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Carriers of algebra of algorithms

Ovsyak V., Ovsyak O.

Measurement Automation Monitoring

2015

Vol. 61, No. 4

98--100

Operations of modified system of algorithm algebras [10, 11] and algebra of algorithms [12-15] are presented in the paper. The paper shows operations of mathematical logic on the three-meaning alphabet. It considers converting of logical to operator values that are performed in the system of algorithmic algebras and its modifications. It presents constants, variables and operators, which are components of models of algorithms and systems, as predicates. It gives a comparative assessment of mono- and polycarrier algebras of algorithms.

Ordered fuzzy numbers

Kosiński W., Prokopowicz P., Ślęzak D.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 3

329-341

Fuzzy counterpart of real numbers is presented. Fuzzy membership functions, which satisfy conditions similar to the quasi-convexity are considered. An extra feature, called the orientation of the curve of fuzzy membership function, is introduced. It leads to a novel concept of an ordered fuzzy number, represented by the ordered pair of real continuous functions. Arithmetic operations defined on ordered fuzzy numbers enable to avoid some drawbacks of the classical approach.