Preference intensity in MCDM when an additive utility function represents DM preferences

We propose a new method for ranking alternatives in multicriteria decision-making problems when there is imprecision concerning the alternative performances, component utility functions and weights. We assume decision maker?s preferences are represented by an additive multiattribute utility function, in which weights can be modeled by independent normal variables, fuzzy numbers, value intervals or by an ordinal relation. The approaches are based on dominance measures or exploring the weight space in order to describe which ratings would make each alternative the preferred one. On the one hand, the approaches based on dominance measures compute the minimum utility difference among pairs of alternatives. Then, they compute a measure by which to rank the alternatives. On the other hand, the approaches based on exploring the weight space compute confidence factors describing the reliability of the analysis. These methods are compared using Monte Carlo simulation.

A fuzzy approach to risk analysis in information systems

Assets are interrelated in risk analysis methodologies for information systems promoted by international standards. This means that an attack on one asset can be propagated through the network and threaten an organization's most valuable assets. It is necessary to valuate all assets, the direct and indirect asset dependencies, as well as the probability of threats and the resulting asset degradation. These methodologies do not, however, consider uncertain valuations and use precise values on different scales, usually percentages. Linguistic terms are used by the experts to represent assets values, dependencies and frequency and asset degradation associated with possible threats. Computations are based on the trapezoidal fuzzy numbers associated with these linguistic terms.

A fuzzy extension of MAGERIT methodology for risk analysis in information systems

We propose a fuzzy approach to deal with risk analysis for information systems. We extend MAGERIT methodology that valuates the asset dependencies to a fuzzy framework adding fuzzy linguistic terms to valuate the different elements (terminal asset values, asset dependencies as well as the probability of threats and the resulting asset degradation) in risk analysis. Computations are based on the trapezoidal fuzzy numbers associated with these linguistic terms and, finally, the results of these operations are translated into a linguistic term by means of a similarity function.

A stepwise fuzzy linear programming model with possibility and necessity relations

Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although conventional LP models require precise data, managers and decision makers dealing with real-world optimization problems often do not have access to exact values. Fuzzy sets have been used in the fuzzy LP (FLP) problems to deal with the imprecise data in the decision variables, objective function and/or the constraints. The imprecisions in the FLP problems could be related to (1) the decision variables; (2) the coefficients of the decision variables in the objective function; (3) the coefficients of the decision variables in the constraints; (4) the right-hand-side of the constraints; or (5) all of these parameters. In this paper, we develop a new stepwise FLP model where fuzzy numbers are considered for the coefficients of the decision variables in the objective function, the coefficients of the decision variables in the constraints and the right-hand-side of the constraints. In the first step, we use the possibility and necessity relations for fuzzy constraints without considering the fuzzy objective function. In the subsequent step, we extend our method to the fuzzy objective function. We use two numerical examples from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and the computational efficiency of the procedures and algorithms. © 2013-IOS Press and the authors. All rights reserved.

An alternative formulation for the fuzzy assignment problem

The existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit measured as crisp. However, in many real applications, costs are not deterministic numbers. This paper develops a procedure based on Data Envelopment Analysis method to solve the assignment problems with fuzzy costs or fuzzy profits for each possible assignment. It aims to obtain the points with maximum membership values for the fuzzy parameters while maximizing the profit or minimizing the assignment cost. In this method, a discrete approach is presented to rank the fuzzy numbers first. Then, corresponding to each fuzzy number, we introduce a crisp number using the efficiency concept. A numerical example is used to illustrate the usefulness of this new method. © 2012 Operational Research Society Ltd. All rights reserved.

Efficiency measurement in fuzzy additive data envelopment analysis

Performance evaluation in conventional data envelopment analysis (DEA) requires crisp numerical values. However, the observed values of the input and output data in real-world problems are often imprecise or vague. These imprecise and vague data can be represented by linguistic terms characterised by fuzzy numbers in DEA to reflect the decision-makers' intuition and subjective judgements. This paper extends the conventional DEA models to a fuzzy framework by proposing a new fuzzy additive DEA model for evaluating the efficiency of a set of decision-making units (DMUs) with fuzzy inputs and outputs. The contribution of this paper is threefold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA, (2) we propose a new fuzzy additive DEA model derived from the a-level approach and (3) we demonstrate the practical aspects of our model with two numerical examples and show its comparability with five different fuzzy DEA methods in the literature. Copyright © 2011 Inderscience Enterprises Ltd.

