Estimating the Solution Sensitivity in Application of the Modified Morphological Analysis Method
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ESTIMATING THE SOLUTION SENSITIVITY IN APPLICATION OF THE MODIFIED MORPHOLOGICAL ANALYSIS METHOD
I. O. Savchenko
UDC 519.87
Abstract. The author proposes a technique to evaluate the sensitivity of a solution, obtained by the modified morphological analysis method, to variations in input data. A new way is proposed to find the probabilities of alternatives in the method. It is used to analyze the sensitivity of pairs of alternatives to rank switching when both initial probability estimates and values of correlation matrix vary. Keywords: sensitivity analysis, morphological analysis method, decision-making support, technology foresight, expert estimation. INTRODUCTION In solving foresight problems [1], the majority of objects, processes, and phenomena under study are characterized by inaccuracy, uncertainty, incompleteness, and fuzziness of information; therefore, traditional mathematical models and approaches are impossible or inexpedient. This gave rise to a number of qualitative analysis methods, one of which is the modified method of morphological analysis (MMMA) [2, 3]. The object of inquiry is represented as a morphological table consisting of its characteristic parameters, each associated with a set of alternatives. To handle the object in such a form, expert evaluation of the probabilities of alternatives and values of correlation matrix is carried out in the MMMA and is then used to calculate the final estimates of the probabilities of alternatives, taking into account possible relations between parameters of the object [3]. These estimates can be used for decision-making or as input data for the second stage of MMMA, at which expected productivities of alternatives of the morphological table are evaluated. Expert evaluation, which is the basis of qualitative analysis methods, is often a unique source of information about foresight objects; however, expert estimates are subjective and only reflect the real world in some approximation. In this connection, if a decision is made on the basis of the results of qualitative analysis methods, there is always a possibility that inaccuracy of input data will lead to erroneous ranking of alternatives. To resolve this issue, sensitivity analysis is sometimes performed. In particular, there are studies in this field for the hierarchy analysis method [4, 5]. Such an approach allows revealing the most critical initial estimates, i.e., the ones that cause changes in the ranks of alternatives in final ranking under smaller deviations. It is necessary to pay special attention to these estimates and probably carry out updating estimation since the obtained information may appear crucial for decision making. The purpose of the present paper is to develop a technique for sensitivity analysis for the MMMA.
Scientific and Training Center “Institute of Applied Systems Analysis” of the National Technical University of Ukraine “KPI,” Ministry of Education and Science of Ukraine and National Academy of Sciences of Ukraine, Kyiv, Ukraine, [email protected]. Translated from Kibernetik
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