Alexander Chunikhin

Alexander Chunikhin

A new class of Semantic Numeration Systems, namely, positive rational Semantic Numeration Systems is introduced. For cardinal semantic operators, differences in the formation of carry (common carry) and remainders are defined. The properties of positive rational Semantic Numeration Systems as dynamical systems are formulated and illustrated through analytical and numerical examples. A first attempt at defining partial integer Semantic Numeration Systems is proposed.

Alexander Chunikhin, Vadym Zhytniuk

The concept of fuzzy cardinal semantic transformation as a basis for creating fuzzy semantic numeration systems is introduced in this work. Both fuzziness of the initial data - cardinals of abstract entities - and fuzziness of the parameters of the cardinal semantic operators are considered. We also expressed cardinal semantic transformations for discrete fuzzy numbers and for continuous triangular fuzzy numbers. The principle of formation of the fuzzy common carry in the cardinal semantic operators with multiple inputs is formed.

Alexander Chunikhin

This work is the first to propose the concept of a semantic numeration system (SNS) as a certain class of context-based numeration methods. The development of the SNS concept required the introduction of fundamentally new concepts such as a cardinal abstract entity, a cardinal semantic operator, a cardinal abstract object, a numeration space. The main attention is paid to the key elements of semantic numeration systems - cardinal semantic operators. A classification of semantic numeration systems is given.