|Article title||MATHEMATICAL LOGIC APPLICATION TO THE SIMULATION PROBLEMS|
|Section||SECTION V. MODELLING OF COMPLEX SYSTEMS|
|Month, Year||07, 2014 @en|
|Abstract||The logic-algebraic aspects of the complicated systems simulation are considered. The possibilities of the mathematical notions and methods application to the analysis of some problems of the knowledge theory are investigated, the possibilities and the boundaries of the well-known notions of isomorphism, homomorphism and their extensions use for the problems of classification, recognition and for the different problems of the knowledge theory are examined. The different algebraic transformations under complicated systems simulation are considered. The variety of such systems are groups, semigroups, rings, fields. The comparison of the isomorphism and homomorphism notions with the point of view not only as for the structure, but as for the functioning is given. The different extensions of the homomorphism notion as the sets and their labels firstly and as the objects of abstract algebra then are reduces. The fuzzy mathematics notions under simulation of the hard formalized control problems in the decision making systems are used. The main classes of the suggested in the paper conception are the isomorphism and homomorphism notions nonseparably connected with the identifying of the different objects. In these terms the formation of the separate abstract notions and the construction of the integral conceptual schemes – models are describes. The conception offered in the paper have its applicability level. All the traditional ideas about the simulation are assumed that perfect model have to be the isomorphic pattern of represented its fragment of actual reality. As long as the ideal is difficulty reach than it is necessary to use the homomorphic models. The process of separation and classification the abstract concepts reflecting the attributes of external world can interpret as some homomorphic transformation. The process of formalization already constructed conceptual scheme in the form of scientific theory can interpret as isomorphic transformation. In the paper mentioned that any homomorphism means the union into equivalence classes of the objects union forming the abstract concepts. In the paper it is suggested to use the ideas of factorization of considered objects systems, introducing on them the different metrics, topologies, partial presetting both the same investigating systems, and the defined on them operations and predicates by simulation.|
|Keywords||Homomorphic transformation; congruence; factor set; simulation; fuzzy sets; degree of fuzzy equality.|
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