Multicriteria analysis in decision making under information uncertainty

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bell-man-Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models (< X, M > models) under deterministic information. 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. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called < X, R > models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example. (c) 2007 Elsevier Inc. All rights reserved.

Multicriteria Evaluation and Optimization of Hierarchical Systems

It is shown that any multicriteria problem can be represented by a hierarchical system. Separate properties of the object are evaluated at the lower level of the system, using a criteria vector, and a composition mechanism is used to evaluate the object as a whole at the upper level. The paper proposes a method to solve complex multicriteria problems of evaluation and optimization. It is based on nested scalar convolutions of vector- valued criteria and allows simple structural and parametrical synthesis of multicriteria hierarchical systems.

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

AMS subject classification: 90C29.

Um estudo algorítmico para otimização do plano de tratamento da radioterapia conformal

This work performs an algorithmic study of optimization of a conformal radiotherapy plan treatment. Initially we show: an overview about cancer, radiotherapy and the physics of interaction of ionizing radiation with matery. A proposal for optimization of a plan of treatment in radiotherapy is developed in a systematic way. We show the paradigm of multicriteria problem, the concept of Pareto optimum and Pareto dominance. A generic optimization model for radioterapic treatment is proposed. We construct the input of the model, estimate the dose given by the radiation using the dose matrix, and show the objective function for the model. The complexity of optimization models in radiotherapy treatment is typically NP which justifyis the use of heuristic methods. We propose three distinct methods: MOGA, MOSA e MOTS. The project of these three metaheuristic procedures is shown. For each procedures follows: a brief motivation, the algorithm itself and the method for tuning its parameters. The three method are applied to a concrete case and we confront their performances. Finally it is analyzed for each method: the quality of the Pareto sets, some solutions and the respective Pareto curves

Decision making in fuzzy environment and multicriteria power engineering problems

This paper presents results of research into the use of the Bellman-Zadeh approach to decision making in a fuzzy environment for solving multicriteria power engineering problems. The application of the approach conforms to the principle of guaranteed result and provides constructive lines in computationally effective obtaining harmonious solutions on the basis of solving associated maxmin problems. The presented results are universally applicable and are already being used to solve diverse classes of power engineering problems. It is illustrated by considering problems of power and energy shortage allocation, power system operation, optimization of network configuration in distribution systems, and energetically effective voltage control in distribution systems. (c) 2011 Elsevier Ltd. All rights reserved.

Generalized Scalarizing Problems GENS and GENSLex of Multicriteria Optimization

* This paper is partially supported by the National Science Fund of Bulgarian Ministry of Education and Science under contract № I–1401\2004 "Interactive Algorithms and Software Systems Supporting Multicriteria Decision Making".

Multicriteria decision making: a case study in the automobile industry

Multi-criteria decision analysis(MCDA) has been one of the fastest-growing areas of operations research during the last decades. The academic attention devoted to MCDA motivated the development of a great variety of approaches and methods within the field. These methods distinguish themselves in terms of procedures, theoretical assumptions and type of decision addressed. This diversity poses challenges to the process of selecting the most suited method for a specific real-world decision problem. In this paper we present a case study in a real-world decision problem arising in the painting sector of an automobile plant. We tackle the problem by resorting to the well-known AHP method and to the MCDA method proposed by Pereira and Fontes (2012) (MMASSI). By relying on two, rather than one, MCDA methods we expect to improve the confidence and robustness of the obtained results. The contributions of this paper are twofold: first, we intend to investigate the contrasts and similarities of the results obtained by distinct MCDA approaches (AHP and MMASSI); secondly, we expect to enrich the literature of the field with a real-world MCDA case study on a complex decision making problem since there is a paucity of applied research work addressing real decision problems faced by organizations.

