Contextual algorithm for decision of fuzzy estimation problems with network-like structure of criteria on the basis of fuzzy measures Sugeno

In this article the algorithm for the decision of alternatives' estimation problems for following conditions is considered. Values of alternative's characteristics (properties) are fuzzy. They are formalized as fuzzy sets. The estimation criteria structure is network-like and is formalized as the oriented graph with one source and many drains. The alternative's estimation result is calculated in criterion-source. Connections between criteria are formalized by fuzzy measures Sugeno. Upper-level criteria are considered as contexts for lower-level criteria. Fuzzy integrals Sugeno or Choquet are used as aggregation operator. In article also the properties of fuzzy measure and fuzzy integrals (Sugeno and Choquet) are analyzed. Properties of fuzzy measure and integrals are comparing with properties of other mathematical tools. As example the car's estimation problem is presented.fuzzy measure (Sugeno); fuzzy integral (Sugeno and Choquet); alternatives estimation; criteria structure

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

Fuzzy Geometry of Phase Space and Quantization of Massive Fields

The quantum space-time and the phase space with fuzzy structure is investigated as the possible quantization formalism. In this theory the state of nonrelativistic particle corresponds to the element of fuzzy ordered set (Foset) - fuzzy point. Due to Foset partial (weak) ordering, particle's space coordinate x acquires principal uncertainty dx. It's shown that Shroedinger formalism of Quantum Mechanics can be completely derived from consideration of particle evolution in fuzzy phase space with minimal number of axioms.Comment: 13 pages, Talk given at QFEXT07 Workshop, Leipzig, Sept. 200

Just How Final are Today's Quantum Structures?

I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and Epistemological Problems", held at the Biannual Symposium of the International Quantum Structures Association, Liptovsky Jan, September 1998. To appear in journal: Soft Computing (2001).Comment: 3 pages, tcilate

Controlling Complexity in Spatial Modelling

The present complexity approach is based on two assumptions: A1: measurability of deviations of outcomes with respect to reference values; A2 : extension of A1 to multi-set analysis. Complexity is then defined in terms of multi-set deviation compared to single-set ones; an interpretation is given in terms of information costs; examples show the relevance of the interpretation. As a useful by-product the explicit solution of the quadratic part of the discrete logistic ? one of the examples ? is derived; a set of pij-numbers is introduced, and a workable method for generating them exposed. Extensions are considered, in particular controllability. A further application is then proposed, namely to hypergraph conflict analysis, in particular conflict resolution. Many decisional conflicts at the spatial level can be axiomatised in this form; it is shown how the use of particular structures ? in the mathematical sense of that word ? of the problem allows of reducing greatly the degree of complexity of the problem, and hence the difficulty of finding a solution.Chaos, complexity, conflict, dynamics, hypergraphs, information

A theory of concepts and their combinations I: The structure of the sets of contexts and properties

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts