Рассматриваются подходы в части многокритериальной оптимизации применительно к материальному обеспечению сил и средств МЧС России в условиях ликвидации последствий крупной чрезвычайной ситуации. В рамках материального обеспечения сил и средств МЧС России рассматривается план подвоза материальных средств, формализуемый в виде множества пар склад - потребитель , и маршруты для перевозки запланированных материальных средств. Предполагается, что показатель надежности плана подвоза материальных средств является величиной, заданной нечетко. Предлагаются подходы к решению указанной задачи, использующие теорию нечетких множеств, нечеткую логику и алгоритм нечеткого вывода Мамдани. Показано, что новизна этих подходов определяется возможностью использования при планировании подвоза материальных средств двух и более критериев в отличие от математических моделей, базирующихся на применении для этих целей лишь одного критерия. Установлено, что использование нечеткого логического вывода при разработке моделей систем в отличие от традиционного математического аппарата обеспечивает требуемый уровень устойчивости к неточностям моделей и их транспарентность. Предложенные теоретические положения иллюстрируются содержательным примером.
At the organization of material support of forces and means of Emercom of Russia being engaged in liquidation of consequences of emergency situations an important role plays the task of selecting, on the one hand of the safest, and on the other hand - possible economical routes on which to perform the supply of material resources for the purposes described above. At the same time (it is very important) the safety performance indicators of roads are not clearly defined a priori. In order to overcome this uncertainty in the source data it is proposed to use the theory of fuzzy sets and fuzzy logic. The article contains a brief summary of the provisions of the branches of mathematics required to solve this problem. The main result of this work is to develop two approaches to assessing the reliability of the plans of supply of material resources to the forces and means of Emercom being engaged in liquidation of consequences of emergency situations. The reliability of a road is proposed to characterize by the truth value of the statement “the road is reliable”, the reliability of a supply plan of material resources refers to the minimum of the reliabilities of routes used in this plan. The reliability of a route is the minimum of the reliabilities of roads, of which the route consists. The specified technique of calculation of reliability of routes and the entire plan is based on the definition of the conjunction of fuzzy statements. To determine the reliability of a road two approaches are considered, which are associated with the calculation of the value of the output indicator “reliability” using the known values of the input parameters. The first indicator - “protection” is measured by the number of the Traffic Police posts of on 100 kilometers of road, and the second “viewing distance” is the average distance at which a side of the road is viewed. In the first approach the output value is considered as a convolution of the input that is performed using the ideas of the theory of vector optimization and ideas of Zadeh and Bellman. The second approach is based on the method of Mamdani fuzzy inference. Here, for given values of the input indicators it is constructed a membership function of the output, provided that the input took the specified values. Obtained by converting a fuzzy set into a crisp number the value of the output indicator is proposed to use as reliability characteristics of the road. In conclusion a relatively simple algorithm is given for selecting the most reliable plans of supply of material resources to the forces of Emercom of Russia and among them of the most cost-effective plans.
The authors declare that there are no conflicts of interest present.