Multicriteria decision making: a case study in the automobile industry

Multi-criteria decision analysis (MCDA) has been one of the fastest-growing areas of operations research during the last decades. The academic attention devoted to MCDA motivated the development of a great variety of approaches and methods within the field. These methods distinguish themselves in terms of procedures, theoretical assumptions and type of decision addressed. This diversity poses challenges to the process of selecting the most suited method for a specific real-world decision problem. In this paper we present a case study in a real-world decision problem arising in the painting sector of an automobile plant. We tackle the problem by resorting to the well-known AHP method and to the MCDA method proposed by Pereira and Fontes (2012) (MMASSI). By relying on two, rather than one, MCDA methods we expect to improve the confidence and robustness of the obtained results. The contributions of this paper are twofold: first, we intend to investigate the contrasts and similarities of the results obtained by distinct MCDA approaches (AHP and MMASSI); secondly, we expect to enrich the literature of the field with a real-world MCDA case study on a complex decision making problem since there is a paucity of applied research work addressing real decision problems faced by organizations.

Comparative analysis of multicriteria decision making methods

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

BeSmart2: A multicriteria decision aid application

This paper presents an improved version of an application whose goal is to provide a simple and intuitive way to use multicriteria decision methods in day-to-day decision problems. The application allows comparisons between several alternatives with several criteria, always keeping a permanent backup of both model and results, and provides a framework to incorporate new methods in the future. Developed in C#, the application implements the AHP, SMART and Value Functions methods.

New directions in Stochastic Multicriteria Acceptability Analysis

Decisions taken in modern organizations are often multi-dimensional, involving multiple decision makers and several criteria measured on different scales. Multiple Criteria Decision Making (MCDM) methods are designed to analyze and to give recommendations in this kind of situations. Among the numerous MCDM methods, two large families of methods are the multi-attribute utility theory based methods and the outranking methods. Traditionally both method families require exact values for technical parameters and criteria measurements, as well as for preferences expressed as weights. Often it is hard, if not impossible, to obtain exact values. Stochastic Multicriteria Acceptability Analysis (SMAA) is a family of methods designed to help in this type of situations where exact values are not available. Different variants of SMAA allow handling all types of MCDM problems. They support defining the model through uncertain, imprecise, or completely missing values. The methods are based on simulation that is applied to obtain descriptive indices characterizing the problem. In this thesis we present new advances in the SMAA methodology. We present and analyze algorithms for the SMAA-2 method and its extension to handle ordinal preferences. We then present an application of SMAA-2 to an area where MCDM models have not been applied before: planning elevator groups for high-rise buildings. Following this, we introduce two new methods to the family: SMAA-TRI that extends ELECTRE TRI for sorting problems with uncertain parameter values, and SMAA-III that extends ELECTRE III in a similar way. An efficient software implementing these two methods has been developed in conjunction with this work, and is briefly presented in this thesis. The thesis is closed with a comprehensive survey of SMAA methodology including a definition of a unified framework.

Spatial multicriteria decision analysis for the siting of on-shore wind power in Kemiönsaari

Wind power is a low-carbon energy production form that reduces the dependence of society on fossil fuels. Finland has adopted wind energy production into its climate change mitigation policy, and that has lead to changes in legislation, guidelines, regional wind power areas allocation and establishing a feed-in tariff. Wind power production has indeed boosted in Finland after two decades of relatively slow growth, for instance from 2010 to 2011 wind energy production increased with 64 %, but there is still a long way to the national goal of 6 TWh by 2020. This thesis introduces a GIS-based decision-support methodology for the preliminary identification of suitable areas for wind energy production including estimation of their level of risk. The goal of this study was to define the least risky places for wind energy development within Kemiönsaari municipality in Southwest Finland. Spatial multicriteria decision analysis (SMCDA) has been used for searching suitable wind power areas along with many other location-allocation problems. SMCDA scrutinizes complex ill-structured decision problems in GIS environment using constraints and evaluation criteria, which are aggregated using weighted linear combination (WLC). Weights for the evaluation criteria were acquired using analytic hierarchy process (AHP) with nine expert interviews. Subsequently, feasible alternatives were ranked in order to provide a recommendation and finally, a sensitivity analysis was conducted for the determination of recommendation robustness. The first study aim was to scrutinize the suitability and necessity of existing data for this SMCDA study. Most of the available data sets were of sufficient resolution and quality. Input data necessity was evaluated qualitatively for each data set based on e.g. constraint coverage and attribute weights. Attribute quality was estimated mainly qualitatively by attribute comprehensiveness, operationality, measurability, completeness, decomposability, minimality and redundancy. The most significant quality issue was redundancy as interdependencies are not tolerated by WLC and AHP does not include measures to detect them. The third aim was to define the least risky areas for wind power development within the study area. The two highest ranking areas were Nordanå-Lövböle and Påvalsby followed by Helgeboda, Degerdal, Pungböle, Björkboda, and Östanå-Labböle. The fourth aim was to assess the recommendation reliability, and the top-ranking two areas proved robust whereas the other ones were more sensitive.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

