Solving game with nature with fuzzy linguistic parameters

The article considers a situation requiring decision making, formalized as a game with nature. To take into account possible uncertainties in estimation of initial parameters of the game of probability of certain states of nature and elements of the payment matrix manifestation, the author proposes their representation in the form of fuzzy, linguistic statements without restrictions on the type of membership functions of corresponding fuzzy sets. It is proposed to take into account the influence of possible states of nature by changing the truth of fuzzy estimates of the consequences of possible decisions (elements of the payment matrix). The choice of the best strategy is based on the integral assessment of the consequences of a possible decision on the whole space of states of nature, obtained in the form of an equivalent fuzzy set with a triangular membership function, with the subsequent calculation of the ratio of the coordinate of the center of gravity of this set to the level of its fuzziness. The value of this ratio, characterizes the level of compliance of available solution options with the preference assumption.