METHOD OF RECOVERY OF PRIORITY VECTOR FOR ALTERNATIVES UNDER UNCERTAINTY OR INCOMPLETE EXPERT ASSESSMENT

Abstract

Aim. The so-called pair-wise comparison method is one of the most popular decision-making procedures owing to its efficiency, flexibility and simplicity. The primary disadvantage of this method in the context of expert evaluation of large numbers of alternatives or within a sufficiently wide field of knowledge is the impossibility to compare each element with each other, both due to the large number of such comparisons, random gaps and difficulties experienced by the expert while comparing some alternatives. The assessments are affected by gaps that complicate decision-making, as most statistical methods are not applicable to incomplete sets of data. The fairly popular algorithm for processing of pair-wise comparison matrices (the Saaty algorithm) cannot work with matrices that predominantly contain zero components. The purpose of the paper is to develop a method of processing comparison matrices in order to obtain weight coefficients (weights) of the considered alternatives that enable quantitative comparisons. Methods. In practice, there are several approaches to managing sets of data with gaps. The first, most easily implementable, approach involves the elimination of copies with gaps from the set with further handling of only complete data. This approach should be used in case gaps in data are isolated. Although even in this case there is a serious risk of “losing” important trends while deleting data. The second approach involves using special modifications of data processing methods that tolerate gaps in sets of data. And, finally, there are various methods of evaluation of missed element values. Those methods help to fill in the gaps in sets of data based on certain assumptions regarding the values of the missing data. The applicability and efficiency of individual approaches, in principle, depends on the number of gaps in data and reasons of their occurrence. In this paper, the pair-wise comparison matrix is considered in the form of a loaded graph, while the alternatives are the nodes and comparisons are the edges of the graph. Respectively, if a pair of alternatives occurs for which the expert could not specify a preference, the corresponding edge is absent. The paper considers a way of removing edges that correspond to the most controversial values, i.e. a cycle breakage algorithm that causes transformation of the initial graph to the spanning tree that allows for unambiguous comparison of any two alternatives. The algorithm of joint alignment of both the upper and lower boundaries of expert assessments is not considered in this paper. Results. The paper gives an example of practical application of the developed algorithm of processing incomplete matrices of pair-wise comparisons of ten objects obtained in a certain expert assessment. It also shows the efficiency of the suggested approach to priority recovery of compared alternatives, explores ways of automating computing and future lines of research. Conclusions. The proposed method can be used in a wide range of tasks of analysis and quantitative evaluation of risks, safety management of complex systems and objects, as well as tasks related to the verification of compliance with the requirements for such highly dependable elements as nuclear reactors, aviation and rocket technology, gas equipment components, etc., i.e. in cases when low (less than 0,01) probabilities of failure per given operation time are to be evaluated, while the failure statistics for such elements in operation is practically nonexistent. The proposed algorithm can be applied in expert assessment in order to identify the type and parameters of time to failure distribution of such highly dependable elements, which in turn will allow evaluating dependability characteristics with the required accuracy