Selecting appropriate bedding to reduce locomotion problems in broilers

Two experiments were carried out at the Poultry Sector of the School of Agrarian Sciences of the Federal University of Grande Dourados to evaluate the incidence of leg problems in broilers reared on two distinct types of bedding material: rice husks or wood shavings, both new and reused. In both trials, a randomized experimental design was applied in factorial arrangement (2 x 2 x 2) using two genetic strains (Cobb® or Ross®); two sexes (male or female), and two litter materials (rice husks or wood shavings). In each trial 1080 one day pullets were reared equally divided in the treatments. The birds were placed in 4.5 m² boxes at a density of 10 birds m-2. All birds were fed diets with equal nutritional density, and water was offered ad libitum. Feeds were divided in three phases: starter diet (1 - 21 days), grower diet (22 - 35 days), and finisher diet (36 - 45 days). on day 45, fifty birds were randomly selected in each experiment to evaluate flock leg problems. The following parameters were analyzed: gait score, incidence of valgus and varus disorder, footpad dermatitis, femoral degeneration, tibial dyschondroplasia, and spondylolisthesis. Ambient temperature during rearing and litter caking and moisture content were recorded in four boxes per treatment. The analytical hierarchy process was used to organize the data into specific criteria. Several criteria, related to the attributes that were determinant according to the statistical analysis, were chosen in order to provide the best input to the process. Results indicated that new wood-shavings bedding was the most appropriate bedding to prevent locomotion problems, followed by new rice husks, reused wood shavings, and reused rice husks. However, when leg problems were associated to sex and genetic strain, male Ross birds strain presented less problems when reared on new rice husks, followed by new wood shavings

Design and implementation of a multicriteria medical decision support system for diagnosis and treatment

Health care providers face the problem of trying to make decisions with inadequate information and also with an overload of (often contradictory) information. Physicians often choose treatment long before they know which disease is present. Indeed, uncertainty is intrinsic to the practice of medicine. Decision analysis can help physicians structure and work through a medical decision problem, and can provide reassurance that decisions are rational and consistent with the beliefs and preferences of other physicians and patients. ^ The primary purpose of this research project is to develop the theory, methods, techniques and tools necessary for designing and implementing a system to support solving medical decision problems. A case study involving “abdominal pain” serves as a prototype for implementing the system. The research, however, focuses on a generic class of problems and aims at covering theoretical as well as practical aspects of the system developed. ^ The main contributions of this research are: (1) bridging the gap between the statistical approach and the knowledge-based (expert) approach to medical decision making; (2) linking a collection of methods, techniques and tools together to allow for the design of a medical decision support system, based on a framework that involves the Analytic Network Process (ANP), the generalization of the Analytic Hierarchy Process (AHP) to dependence and feedback, for problems involving diagnosis and treatment; (3) enhancing the representation and manipulation of uncertainty in the ANP framework by incorporating group consensus weights; and (4) developing a computer program to assist in the implementation of the system. ^