sustainНадежностьDependability1729-26462500-3909RAMS Journal Limited liability company10.21683/1729-2646-2015-0-4-16-29sustain-100Research ArticleСТРУКТУРНАЯ НАДЕЖНОСТЬ. ТЕОРИЯ И ПРАКТИКАSTRUCTURAL RELIABILITY. THE THEORY AND PRACTICEРАНЖИРОВАНИЕ ЭЛЕМЕНТОВ СИСТЕМЫ НА ОСНОВЕ НЕЧЕТКИХ ОТНОШЕНИЙ: МЕТОД НАИМЕНЬШЕГО ВЛИЯНИЯRANKING OF SYSTEM ELEMENTS ON THE BASIS OF FUZZY RELATIONS: THE LEAST INFLUENCE METHODРотштейнА. П.RotsteinA. P.

доктор технический наук, профессор, профессор кафедры управления промышленностью

Doctor of Technical Sciences, Professor, Professor of Chair Industrial Management

alexrot@inbox.ruИерусалимский политехнический институтИзраильTechnological University of JerusalemIsrael201506072016041629Copyright © Ротштейн А.П., 20162016Ротштейн А.П.Rotstein A.P.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.dependability.ru/jour/article/view/100

В этой статье предложен новый метод ранжирования элементов при обеспечении надежности систем с применением теории нечетких отношений. Задача ранжирования сведена к автоматической классификации на основе транзитивного замыкания нечеткого отношения сходства. Это позволяет разбивать множество элементов системы на непересекающиеся классы, не различимые по важности.

Для построения нечеткого отношения сходства каждый элемент системы представляется в виде вектора влияний. Мерой сходства пары элементов является расстояние между двумя векторами. Степень влияния каждого элемента предложено вычислять методом наименьшего влияния, который использует экспертные знания о наименьшем влиянии элемента и сравнение с ним других влияний по 9-бальной шкале Саати.

Предложенный метод свободен от допущения о независимости элементов и бинарном характерe надежности: «есть отказ - нет отказа». Возможными сферами применения предложенного метода являются системы с плохо определенной структурой и многофункциональными элементами: организационные, эргатические, военные и т.п.

This paper proposes a new method of ranking of elements to ensure the reliability of systems with application of the fuzzy relations theory. The ranking problem is formulated as automatic classification on the basis of the transitive closure of similarity fuzzy relation. It makes possible to divide a set of system’s elements into disjoint classes undistinguishable by importance.

For construction of a similarity fuzzy relation, each element of a system is represented in the form of a vector of influences. A measure of similarity of pair of elements is the distance between two vectors. Degree of influence of each element is proposed to be calculated by a method of the least influence, which uses expert knowledge about the least influence of an element and comparison of other influences with it by the 9-point Saaty scale.

The proposed method is free from assumption on independence of elements and binary character of reliability: «there is a fault – there is no fault». Possible fields of application of the proposed method are systems with ill-defined structure and multifunctional elements, e.g. organizational, ergatic, military ones, etc.

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The authors declare that there are no conflicts of interest present.