of consistency along the monograph. The main changes are: (1) Chapter 3 contains an additional section, Section 3. 3, on the - erage lexicographic value, which is a recent one-point solution concept de?ned on the class of balanced crisp games. (2) Chapter 4 is new. It o?ers a brief overview on solution c- cepts for crisp games from the point of view of egalitarian criteria, and presents in Section 4. 2 a recent set-valued solution concept based on egalitarian considerations, namely the equal split-o? set. (3)Chapter5isbasicallyanenlargedversionofChapter4ofthe?rst edition because Section 5. 4 dealing with the relation between convex games and clan games with crisp coalitions is new.
Soft Computing In Human Related Sciences
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Author : Horia-Nicolai L Teodorescu
language : en
Publisher: CRC Press
Release Date : 1999-04-29
Soft Computing In Human Related Sciences written by Horia-Nicolai L Teodorescu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-29 with Computers categories.
Hard boundaries have traditionally existed between such fields as fuzzy systems, neural networks, genetic algorithms, chaotic systems and expert systems. Gradually those boundaries are tending to vanish and "soft computing"-based systems that mix these different approaches have begun to emerge. Soft Computing Techniques in Human-Related Sciences focuses on the use of novel techniques such as artificial neural networks, fuzzy logic and genetic algorithms to solve practical problems related to humans: their activities, health and social needs. This volume illustrates and presents in an organized manner some of the recent progress in the applications of soft computing to fields related to social science, medical science, psychology, psychiatry , management of health and community services, and humanoid robots. Soft Computing Techniques in Human-Related Sciences begins with an introductory chapter to aid newcomers with the basic concepts, and progresses to the methodology of the use of soft computing in robotics, prosthetics, medicine, psycchology and man-machine interaction.