The essence of complex system content is determined by the natural directivity of a large in amount list of factors, which is submitted for consideration by the decision-maker (DM), while describing its time functioning process. A complex system has a property of forming its own behavior of the process development of its time functioning. A cognitive model of functioning process provides expert determination of factors significance in accordance with their multi-consequence as membership function values of kernel fuzzy subset of fuzzy binary relation of factors strict preference, which form the entire finite set. Variables that correspond to factors are random and non-mass character and are changeable in time. That’s why a cognitive model corresponds to the state when t=τ and a complex system is functioning, and the assumed α value of membership function of kernel fuzzy subset of fuzzy binary relation of strict preference selects, when t=τ, a clear subset of influencing factors, as a decision-maker understands, on the own behavior of process development of complex system functioning. The estimation of the effectiveness and decisionmaking risk concerning the predictable content of a clear subset of factors with the accepted α for realization of purposeful influence to prevent negative tendencies of forming its own behavior of the process development of complex system functioning.
a complex system, a fuzzy subset, a subset of influence factors, efficiency, risk, decision-making