130 research outputs found

    Fuzzy Geometry of Phase Space and Quantization of Massive Fields

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    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

    (Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces

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    We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in a certain approximation, can be visualized as a time-dependent random graph. This strand of ideas is merged with another one, deriving from ideas, developed some time ago by Menger et al, that is, the concept of probabilistic- or random metric spaces, representing a natural extension of the metrical continuum into a more microscopic regime. It is our general goal to find a better adapted geometric environment for the description of microphysics. In this sense one may it also view as a dynamical randomisation of the causal-set framework developed by e.g. Sorkin et al. In doing this we incorporate, as a perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor changes added relating to previous wor

    Statistical Approach to Fuzzy Cognitive Maps

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    Fuzzy cognitive maps are studied from statistical standpoint. An analogy between these maps and linear regression and logistic regression models is drawn. Practical examples are also provided.Peer reviewe

    The Universal Plausibility Metric (UPM) & Principle (UPP)

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    <p>Abstract</p> <p>Background</p> <p>Mere possibility is not an adequate basis for asserting scientific plausibility. A precisely defined universal bound is needed beyond which the assertion of <it>plausibility</it>, particularly in life-origin models, can be considered operationally falsified. But can something so seemingly relative and subjective as plausibility ever be quantified? Amazingly, the answer is, "Yes." A method of objectively measuring the plausibility of any chance hypothesis (The Universal Plausibility Metric [UPM]) is presented. A numerical inequality is also provided whereby any chance hypothesis can be definitively falsified when its UPM metric of ξ is < 1 (The Universal Plausibility Principle [UPP]). Both UPM and UPP pre-exist and are independent of any experimental design and data set.</p> <p>Conclusion</p> <p>No low-probability hypothetical plausibility assertion should survive peer-review without subjection to the UPP inequality standard of formal falsification (ξ < 1).</p

    From fuzzy data to functional relationships

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    AbstractThe paper begins with a discussion and proposals on how to specify fuzzy data, especially from pseudo-exact point-shaped observations. Then the problems in finding a local approximation of the unknown functional relationship assumed to be valid are considered. For the next stage of the investigation, a family of functional relationships is chosen, and several methods are presented to estimate the parameter of this family using the specified fuzzy data. The methods are illustrated by an example
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