Shtankevych O. Models and Methods of Automated Support in Hierarchical and Network Decision Making Systems

In this paper we develop new mathematical models and methods for solving complex multi criteria decision making problems with unformalized global decision goal. We propose new information technology to support decision making process. New decision support software is developed based on proposed information technology. First we investigate known decision support methods and put under lens their benefits and drawbacks. We concentrate on the most efficient and widely used methods for solving multi criteria decision making problems - the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP) by T. Saaty. We conclude on the following limitations of these methods: low robustness of the proposed priorities searching technique in case of significant error rate in experts' evaluations, impossibility to solve problems with large amount of alternatives and evaluation criteria, necessity to request and process a lot of information on experts' evaluations in case of high dimensional problems. We propose new linear programming optimization models for priorities searching by pair wise comparison matrices. The new models rely on and efficiently utilize additional information on type of error distribution in experts' evaluations when such information is available. Information on possible underestimation or overestimation of analyzed object's value in experts' evaluations is transformed into constraints of a linear programming problem. This allows to intelligently guide the process of priorities searching and improve efficiency of obtained objects' priorities even in the case of high rate of error in the elements of empirical pairwise comparison matrices. We develop new approach for sparse block wise filling of high dimensional comparison matrices when a big number of objects must be analyzed under a single criterion. Comparison matrices do not need to be completely filled and zero elements may remain in some positions. Some essential constraints must be satisfied to make recovery of priorities possible. The proposed approach reduces the amount of information which must be processed by human experts while evaluating many alternatives under a single criterion. Meanwhile the proposed approach occurred to be an efficient preliminary ordering technique in the case of a high error rate in experts' evaluations. We develop a validation framework to evaluate the efficiency of the proposed methods for objects priorities searching. In the process of validation we start with ideal priorities and fill up pair wise comparison matrices. We simulate possible errors in experts' evaluations using various types of statistical distribution. We run both proposed optimization methods and classic method to recover the priorities. To validate the block wise partial filling technique we randomly turn into zero some elements of comparison matrices. Euclidian distance metric is used to evaluate the resulting set of priorities by comparing to original true set. Based on conducted statistical experiments we compose a practical usage guidance on the proposed approaches for priorities searching. Depending on simulated type of error distribution and additional information on overestimations in experts' evaluations proposed methods give priorities which are up to ten times closer to the original true values by the Euclidian distance metric comparing to the classic method. The modification of the AHP method for solving high dimensional decision making problems is formulated. We use proposed linear optimization models and block wise matrix filling technique together with a new computational algorithm for efficient objects priorities searching in hierarchical decision making problems with extra high number of alternatives and high error rate in experts' evaluations. We expand all theoretical results obtained for AHP to use in the ANP method. We formulate modified ANP method to solve network based decision making problems with "back links" of influence and extra high quantity of analyzed objects. We present demonstrative examples of solving decision making tasks by means of the proposed AHP and ANP modifications. We propose new regression methods for decision function recovery when the problem of recovery is well-posed. This problem is solved in its general formulation - recovery of unknown function by proposed redundant functional description and limited experimental results set available. Objects priorities found by the means of AHP or ANP make up the limited experimental data set. We expand the proposed methods for the case of an error present in available experimental data. We propose to use the new regression methods for searching the decision function in complex decision making problems and meanwhile remark that the methods have general practical value. Based on the new theoretical results a new information technology of automated decision support is developed. Moving further we develop the decision support software which utilizes the modified ANP method with new mathematical models and methods integrated into it. The software has distributed architecture, operates in local area network and supports remote user access.