Fuzzy knowledge-based approach to treating uncertainty in inventory control

Inventory control in complex manufacturing environments encounters various sources of uncertainity and imprecision. This paper presents one fuzzy knowledge-based approach to solving the problem of order quantity determination, in the presence of uncertain demand, lead time and actual inventory level. Uncertain data are represented by fuzzy numbers, and vaguely defined relations between them are modeled by fuzzy if-then rules. The proposed representation and inference mechanism are verified using a large numbers of examples. The results of three representative cases are summarized. Finally a comparison between the developed fuzzy knowledge-based and traditional, probabilistic approaches is discussed.

A New Approach to Fuzzy Arithmetic

This work shows an application of a generalized approach for constructing dilation-erosion adjunctions on fuzzy sets. More precisely, operations on fuzzy quantities and fuzzy numbers are considered. By the generalized approach an analogy with the well known interval computations could be drawn and thus we can define outer and inner operations on fuzzy objects. These operations are found to be useful in the control of bioprocesses, ecology and other domains where data uncertainties exist.

Carbon efficiency evaluation:an analytical framework using fuzzy DEA

Data Envelopment Analysis (DEA) is a powerful analytical technique for measuring the relative efficiency of alternatives based on their inputs and outputs. The alternatives can be in the form of countries who attempt to enhance their productivity and environmental efficiencies concurrently. However, when desirable outputs such as productivity increases, undesirable outputs increase as well (e.g. carbon emissions), thus making the performance evaluation questionable. In addition, traditional environmental efficiency has been typically measured by crisp input and output (desirable and undesirable). However, the input and output data, such as CO2 emissions, in real-world evaluation problems are often imprecise or ambiguous. This paper proposes a DEA-based framework where the input and output data are characterized by symmetrical and asymmetrical fuzzy numbers. The proposed method allows the environmental evaluation to be assessed at different levels of certainty. The validity of the proposed model has been tested and its usefulness is illustrated using two numerical examples. An application of energy efficiency among 23 European Union (EU) member countries is further presented to show the applicability and efficacy of the proposed approach under asymmetric fuzzy numbers.

Gráficos de controle: aspectos teóricos e práticos a partir da ótica da lógica formal e da lógica fuzzy

O presente trabalho faz um enlace de teorias propostas por dois trabalhos: Transformação de valores crisp em valores fuzzy e construção de gráfico de controle fuzzy. O resultado desse enlace é um gráfico de controle fuzzy que foi aplicado em um processo de produção de iogurte, onde as variáveis analisadas foram: Cor, Aroma, Consistência, Sabor e Acidez. São características que dependem da percepção dos indivíduos, então a forma utilizada para coletar informações a respeito de tais característica foi a análise sensorial. Nas analises um grupo denominado de juízes, atribuía individualmente notas para cada amostra de iogurte em uma escala de 0 a 10. Esses valores crisp, notas atribuídas pelos juízes, foram então, transformados em valores fuzzy, na forma de número fuzzy triangular. Com os números fuzzy, foram construídos os gráficos de controle fuzzy de média e amplitude. Com os valores crisp foram construídos gráficos de controle de Shewhart para média e amplitude, já consolidados pela literatura. Por fim, os resultados encontrados nos gráficos tradicionais foram comparados aos encontrados nos gráficos de controle fuzzy. O que pode-se observar é que o gráfico de controle fuzzy, parece satisfazer de forma significativa a realidade do processo, pois na construção do número fuzzy é considerada a variabilidade do processo. Além disso, caracteriza o processo de produção em alguns níveis, onde nem sempre o processo estará totalmente em controle ou totalmente fora de controle. O que vai ao encontro da teoria fuzzy: se não é possível prever com exatidão determinados resultados é melhor ter uma margem de aceitação, o que implicará na redução de erros.

