Inverted prioritization in AHP: evolution strategy and direct inversion | Inverzna prioritizacija u AHP: evolutivna strategija i direktni postupak
2011
Srđević, B., Poljoprivredni fakultet, Novi Sad (Serbia) | Blagojević, B., Poljoprivredni fakultet, Novi Sad (Serbia) | Srđević, Z., Poljoprivredni fakultet, Novi Sad (Serbia)
Important part of the Analytic Hierarchy Process method (AHP) is computing of so called priority vector, i.e. weights of the decision elements involved in pair-wise comparisons and creation of the reciprocal judgment matrix. Standard AHP derives this vector as the principal eigenvector of a matrix, and method used for this is known as Eigenvector Method. However, it is well known that deriving priority vector is underdetermined problem with practically indefinite set of possible solutions (matrices). In fact, the matrix space is enlarging dramatically with raising the number of decision elements and order of the related matrix. This is mainly due to inherent inconsistencies of the decision maker’s pair wise comparisons and limitations imposed by using certain ratio scale. In this paper, inversion problem is stated and solved with the use of: 1) Evolution strategy algorithm as an efficient stochastic search engine: for given priority vector identify most probable reciprocal matrix from which the vector could be derived and 2) Direct inversion method. When direct inversion method is used, all values are mapped according to original Saaty’s scale. Solving mechanism is based on original Saaty’s scale [1/9, 1/8, ..., 1/2, 1, 2, ..., 9] with fitness function defined as closeness of any individual priority vector, derived from generated matrix, to the given priority vector. An example application of proposed approaches is given, followed by brief discussion.
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