Eventology versus contemporary theories of uncertainty

The development of probability theory together with the Bayesian approach in the three last centuries is caused by two factors: the variability of the physical phenomena and partial ignorance about them. As now it is standard to believe [Dubois, 2007], the nature of these key factors is so various, that their descriptions are required special uncertainty theories, which differ from the probability theory and the Bayesian credo, and provide a better account of the various facets of uncertainty by putting together probabilistic and set-valued representations of information to catch a distinction between variability and ignorance. Eventology [Vorobyev, 2007], a new direction of probability theory and philosophy, offers the original event approach to the description of variability and ignorance, entering an agent, together with his/her beliefs, directly in the frameworks of scientific research in the form of eventological distribution of his/her own events. This allows eventology, by putting together probabilistic and set-event representation of information and philosophical concept of event as co-being [Bakhtin, 1920], to provide a unified strong account of various aspects of uncertainty catching distinction between variability and ignorance and opening an opportunity to define imprecise probability as a probability of imprecise event in the mathematical frameworks of Kolmogorov's probability theory [Kolmogorov, 1933].uncertainty, probability, event, co-being, eventology, imprecise event

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Belief functions on MV-algebras of fuzzy sets: An overview

Belief functions are the measure theoretical objects Dempster-Shafer evidence theory is based on. They are in fact totally monotone capacities, and can be regarded as a special class of measures of uncertainty used to model an agent's degrees of belief in the occurrence of a set of events by taking into account different bodies of evidence that support those beliefs. In this chapter we present two main approaches to extending belief functions on Boolean algebras of events to MV-algebras of events, modelled as fuzzy sets, and we discuss several properties of these generalized measures. In particular we deal with the normalization and soft-normalization problems, and on a generalization of Dempster's rule of combination. © 2014 Springer International Publishing Switzerland.The authors also acknowledge partial support by the FP7-PEOPLE-2009-IRSES project MaToMUVI (PIRSES-GA-2009- 247584). Also, Flaminio acknowledges partial support of the Italian project FIRB 2010 (RBFR10DGUA-002), Kroupa has been supported by the grant GACR 13-20012S, and Godo acknowledges partial support of the Spanish projects EdeTRI (TIN2012-39348-C02-01) and Agreement Technologies (CONSOLIDER CSD2007-0022, INGENIO 2010).Peer Reviewe

The VEX-93 environment as a hybrid tool for developing knowledge systems with different problem solving techniques

The paper describes VEX-93 as a hybrid environment for developing knowledge-based and problem solver systems. It integrates methods and techniques from artificial intelligence, image and signal processing and data analysis, which can be mixed. Two hierarchical levels of reasoning contains an intelligent toolbox with one upper strategic inference engine and four lower ones containing specific reasoning models: truth-functional (rule-based), probabilistic (causal networks), fuzzy (rule-based) and case-based (frames). There are image/signal processing-analysis capabilities in the form of programming languages with more than one hundred primitive functions. User-made programs are embeddable within knowledge basis, allowing the combination of perception and reasoning. The data analyzer toolbox contains a collection of numerical classification, pattern recognition and ordination methods, with neural network tools and a data base query language at inference engines's disposal. VEX-93 is an open system able to communicate with external computer programs relevant to a particular application. Metaknowledge can be used for elaborate conclusions, and man-machine interaction includes, besides windows and graphical interfaces, acceptance of voice commands and production of speech output. The system was conceived for real-world applications in general domains, but an example of a concrete medical diagnostic support system at present under completion as a cuban-spanish project is mentioned. Present version of VEX-93 is a huge system composed by about one and half millions of lines of C code and runs in microcomputers under Windows 3.1.Postprint (published version

An introduction to DSmT

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout this presentation to show the efficiency and the generality of this new approach