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| Number: |
A100300503
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| Name: |
Mathematical Foundation of Inference and Decision under Uncertainty |
| Investigator: |
| Hajek Petr, Prof. RNDr. DrSc. |
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Duration: |
1.1.2005 - 31.12.2009 |
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| Annotation: |
The project is planned to be a natural common continuation of a grant
project dedicated to mathematical foundations of fuzzy logics and of
logics of belief and of a grant project dedicated to alternative
(non-probabilistic) models and tools for managing uncertainty understood as randomness (possibilistic measures, measures with non-numerical values). The research will naturally continue in both directions, but a new twist is in systematic attention paid to the creative combination and common generalization of both. In mathematical fuzzy propositional and predicate logic, formal theory of syntax and semantics of new calculi based on the basic fuzzy logic BL will be developed; in the theory of models of randomness, various new measures will be presented and confronted with those already known. The combination of both approaches will concern fuzzy logics of beliefs, possibilistic measures for fuzzy events, testing of fuzzy hypotheses as well as non-truth functional fuzzy logics. |
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| Number: |
A1030003
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| Name: |
Polynomial and structured matrices |
| Investigator: |
| Fiedler Miroslav, Prof. RNDr. DrSc. |
| Fiedler Miroslav, Prof. RNDr. DrSc. |
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Duration: |
1.1.2000 - 31.12.2002 |
| Co-Investigators: |
| Vavrin Zdenek, RNDr. CSc. (MU AV CR) |
| Vavrin Zdenek, RNDr. CSc. (MU AV CR) |
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| Annotation: |
Using the recently obtaind results on companions and infinite companions of matrix polynomials, we expect to extend the known results about matrices ocurring in linear control systems to block matrices. Applications to solving systems of linear difference equations and linear differential equations with constant coefficients are also expected. In various classes of structured matrices (e.g. Hankel, Loewner, Cauchy as well as P-matrices, M-matrices, totally nonegative matrices atc.) spectral properties, inverse eqigenvalue problems, operations within the classes and relations between the classes will be studies. Some links to geometry and some applications of the results cal also be expected. |
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| Number: |
A1030004
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| Name: |
Mathematical foundations of inference under vagueness uncertainty |
| Investigator: |
| Hajek Petr, Prof. RNDr. DrSc. |
| Hajek Petr, Prof. RNDr. DrSc. |
| Hajek Petr, Prof. RNDr. DrSc. |
| Hajek Petr, Prof. RNDr. DrSc. |
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Duration: |
1.1.2000 - 31.12.2004 |
| Co-Investigators: |
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| Annotation: |
The project builds on the results of our preceding intensive study of many-valued logic and logics of belief that has contributed significantly to the development of their systematic mathematical and logical theory and has opened new problems as well as a way to a logical analysis of techniques of fuzzy logic (in the broad sense). This will be an advanced study of infinite-valued, modal and nonmonotonic logics (including pssobilistic and Dempster-Shafer belief logics), an analysis of fundamental mathematical theories inside these logics and development of a theory of finite models of fuzzy logic in connection with computational complexity and data analysis. |
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| Number: |
A1030103
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| Name: |
Scalable Sparse Linear Algebraic Solvers: Analysis, Development, Implementation and Application |
| Investigator: |
| Tuma Miroslav, Prof. Ing. CSc. |
| Tuma Miroslav, Prof. Ing. CSc. |
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Duration: |
1.1.2001 - 31.12.2003 |
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| Annotation: |
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| Number: |
A1030302
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| Name: |
Special classes of matrices |
| Investigator: |
| Fiedler Miroslav, Prof. RNDr. DrSc. |
| Fiedler Miroslav, Prof. RNDr. DrSc. |
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Duration: |
1.1.2003 - 31.12.2005 |
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| Annotation: |
Investigation of special classes of matrices of the following kind: 1. Matrices determined by inequalities, such as nonnegative matrices, M-matrices and their inverses, totally positive matrices, distance matrices, etc.
2. Matrices determined by a system of equalities, or determined by a system of parameters, such as Hankel, Toeplitz, Loewner, tridiagonal, acyclic matrices, etc.
Investigation of various characteristics and algebraic properties of such classes, e.g. spectral properties, as well as of mutual relationships between special classes. |
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