Method of the vector of similarity to ideal solution in alternatives

A method for solving multiple-attribute decision-making problems at one criterion level is discussed, followed by a presentation of a method based on compromise programming elements, Lp metrics and the TOPSIS method. Suggestions for forming the initial decision-making matrix have been given as well as for the transformation of multiple criteria values. Compromise solutions are obtained based on the values of Lp metrics functions and their combinations with coefficients - functions of relative credibility depending on solution dimensions. The obtained solutions depend on the parameter p in Lp metrics, parameter p being a balancing factor between the solution with the highest total utility and the solution with minimax deviations of criteria values from the ideal and negative-ideal solutions. If a unique solution is required, it is obtained by encompassing all Lp metrics functions and by applying the vector of similarity to ideal solution, which also includes the negative-ideal solution influence. The article shows a method for obtaining compromise solutions based on the values of elements of partial similarity to ideal vectors and the influence of a subjectivelly determined negative ideal on solutions. The method application has been illustrated by a numerical example.