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A method of solving the selection problems with fuzzy parameters by means of a special algebraic structure is proposed. To construct such an algebraic structure, we propose a special transformation of existing fuzzy numbers to the simpler form (L or R number) while keeping the most of the initial expert information. This structure avoids deficiencies limiting applicability of the other known structures, such as unjustified extension of the uncertainty, violation of certain natural relations, openness of the carrie...