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Comparison of fuzzy numbers on the basis of construction linear order relation


V.G. Chernov – Dr.Sc.(Econ.), Professor, Department of Computer Engineering and Control Systems, Vladimir State University named after A.&N. Stoletovs

For a large class of tasks related to the investigation of operations, the presentation of the initial data in the form of payment matrices is used: games simulating conflict situations; games with nature (statistical games); tasks of multi-criteria alternative choice; decision-making under conditions of uncertainty. In these problems, the maximin (minimax) principle is often used to find the best solution, because of its simplicity of implementation and interpretation of the results obtained. Traditionally, elements of payment matrices are appointed by experts and presented in point, numeric form, which contradicts the nature of expert assessments, which inherently inherent uncertainty. The use of fuzzy numbers in setting payment matrices allows you to consider the uncertainty of expert assessments when solving these problems. At the same time, the implementation of the maximin (minimax) principle with fuzzy elements of payment matrices involves a comparison of fuzzy numbers, which is more complex than comparison of point numbers. The article proposes a linguistic method for comparing fuzzy numbers, in which the estimation of the truth of a linguistic statement is used to construct a linear order relation on the set of fuzzy numbers forming a payment matrix. Unlike the known method, the proposed method for comparing fuzzy numbers assumes a minimal participation of the person making the decision, does not impose restrictions on the nature of the fuzzy-number membership functions, is simply formalized and programmed.

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