Guram Tsertsvadze

In the present work the problems related to the construction of a probabilistic model of the Cartesian product of canonically conjugated fuzzy subsets is investigated. The case of the Cartesian product of two fuzzy subsets with commuting colors is considered in detail. It is shown that the model most fully reflects the special "additional" nature of the connection between two canonically conjugated colors in a form of the uncertainty principle for the corresponding dispersions.

In the present work is considered an approach, according to which canonically conjugate colors in the theory of fuzzy sets are related to the properties of information functions and noncommutative linear operators in Gilbert's space: each information state corresponds to the estimation of compatibility function, every color – to the operator. It is supposed that color, as some property (attribute), characterizing a condition of a system, can receive different values called by eigenvalues of this color. The cases of discrete and continuous spectrum of eigenvalues of color are considered. The example of calculation of conditional computable values of color is given.

ნაშრომში განხილულია გარკვეული კლასის გამოთვლითი ამოცანებისათვის სპეციალურად შექმნილი პროგრამების ვერიფიკაციის შესაძლებლობა Model checking-ის მეთოდის გამოყენებით პროგრამებში პარალელიზმის განსაკუთრებულობის გათვალისწინებით. პროგრამის სისწორის დამტკიცება განსხვავდება ტრადიციულისაგან და დაიყვანება არა მარტო ცალკეული განშტოების ვერიფიკაციაზე, არამედ განშტოებების ურთიერთმოქმედების ანალიზზე მათი პარალელური სტრუქტურის გათვალისწინებით.

The paper discusses the possibility of verifying programs for certain classes of computational tasks using the Model checking method, taking into account the specificity of parallelism in programs. The validation of the program differs from the traditional one and is reduced not only to the verification of individual branches, but also to the analysis of the interaction of branches by considering their parallel structure.

A conditional characteristic function of color and conditional computable values of color are considered. When calculating the compatibility function of the Cartesian product of two fuzzy canonically conjugate subsets, we will proceed from the corresponding characteristic function.

Cases of Cartesian product of two fuzzy subsets with both commuting and non-commuting colors are considered.

It is shown that from the probability model of the Cartesian product of two fuzzy subsets, a relation follows, establishing a relationship between the variances of canonically conjugate colors.

The generalized information theory is constructed on the base of chromotheory of canonicaly conjugate fuzzy subsets. This allows us to process the objective and subjective information simultaneously and carry informational functions in the Hilbert space, where the colours will be presented as linear operator. Using this approaches we can establish the commutation conditions for operators that are corresponding to various colours, i. e. to receive the analogues of Heisenberg principle for knowledge presentation and construction of arithmetic of fuzzy numbers, which allows us development of fuzzy information processing methods and decision making algorithms.

On the base of canonically conjugate fuzzy subsets we construct the optimal arithmetic of canonically conjugate fuzzy real numbers, which allows consideration of the combined statistics (probabilistic and possibilistic) of natural language. Constructed formalism permits to investigate the quantitive aspects of the natural languages structures. Carrying out possibility analysis of language is a cardinal problem of quantitative descriptions

of language, that is very important from the point of view of creation of the future generations of computers, where communication of the consumer with a computer will occur

in a natural language.

The theory of canonically conjugate fuzzy subsets is presented. The Heizenberg’s principle’s analog principle is established. In Hilbert space the informational functions and joint membership functions are defined. In the work colour operators, Zadeh operators and corresponding commutativity relations are presented

The new chromo theory of canonically conjugate fuzzy subsets is presented. The Heisenberg’s principle’s analog principle is established. In Hilbert space the informational functions and joint membership functions are defined. In the work Zadeh operators, color operators and corresponding commutatively relations are presented.

The experton theory is presented in a such form that permits to use it directly for decision making. The new form of experton theory is applied to scientific themes presented on the concurs. Each them is characterized by some attributes in 10 point system. The algorithm of decision making is presented by some rules of matrix transformations. Shortly the expertons algebraic properties are considered.

The new chromotheory of canonicaly conjugate fuzzy subsets is presented. The Heizenberg’s principle’s analog principle is established. In Hilbert space the informational functions and joint membership functions are defined. In the work Zadeh operators, colour operators and corresponding commutativity relations are presented.  

Doctoral Thesis Referee

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Scientific editor of monographs in foreign languages

Scientific editor of a monograph in Georgian

Editor-in-Chief of a peer-reviewed or professional journal / proceedings

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Member of the editorial board of a peer-reviewed scientific or professional journal / proceedings

Participation in a project / grant funded by an international organization

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Membership of the Georgian National Academy of Science or Georgian Academy of Agricultural Sciences

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