The idea of soft computing emerged in the early 1990s from the fuzzy systems c- munity, and refers to an understanding that the uncertainty, imprecision and ig- rance present in a problem should be explicitly represented and possibly even - ploited rather than either eliminated or ignored in computations. For instance, Zadeh de?ned ‘Soft Computing’ as follows: Soft computing differs from conventional (hard) computing in that, unlike hard computing, it is tolerant of imprecision, uncertainty and partial truth. In effect, the role model for soft computing is the human mind. Recently soft computing has, to some extent, become synonymous with a hybrid approach combining AI techniques including fuzzy systems, neural networks, and biologically inspired methods such as genetic algorithms. Here, however, we adopt a more straightforward de?nition consistent with the original concept. Hence, soft methods are understood as those uncertainty formalisms not part of mainstream s- tistics and probability theory which have typically been developed within the AI and decisionanalysiscommunity.Thesearemathematicallysounduncertaintymodelling methodologies which are complementary to conventional statistics and probability theory.

Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy interval analysis with probabilistic methods. This book gathers contributions to the 4th International Conference on Soft methods in Probability and Statistics. Its aim is to present recent results illustrating such new trends that enlarge the statistical and uncertainty modeling traditions, towards the handling of incomplete or subjective information. It covers a broad scope ranging from philosophical and mathematical underpinnings of new uncertainty theories, with a stress on their impact in the area of statistics and data analysis, to numerical methods and applications to environmental risk analysis and mechanical engineering. A unique feature of this collection is to establish a dialogue between fuzzy random variables and imprecise probability theories.

This book highlights recent research on interval methods for solving nonlinear constraint satisfaction, optimization and similar problems. Further, it presents a comprehensive survey of applications in various branches of robotics, artificial intelligence systems, economics, control theory, dynamical systems theory, and others. Three appendices, on the notation, representation of numbers used as intervals’ endpoints, and sample implementations of the interval data type in several programming languages, round out the coverage.

This book examines in detail the planning and modelling of local infrastructure like energy systems, including the complexities resulting from various uncertainties. Readers will discover the individual steps involved in infrastructure planning in cities and territories, as well as the primary requirements and supporting quality factors. Further topics covered concern the field of uncertainty and its synergies with infrastructure planning. Theories, methodological backgrounds and concrete case studies will not only help readers to understand the proposed methodologies for modelling and uncertainty analysis, but will also show them how these approaches are implemented in practice.

The book constitutes the refereed proceedings of the 13th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2010, held in Dortmund, Germany from June 28 - July 2, 2010. The 77 revised full papers were carefully reviewed and selected from 320 submissions and reflect the richness of research in the field of Computational Intelligence and represent developments on topics as: machine learning, data mining, pattern recognition, uncertainty handling, aggregation and fusion of information as well as logic and knowledge processing.

Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (stochastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc. About ten years ago the idea of establishing a recurrent forum for discussing new trends in the before-mentioned context was born and resulted in the first International Conference on Soft Methods in Probability and Statistics (SMPS) that was held in Warsaw in 2002. In the following years the conference took place in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). In the current edition the conference returns to Oviedo. This edited volume is a collection of papers presented at the SMPS 2010 conference held in Mieres and Oviedo. It gives a comprehensive overview of current research into the fusion of soft methods with probability and statistics.

This book is composed of selected papers from the Sixteenth National Conference on Operational and Systems Research, BOS-2020, held on December 14-15, 2020, one of premiere conferences in the field of operational and systems research. The second is the Nineteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, IWIFSGN 2020, held on December 10-11, 2020, in Warsaw, Poland, in turn—one of premiere conferences on fuzzy logic, notably on extensions of the traditional fuzzy sets, also comprising a considerable part on the generalized nets (GNs), an important extension of the traditional Petri nets. A joint publication of selected papers from the two conferences follows a long tradition of such a joint organization and—from a substantial point of view—combines systems modeling, systems analysis, broadly perceived operational research, notably optimization, decision making, and decision support, with various aspects of uncertain and imprecise information and their related tools and techniques.

This book comprises a selection of papers from IFSA 2007 on new methods and theories that contribute to the foundations of fuzzy logic and soft computing. Coverage includes the application of fuzzy logic and soft computing in flexible querying, philosophical and human-scientific aspects of soft computing, search engine and information processing and retrieval, as well as intelligent agents and knowledge ant colony.

Soft Computing is a complex of methodologies that includes artificial neural networks, genetic algorithms, fuzzy logic, Bayesian networks, and their hybrids. It admits approximate reasoning, imprecision, uncertainty and partial truth in order to mimic the remarkable human capability of making decisions in real-life, ambiguous environments. Soft Computing has therefore become popular in developing systems that encapsulate human expertise. 'Applications of Soft Computing: Updating the State of Art' contains a collection of papers that were presented at the 12th On-line World Conference on Soft Computing in Industrial Applications, held in October 2007. This carefully edited book provides a comprehensive overview of the recent advances in the industrial applications of soft computing and covers a wide range of application areas, including design, intelligent control, optimization, signal processing, pattern recognition, computer graphics, production, as well as civil engineering and applications to traffic and transportation systems. The book is aimed at researchers and practitioners who are engaged in developing and applying intelligent systems principles to solving real-world problems. It is also suitable as wider reading for science and engineering postgraduate students.

Annotation The three volume set LNAI 6096, LNAI 6097, and LNAI 6098 constitutes the thoroughly refereed conference proceedings of the 23rd International Conference on Industrial Engineering and Other Applications of Applied Intelligend Systems, IEA/AIE 2010, held in Cordoba, Spain, in June 2010. The total of 119 papers selected for the proceedings were carefully reviewed and selected from 297 submissions.