## Volume 2, No. 3, 2007

#### Articles

- Martsenyuk M.A.

**«Matrix representation of fuzzy logic»**

Matrix representation of fuzzy logic is developed. Analysis of logic laws is given and it is cleared up which ones are become incorrect for fuzzy operations. It is shown that fuzzy logic deduction is equivalent to solving of some matrix equations. As a measure of fuzziness the entropy is proposed. Realization of the proposed fuzzy logic representation is correspond to some ramified current circuit. Linguistic variables are presented as vector fields. The operations with linguistic variables have to be additionally determined by the rules proposed by L.Zadeh or by vector logic rules. Some examples of fuzzy deduction are considered. In the conclusion generalization of the fuzzy logic to the many-valued variables and the coupling of vector fuzzy logic with quantum logic are discussed.Resources: elibrary.ru.

- Ojha A., Mahapatra T., Mondal S., Maiti M.

**«Capacitated, multi-objective, solid transportation problem with fuzzy fixed charge and partial varying charges, vechicle cost, fuzzy resources, demands and conveyances»**(in English)

In this paper, a capacitated, multi-objective, solid transportation problem with imprecise resources, fuzzy demands, uncertain conveyance and other costs are considered. Other costs include fuzzy direct charge, fuzzy charge inversely varying with transported quantity, fuzzy fixed charge and deterministic vechicle cost. The transportation problem has been formulated as a constrained fuzzy linear programming problem, transformed into equivalent crisp multi-objective problem using fuzzy interval approximation and then solved by interactive fuzzy programming technique (IFPT) and Generalized Reduced Gradient (GRG) method. An illustrative numerical example is demonstrated to find the optimal solution of the proposed model. The Pareto optimality of the solution is tested.Resources: elibrary.ru.

- Filatova N.N., Valdes A., Al-Nazhar N.K.

**«Algorithm for recognition of two classes of respiratory noise based on the fuzzy rules»**

In clause the questions of creation based on the fuzzy rules algorithm for recognition of two classes of respiratory noise are considered. The algorithm is based on two procedures. The first procedure - description of respiratory noise by a set of linguistic attributes. The second - procedure of a logic conclusion (Fuzzy conclusion) based on rules, determining border of classes.Resources: elibrary.ru.

- Yarushkina N.G.

**«Fuzzy systems: towards and results overview»**

It is proposed an fuzzy systems overview based on proceedings of IFSA'05 and IFSA'07 international conferences.Resources: elibrary.ru.

#### Short Communications

- Makarov A.N., Korneyev K.B.

**«Forecasting of operational reliability on the basis of methods of fuzzy logic»**

Forecasting of operational reliability of elements of electric circuits deals with the necessity of use of input parameters difficultly formulated in a numerical kind describing operational characteristics of electro-contact connections. Most effectively the opportunity of input of non-numerical values is realized by use of linguistic variables and the mathematical apparatus of fuzzy logic.Resources: elibrary.ru.