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Triangular Norms

Author: Erich Peter Klement

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 391

ISBN-13: 9401595402

This book discusses the theory of triangular norms and surveys several applied fields in which triangular norms play a significant part: probabilistic metric spaces, aggregation operators, many-valued logics, fuzzy logics, sets and control, and non-additive measures together with their corresponding integrals. It includes many graphical illustrations and gives a well-balanced picture of theory and applications. It is for mathematicians, computer scientists, applied computer scientists and engineers.

Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms

Author: Erich Peter Klement

Publisher: Elsevier

Published: 2005-03-25

Total Pages: 491

ISBN-13: 0080459536

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This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces. Key Features: - Complete state of the art of the importance of triangular norms in various mathematical fields - 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications - Chapter authors are leading authorities in their fields - Triangular norms on different domains (including discrete, partially ordered) are described - Not only triangular norms but also related operators (aggregation operators, copulas) are covered - Book contains many enlightening illustrations · Complete state of the art of the importance of triangular norms in various mathematical fields · 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications · Chapter authors are leading authorities in their fields · Triangular norms on different domains (including discrete, partially ordered) are described · Not only triangular norms but also related operators (aggregation operators, copulas) are covered · Book contains many enlightening illustrations

Associative Functions: Triangular Norms And Copulas

Author: Claudi Alsina

Publisher: World Scientific

Published: 2006-02-22

Total Pages: 253

ISBN-13: 9814478520

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The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the “triangular norms” introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis.This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.

Neutrosophic Triangular Norms and Their Derived Residuated Lattices

Author: Qingqing Hu

Publisher: Infinite Study

Published:

Total Pages: 22

ISBN-13:

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Neutrosophic triangular norms (t-norms) and their residuated lattices are not only the main research object of neutrosophic set theory, but also the core content of neutrosophic logic. Neutrosophic implications are important operators of neutrosophic logic. Neutrosophic residual implications based on neutrosophic t-norms can be applied to the fields of neutrosophic inference and neutrosophic control. In this paper, neutrosophic t-norms, neutrosophic residual implications, and the residuated lattices derived from neutrosophic t-norms are investigated deeply. First of all, the lattice and its corresponding system are proved to be a complete lattice and a De Morgan algebra, respectively. Second, the notions of neutrosophic t-norms are introduced on the complete lattice discussed earlier. The basic concepts and typical examples of representable and non-representable neutrosophic t-norms are obtained. Naturally, De Morgan neutrosophic triples are defined for the duality of neutrosophic t-norms and neutrosophic t-conorms with respect to neutrosophic negators. Third, neutrosophic residual implications generated from neutrosophic t-norms and their basic properties are investigated. Furthermore, residual neutrosophic t-norms are proved to be infinitely -distributive, and then some important properties possessed by neutrosophic residual implications are given. Finally, a method for producing neutrosophic t-norms from neutrosophic implications is presented, and the residuated lattices are constructed on the basis of neutrosophic t-norms and neutrosophic residual implications.

Triangular Norm-Based Measures and Games with Fuzzy Coalitions

Author: D. Butnariu

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 207

ISBN-13: 9401736022

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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].

A NOVEL TRIANGULAR INTERVAL TYPE-2 INTUITIONISTIC FUZZY SETS AND THEIR AGGREGATION OPERATORS

Author: HARISH GARG

Publisher: Infinite Study

Published:

Total Pages: 25

ISBN-13:

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The objective of this work is to present a triangular interval type2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws.

Triangular Norms

Author:

Publisher:

Published: 1999

Total Pages: 137

ISBN-13:

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Knowledge and Systems Engineering

Author: Van Nam Huynh

Publisher: Springer Science & Business Media

Published: 2013-10-01

Total Pages: 422

ISBN-13: 3319027417

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The field of Knowledge and Systems Engineering (KSE) has experienced rapid development and inspired many applications in the world of information technology during the last decade. The KSE conference aims at providing an open international forum for presentation, discussion and exchange of the latest advances and challenges in research of the field. These proceedings contain papers presented at the Fifth International Conference on Knowledge and Systems Engineering (KSE 2013), which was held in Hanoi, Vietnam, during 17–19 October, 2013. Besides the main track of contributed papers, which are compiled into the first volume, the conference also featured several special sessions focusing on specific topics of interest as well as included one workshop, of which the papers form the second volume of these proceedings. The book gathers a total of 68 papers describing recent advances and development on various topics including knowledge discovery and data mining, natural language processing, expert systems, intelligent decision making, computational biology, computational modeling, optimization algorithms, and industrial applications.

Advances in Fuzzy Logic and Technology 2017

Author: Janusz Kacprzyk

Publisher: Springer

Published: 2017-08-30

Total Pages: 712

ISBN-13: 3319668307

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This volume constitutes the proceedings of two collocated international conferences: EUSFLAT-2017 – the 10th edition of the flagship Conference of the European Society for Fuzzy Logic and Technology held in Warsaw, Poland, on September 11–15, 2017, and IWIFSGN’2017 – The Sixteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, held in Warsaw on September 13–15, 2017. The conferences were organized by the Systems Research Institute, Polish Academy of Sciences, Department IV of Engineering Sciences, Polish Academy of Sciences, and the Polish Operational and Systems Research Society in collaboration with the European Society for Fuzzy Logic and Technology (EUSFLAT), the Bulgarian Academy of Sciences and various European universities. The aim of the EUSFLAT-2017 was t o bring together theoreticians and practitioners working on fuzzy logic, fuzzy systems, soft computing and related areas and to provide a platform for exchanging ideas and discussing the latest trends and ideas, while the aim of IWIFSGN’2017 was to discuss new developments in extensions of the concept of a fuzzy set, such as an intuitionistic fuzzy set, as well as other concepts, like that of a generalized net. The papers included, written by leading international experts, as well as the special sessions and panel discussions contribute to the development the field, strengthen collaborations and intensify networking.

Artificial Intelligence and Soft Computing, Part I

Author: Leszek Rutkowski

Publisher: Springer Science & Business Media

Published: 2010-06

Total Pages: 695

ISBN-13: 3642132073

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The LNAI series reports state-of-the-art results in artificial intelligence research, development, education, at a high level and in both printed and electronic form. Enjoying tight cooperation with the R&D community, with numerous individuals, as well as with prestigious organizations and societies, LNAI has grown into the most comprehensive artificial intelligence research forum available. The scope of LNAI spans the whole range of artificial intelligence and intelligent information processing including interdisciplinary topics in a variety of application fields.