Modelagem em programação linear para resolução de jogos fuzzy intervalares

A teoria de jogos modela estratégias entre agentes (jogadores), os quais possuem recompensas ao fim do jogo conforme suas ações. O melhor par de estratégias para os jogadores constitui uma solução de equilíbrio. Porém, nem sempre se consegue estimar os dados do problema. Diante disso, os parâmetros incertos presentes em modelos de jogos são formalizados pela teoria fuzzy. Assim, a teoria fuzzy auxilia a teoria de jogos, formando jogos fuzzy. Dessa forma, parâmetros, como as recompensas, tornam-se números fuzzy. Mais ainda, quando há incerteza na representação desses números fuzzy utilizam-se os números fuzzy intervalares. Então, neste trabalho modelos de jogos fuzzy intervalares são analisados e métodos computacionais são desenvolvidos para a resolução desses jogos. Por fim, realizam-se simulações de programação linear para observar melhor a aplicação das teorias estudadas e avaliar a proposta.

Probabilistic Security Constrained Fuzzy Power Flow Models

In restructured power systems, generation and commercialization activities became market activities, while transmission and distribution activities continue as regulated monopolies. As a result, the adequacy of transmission network should be evaluated independent of generation system. After introducing the constrained fuzzy power flow (CFPF) as a suitable tool to quantify the adequacy of transmission network to satisfy 'reasonable demands for the transmission of electricity' (as stated, for instance, at European Directive 2009/72/EC), the aim is now showing how this approach can be used in conjunction with probabilistic criteria in security analysis. In classical security analysis models of power systems are considered the composite system (generation plus transmission). The state of system components is usually modeled with probabilities and loads (and generation) are modeled by crisp numbers, probability distributions or fuzzy numbers. In the case of CFPF the component’s failure of the transmission network have been investigated. In this framework, probabilistic methods are used for failures modeling of the transmission system components and possibility models are used to deal with 'reasonable demands'. The enhanced version of the CFPF model is applied to an illustrative case.

Selection method for sustainable building

For a sustainable building industry, not only should the environmental and economic indicators be evaluated but also the societal indicators for building. Current indicators can be in conflict with each other, thus decision making is difficult to clearly quantify and assess sustainability. For the sustainable building, the objectives of decreasing both adverse environmental impact and cost are in conflict. In addition, even though both objectives may be satisfied, building management systems may present other problems such as convenience of occupants, flexibility of building, or technical maintenance, which are difficult to quantify as exact assessment data. These conflicting problems confronting building managers or planners render building management more difficult. This paper presents a methodology to evaluate a sustainable building considering socio-economic and environmental characteristics of buildings, and is intended to assist the decision making for building planners or practitioners. The suggested methodology employs three main concepts: linguistic variables, fuzzy numbers, and an analytic hierarchy process. The linguistic variables are used to represent the degree of appropriateness of qualitative indicators, which are vague or uncertain. These linguistic variables are then translated into fuzzy numbers to reflect their uncertainties and aggregated into the final fuzzy decision value using a hierarchical structure. Through a case study, the suggested methodology is applied to the evaluation of a building. The result demonstrates that the suggested approach can be a useful tool for evaluating a building for sustainability.

Dominance Measuring Method Performance under Incomplete Information about Weights.

In multi-attribute utility theory, it is often not easy to elicit precise values for the scaling weights representing the relative importance of criteria. A very widespread approach is to gather incomplete information. A recent approach for dealing with such situations is to use information about each alternative?s intensity of dominance, known as dominance measuring methods. Different dominancemeasuring methods have been proposed, and simulation studies have been carried out to compare these methods with each other and with other approaches but only when ordinal information about weights is available. In this paper, we useMonte Carlo simulation techniques to analyse the performance of and adapt such methods to deal with weight intervals, weights fitting independent normal probability distributions orweights represented by fuzzy numbers.Moreover, dominance measuringmethod performance is also compared with a widely used methodology dealing with incomplete information on weights, the stochastic multicriteria acceptability analysis (SMAA). SMAA is based on exploring the weight space to describe the evaluations that would make each alternative the preferred one.

A new dominance intensity method to deal with ordinal information about a DM's preferences within MAVT

Dominance measuring methods are a new approach to deal with complex decision-making problems with imprecise information. These methods are based on the computation of pairwise dominance values and exploit the information in the dominance matrix in dirent ways to derive measures of dominance intensity and rank the alternatives under consideration. In this paper we propose a new dominance measuring method to deal with ordinal information about decision-maker preferences in both weights and component utilities. It takes advantage of the centroid of the polytope delimited by ordinal information and builds triangular fuzzy numbers whose distances to the crisp value 0 constitute the basis for the de?nition of a dominance intensity measure. Monte Carlo simulation techniques have been used to compare the performance of this method with other existing approaches.