A Minkowskian theory of observation: Application to uncertainty and fuzziness |
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| Institution: | 1. Peter Grünberg Research Center, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;2. Department of Management, Hohai University, Nanjing 211100, China;3. College of Precision Instruments & Opto-electronics Engineering, Tianjin University, Tianjin 300072, China;1. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Baja California, A.P. 1880, C.P. 22860, Ensenada, Baja California, México;2. División de Ciencias e Ingenierías Campus León, Universidad de Guanajuato, A.P. E-143, C.P. 37150, León, Guanajuato, México;1. Department of Mathematics, University of Bergen, Norway;2. School of Mathematics, Statistics and Op. Research, Victoria University of Wellington, New Zealand;1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;2. Skolkovo Institute of Science and Technology, Skolkovo 143026, Russia;3. L. D. Landau Institute for Theoretical Physics, Chernogolovka 142432, Russia;4. Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia |
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| Abstract: | This paper examines various ways to introduce subjectivity in the measures of uncertainty. In the first part, by using a simple physical remark concerning discrete entropy in Shannon sense, we derive a so-called ‘complete discrete entropy’ which provides a unified approach to discrete and continuous entropy, and applies directly to variables which involves both probability and possibility.In the second part, by using three elementary axioms, we derive a Minkowskian theory of observation which holds when the observable is a pair (syntax, semantics) and which involves a parameter which is directly related to the subjectivity of the observer. This model is then applied to the observation of uncertainty, transinformation and membership, in which case it provides a new approach to fuzzy number. |
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