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Method of inference with fuzzy situational net


M. M. Zernov

The problems of inference with Fuzzy Situational Net (FSN) are considered in this article. The FSN is graph, which nodes represent the states of system under control and transfers represent controlling decisions. Using FSN allows predicting possible system states after implementing a series of controlling influences. The main problems of FSN inference are: searching the best controlling scenario, leading system from the current state to the best of attainable states (or a set of possible states); predicting the results of some controlling scenario (especially with partly defined controlling sequences). The method of inference with FSN is offered. The method bases on that fact that main problems of FSN inference reduce to the problem of search a sub graph of special form. The sub graph topology is defined by the FSN kind and current problem limitations. If FSN takes into account stochastic event uncertainty for controlling influences, the inference result must answer a multivariate scenario of control. The sub graph in this case represents a tree. Otherwise scenario becomes single-version and sub graph represents a chain. The offered method consists of four mane steps. The first one is sub graph topology definition. The second – finding nodes estimates. The third – finding transfers estimates. And the fourth step is getting optimal sub graph. The last step may be implemented in two different ways. The first way is to form all permitted inference sub graphs, and after that find their estimates. The sub graph with the best estimate is the sought one. Another way is to construct the optimal sub graph with the best total estimate. The offered method uses three estimate models together. They are: the model of system under control state estimate (de-fines the nodes estimates), the model of controlling decisions estimates (defines the transfer estimates), and the model of controlling scenario estimate (defines the sub graph estimate). All of this estimate models are represented as a functions. These functions arguments are appropriate topology elements. The value range for estimate functions may be certain numbers from [0; 1] interval, as fuzzy numbers from the same interval. The node estimate function defines the state correspondence to adopted system of preferences and quality criteria. It allows defining target states or a preferred set of attainable states. The transfer estimate function allows getting a controlling decision value for obtaining preferred states. In the case of multivariate scenario it may use a set of decision estimate strategies. And the last estimate function defines total controlling scenario estimate. It may depend on nodes and transfers estimates only, but it may also depend on common sub graph parameters, such as length of chain, leading to target states of system under control.
May 29, 2020

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