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City simulation software for modeling, planning, and strategic assessment of territorial city units
Svítek, M. ; Přibyl, O. ; Vorel, J. ; Garlík, B. ; Resler, Jaroslav ; Kozhevnikov, S. ; Krč, Pavel ; Geletič, Jan ; Daniel, Milan ; Dostál, R. ; Janča, T. ; Myška, V. ; Aralkina, O. ; Pereira, A. M.
SVÍTEK, M., PŘIBYL, O., VOREL, J., GARLÍK, B., RESLER, J., KOZHEVNIKOV, S., KRČ, P., GELETIČ, J., DANIEL, M., DOSTÁL, R., JANČA, T., MYŠKA, V., ARALKINA, O., PEREIRA, A. M. City simulation software for modeling, planning, and strategic assessment of territorial city units. 1.1. Prague: CTU & ICS CAS, 2021. Technical Report. ABSTRACT: The Smart Resilience City concept is a new vision of a city as a digital platform and eco-system of smart services where agents of people, things, documents, robots, and other entities can directly negotiate with each other on resource demand principals providing the best possible solution. It creates the smart environment making possible self-organization in sustainable or, when needed, resilient way of individuals, groups and the whole system objectives.
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Indecisive Belief Functions
Daniel, Milan
This study presents an idea of indecisive functions, their general and also special definitions, plausibility and pignistic indecisive belief functions. The rich structure of indecisive belief functions is studied in general, and also in special views: both general substructures and indecisive belief functions on three-element and general finite frames of discernment. We are focused to pignistic and contour (plausibility) indecisive belief functions, including their mutual relationship in our study. The later have interesting algebraic structure related to Dempster’s rule of combination.
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Homomorphic Coordinates of Dempster’s Semigroup
Daniel, Milan
Coordinates of belief functions on two-element frame of discernment are defined using homomorphisms of Dempster’s semigroup (the algebra of belief functions with Dempster’s rule). Three systems of the coordinates (h-f, h-f0, and coordinates based on decomposition of belief functions) are analysed with a focus to their homomorphic properties. Further, ideas of generalisation of the investigated systems of coordinates to general finite frame of discernment are presented.
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An Interpretation of Conflicting Parts of Belief Functions on Two-Element Frame of Discrement
Daniel, Milan
When combining belief functions by the conjunctive rules of combination, conflicts often appear, which are assigned to empty set by un-normalized conjunctive rule or normalized by Dempster's rule of combination. This contribution is devoted to an interpretation of the conflicting part of a belief function on a two-element frame of discernment. It is based on the author's idea of the unique decomposition of such function into its conflicting and non-conflicting part (CJS 2010, Otaru). A relation of conflicting part of a belief function to internal conflict of the function is also studied and a new definition of internal conflict is introduced. New internal conflict is compared with the previous approaches. Keywords: Belief function, Dempster-Shafer theory, uncertainty, Dempster's semigroup, internal conflict, conflict between belief functions, non-conflicting part of belief function, conflicting part of belief function.
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Introduction to Algebra of Belief Functions on Three-element Frame of Discernment - A General Case
Daniel, Milan
This contribution presents the second part of the introductive study of algebraic structure of belief functions (BFs) on 3-element frame of discernment. Algebraic method by Hájek & Valdés for BFs on 2-element frames is generalized to larger frame of discernment. Due to complexity of the algebraic structure, the study is divided into 2 parts, the present one is devoted to a case of general BFs. The definition of Dempster's semigroup (an algebraic structure) of BFs on 3-element frame is recalled from the first part of the study. Results related to Bayesian and quasi Bayesian BFs from the first part are also briefly recalled. Further substructures related to another subsets of general BFs are described and analyzed (including idempotents, simple complementary BFs, generalizations of subsemigroups of simple BFs) and subalgebras isomorphic to Dempster's semigroup on 2-element frame of discernment. Ideas and open problems for future research are presented.
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