## Volume 2, No. 2, 2007

- Bronevich A.G., Karkishchenko A.N.

**«The description of fuzzy measures in the framework of probabilistic approach»**

An algebraic investigation of fuzzy measures (monotone normalized set functions) is carried out in the paper. These set functions can be interpreted as lower estimates of probabilities. We investigate properties of convex families of fuzzy measures, that are called statistically consistent measures, generalized coherent lower probabilities, coherent lower probabilities, 2-monoitone measures. The paper results are the detailed algebraic description of the pointed families of fuzzy measures, properties of their set theoretical inclusion, and sufficient and necessary features of a fuzzy measure to be in these families.Resources: elibrary.ru.

- Utkin L.V., Simanova N.V.

**«Analytic hierarchy process under partial information about criteria and alternatives»**

A new method of a multi-criteria decision problem based on the analytic hierarchy process (AHP) under condition that experts compare not only single alternatives and criteria, but also their groups is proposed in the paper. The standard AHP can not be used under such the expert estimation. Therefore, the proposed method is a modification of the AHP where the expert estimates are processed by means of Dempster-Shafer theory. A numerical example illustrates and explains the method.Resources: elibrary.ru.

- Orlov S.V.

**«About one mechanism of statement of the diagnosis in an expert system of medical diagnostics»**

The method of increase of accuracy of statement of the diagnosis in expert system of the medical diagnostics, based on use of model of a condition of the patient is offered. The subsystem of a logic conclusion, diagnostic linguistic model and the mechanism of statement of the diagnosis in the automized system of the medical diagnostics created on the basis of the Tula state university is considered.Resources: elibrary.ru.

- Barun Das, Manas Kr. Maiti, Samarjit Kar, Manoranjan Maiti

**«Fuzzy interactive and Necessity approach»**(in English)

An economic production quantity model with storage space and budget constraints of a volume flexible manufacturing system for deteriorating items is considered. Here it is assumed that the demand rate is constant upto a certain level of stock and after that it depends on stock itself. The unit production cost is taken to be a function of the finite production rate. Here, the inventory costs, selling price, storage space, and available budget are defined imprecisely. Thus the model is developed with variable demand and unit cost in fuzzy environment with fuzzy resource and fuzzy parameters in the objective function.Resources: elibrary.ru.

- Pravati Maity, Manas Kumar Maiti

**«An EOQ model with fuzzy random planning horizon»**(in English)

An economic order quantity (EOQ) inventory model is developed over a fuzzy random planning horizon incorporating inflation and time value of money. It is assumed that planning horizon follows exponential distribution with imprecise parameter (fuzzy) parameter. The model is formulated using profit maximization principle and nearest interval corresponding to the expected total profit is obtained. Finally the problem is transferred to a Multi-objective programming problem and solved via Multi-Objective Genetic Algorithm (MOGA). For a particular case when parameter of the distribution of planning horizon is crisp, a closed form solution is obtained for expected total profit. The model is illustrated with some numerical examples.Resources: elibrary.ru.