Issue 1, 2015

Krivulin N. K., Gladkikh I. V. Computation of the Consistent Pairwise Comparison Matrix in Marketing Research by Using Methods of Tropical Mathematics.

In the paper, a problem of rating alternatives based on their pairwise comparisons is considered, which arises in the analysis of consumer preferences in marketing research. Questions of constructing pairwise comparison matrices are discussed, and the problem of the consistency of such matrices is examined. The rating problem is formulated as a problem of approximating the pairwise comparison matrix by a consistent matrix. A short overview is given of necessary notions and results of tropical mathematics, whose methods are then used for unified representation and complete solution of the approximation problems in the form of expressions, ready for direct numerical computation. A common approach is applied to approximating both multiplicative and additive pairwise comparison matrices. New solutions are proposed to the problems of approximation of symmetrically reciprocal and skew-symmetrical matrices, as well as of arbitrary multiplicative and additive pairwise comparison matrices. The solutions obtained are extended to the case of rating alternatives on the basis of simultaneous approximation of several matrices. To illustrate the results, numerical examples of calculating the vector of ratings of alternatives are presented for a problem in which a buyer analyzes the significance of key characteristics of the supply of sellers to select a seller in a competitive B2B market. Keywords: marketing research, analysis of consumer preferences, methods of pairwise comparison, tropical mathematics, approximation problem, pairwise comparison matrix, vector of ratings of alternatives.

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