Edgeworth-Pareto Principle

European Journal of Operational Research, 2007

Most of the approaches to decision problems under uncertainty are based on decision paradigms, generally associated to an optimization process that leads to a final solution. For the Decision Maker, the basic decision is thus what paradigm to choose, the rest of the procedure being mainly technical.

Management Science, 1992

Doklady Mathematics, 2011

Optimization and Engineering, 2011

There exist two major classes of problems, which need the use of a multicriteria approach: problems whose solution consequences cannot be estimated with a single criterion and problems that, initially, may require a single criterion, but their unique solutions are unachievable, due to the existence of decision uncertainty regions, which can be contracted using additional criteria. According to this, two classes of multicriteria models ( > < M X , and > < R X , models) can be constructed. The Bellman-Zadeh approach to decision making in a fuzzy environment is utilized for analyzing > < M X , models. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The analysis of > < R X , models (which contain fuzzy preference relations as criteria of optimality) is based on fourth techniques for fuzzy preference modeling. They permit the evaluation, comparison, selection, prioritization, and/or ordering of alternatives with the use of quantitative as well as qualitative estimates based on knowledge, experience, and intuition of professionals. With the availability of different techniques, the most appropriate one can be chosen, considering possible sources of information and its uncertainty. The analysis of > < M X , and > < R X , models serves as parts of a general scheme for multicriteria decision making under information uncertainty. This scheme is also associated with a generalization of the classic approach to considering the uncertainty of information (based on analyzing payoff matrices constructed for different combinations of solution alternatives and states of nature) in monocriteria decision making to multicriteria problems. 2.

2012

Abstract In this study we consider multicriteria decision making (MCDM) problems involving equity concerns, which are frequently encountered in real life, especially in public sector. In most of these problems the aim is to rank, sort or select the best alternative from a given set of alternatives. One solution approach for MCDM problems is based on taking into account value judgements which the Decision Maker (DM) has provided.

A new mathematical model for multicriteria decision making: MARICA model

According to the European Railway Agency in the European Union every year on railway level crossings (RLC) occurs over 1200 traffic accident in which life loses more than 400 people. In addition to the tunnel and specific locations that are identified as black spots on the roads, RLC have been identified as potential weak points in road infrastructure that significantly jeopardize traffic safety. In Serbia exists about 2350 RLC, one of which is part the secured by systems of active and passive safety (traffic signs, light signals, sound signals, barriers, etc..). Insurance RLC is a material expenditure. The RLC selection process for installation of security equipment accompanied by a greater or lesser degree of criteria vagueness that are necessary for making the relevant decisions. For exploitation these uncertainties and vagueness in this paper was used fuzzy logic. This paper presents the application of a new method of multi-criteria decision-making (Multi-Atributive Real-Ideal Comparative Analysis - MARICA), which represents support in the selection process for RLC to invest in safety equipment. Identified are eight criteria that influence the investment decision. MARICA method was tested on the example of choice of eight RLC for investing in safety equipment. Keywords: mathematical decision making model, Multicriteria decision making, MARICA, DEMATEL

2005

In this note we consider a multicriteria decision problem where the decision maker know the the state of the world but the set of consequences is multidimensional. We suppose that a value function is specified over the attribute of the decision problem and we analyze some classes of non additive functions that can represent interaction between criteria.

Optimization and Engineering, 2013

Ekonomski horizonti, 2018

Multicriteria analysis and its methods have developed very rapidly in the last few decades. Basically, multicriteria analysis deals with solving unstructured management problems and, in practical terms, facilitates making an optimal decision. In order to make a good decision, however, it is necessary to specify possible alternatives by defining appropriate criteria. Multicriteria analysis belongs to the decisionmaking field, where the following meet: economics, mathematics, statistics, psychology, sociology, organizational theory, philosophy, information technology and other sciences.

DS 31: Proceedings of ICED 03, the 14th International Conference on Engineering Design, Stockholm, 2003

Selecting among alternatives is a central and frequent decision in design. This selection is often done to satisfy multiple criteria and with imperfect information. This paper proposed a new method for handling extreme uncertainty in multicriteria decision-making based on Analytic Hierarchy Process (AHP) and info-gap models of uncertainty. The method foundation is briefly reviewed and it is illustrated on a simple problem. Subsequently, the paper formulates a new problem in decision-making with a proposed solution. Instead of asking how to exercise "good" (we say good because there is no best) selection practice (e.g., selection among alternative product concepts), the decision setup changes to include resources, and the question becomes: how to spend them optimally to improve information quality for making choices that are more robust. The new method is illustrated on a simple selection problem.