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Method of construction of fuzzy estimation models of complex systems accounting inconsistency of general and particular goals

Keywords:

V. S. Lavrukhin, A. S. Fedulov


The problem of construction of estimation models of systems is considered. One of the first problem definition of construction of fuzzy estimation models proposed by R. Bellman and L. Zadeh is described. Its advantages and disadvantages are considered. So the important conclusion about equivalence of constraints and goals in case of their definition in terms of fuzzy sets was drawn in statement by R. Bellman and L. Zadeh. But possibility of having different degrees of consistency between particular and general goals was not discounted. Earlier offered algorithms are considered. Their restrictions are shown This disadvantage is connected with the fact that the output fuzzy set of attainment’s degree of general goal explicitly contains fuzzy sets of attainment’s degree of particular goals. Specifically it leads to the fact that the algorithm is invalid in case where some particular goal is defined as inconsistent with general goal, or as antigoal. One must mention that definition of inconsistent goals is quite acceptable in complex systems. So the problem of development of algorithm of construction fuzzy estimation models of complex systems accounting possible inconsistency between some particular and general goals is rather urgent. The variant of modification of algorithm is offered. The main distinction of the given method is the fact that the output fuzzy set of attainment’s degree of general goal explicitly does not contain fuzzy sets of attainment’s degree of particular goals. It allows taking into the account possible inconsistency between particular and general goal. The detailed description of proposed algorithm is given. The illustrative example of construction of fuzzy estimation model is presented. The general goal is the growth of profit, particular goals are receipts increase and expenditures rise. Based on this example and series of other experiments with the proposed method the conclusion about adequacy of constructed fuzzy estimation models of attainment of general goal of complex system using degrees of attainment of particular goals accounting possible inconsistency between some particular and general goals is drawn.
References:
May 29, 2020

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