A Method for Solving a Class of Multiple-Criteria Analysis Problems

AMS subject classification: 90C29.The paper proposes an interactive method solving the multiple criteria choice problem (MCCP) with a large number of discrete alternatives and a small number of quantitative criteria. The decision maker (DM) sets his preferences in terms of desired directions of improving or relaxing of the criteria. On this base the so called reference cone is constructed. A small subset of relatively closed alternatives is defined according to this cone and to the maximal deterioration of the criteria values at each iteration. This subset is evaluated by the DM, who selects the most preferred alternative or enters his/her new preferences. The method suggested has user-friendly dialog. It enables the DM to explore the set of alternatives comparatively quickly and easy. The method is included in a DSS. It is tested by a number of real multiple criteria choice problems

Multiple Criteria Analysis for Regional Water Quality Management: The Nitra River Case

This Working Paper documents the implementation of an element of a Decision Support System (DSS) for regional water quality management, applied in cooperation with the Water Research Institute (VUVH, Bratislava) and the Vah River Basin Authority to the Nitra River case study in Slovakia. Several re-usable, modular software tools have been developed and implemented -- a problem-specific generator to produce the core part of the mathematical programming model, tools for the generation and interactive modification of multicriteria problems, and a solver for the resulting mixed-integer optimization problem. Provided in the paper are the following: a complete formulation of the mathematical model (including the applied well-known dissolved oxygen model), a detailed discussion of the data used, documentation of the developed software, an overview of results which might be of interest, and recommendations for future work. Emphasis is placed on the advantages of multicriteria analysis for the regional water quality management problem

Appendix A: MCA Terminology

This appendix reviews the terminology of multiple criteria analysis

User Guide to MCA: Multiple Criteria Analysis of Discrete Alternatives with a Simple Preference Specification

This report provides detailed information about using the MCA, which is the Web-based application formultiple criteria analysis of discrete alternatives with a simple preference specification. MCA in its currently available version supports analysis of a set of discrete alternatves, defined either interactively or through a prepared file. Each alternative is characterized by several attributes (indicators) that serve for specification of criteria. MCA has been designed for problems having large numbers of alternatives and of criteria. However, it can also be used for problems with small numbers of criteria and/or alternatives. The report is composed of two main parts. The first one provides an overview of the MCA and summarize the methodology of multiple criteria analysis implemented in the MCA. The second part consists of the step-by-step detailed tutorial to the MCA organized into three stages corresponding to (1) basic funtions of the MCA, (2) specification of problems, instances, and analyses, and (3) interactive multiciteria analysis process

Multiple Criteria Analysis of Discrete Alternatives with a Simple Preference Specification: Pairwise-outperformance based Approaches

Many methods have been developed for multiple criteria analysis and/or ranking of discrete alternatives. Most of them require complex specification of preferences. Therefore, they are not applicable for problems with numerous alternatives and/or criteria, where preference specification by the decision makers can hardly be done in a way acceptable for small problems, e.g., for pair-wise comparisons. In this paper we describe several new methods implemented for a real-life application dealing with muti-criteria analysis of future energy technologies. This analysis involves large numbers of both altrnatives and criteria. Moreover, the analysis was made by a large number of stakeholders without expeience in analytical methods. Therefore, a simple method for interactive preference specification was a condition for the analysis. The paper presents a number of new methods based on the developed out performance aggregations that take into account inter-alternative factors. Finally, a comparison of methods and experience of using them is discussed

Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process

We propose to extend the aggregation scheme of Saaty’s AHP, from the stan- dard weighted averaging to the more general Choquet integration. In our model, a measure of inconsistency between criteria is derived from the main pairwise comparison matrix and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean in the con- sistency case. In the general inconsistency case, however, the new aggregation scheme based on Choquet integration tends to attenuate (resp. emphasize) the priority values of the criteria with higher (resp. lower) average inconsistency with the remaining criteria.Aggregation Functions, Multiple Criteria Analysis, AHP, Inconsintency, non-additive measures, Choquet integral, and Shapley values.