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.

Dominance measuring methods within MAVT/MAUT with imprecise information concerning decision-makers'preferences

Dominance measuring methods are an approach for dealing with complex decision-making problems with imprecise information within multi-attribute value/utility theory. These methods are based on the computation of pairwise dominance values and exploit the information in the dominance matrix in different ways to derive measures of dominance intensity and rank the alternatives under consideration. In this paper we review dominance measuring methods proposed in the literature for dealing with imprecise information (intervals, ordinal information or fuzzy numbers) about decision-makers? preferences and their performance in comparison with other existing approaches, like SMAA and SMAA-II or Sarabando and Dias? method.

Toma de decisiones en grupo con información parcial y veto basada en medidas de la intensidad de dominancia

En la mayoría de problemas de decisión a los que nos enfrentamos no hay evidencia sobre cuál es la mejor elección debido a la complejidad de los mismos. Esta complejidad está asociada a la existencia de múltiples objetivos conflictivos y a que en muchos casos solo se dispone de información incompleta o imprecisa sobre los distintos parámetros del modelo de decisión. Por otro lado, el proceso de toma de decisiones se puede realizar en grupo, debiendo incorporar al modelo las preferencias individuales de cada uno de los decisores y, posteriormente, agregarlas para alcanzar un consenso final, lo que dificulta más todavía el proceso de decisión. La metodología del Análisis de Decisiones (AD) es un procedimiento sistemático y lógico que permite estructurar y simplificar la tarea de tomar decisiones. Utiliza la información existente, datos recogidos, modelos y opiniones profesionales para cuantificar la probabilidad de los valores o impactos de las alternativas y la Teoría de la Utilidad para cuantificar las preferencias de los decisores sobre los posibles valores de las alternativas. Esta tesis doctoral se centra en el desarrollo de extensiones del modelo multicriterio en utilidad aditivo para toma de decisiones en grupo con veto en base al AD y al concepto de la intensidad de la dominancia, que permite explotar la información incompleta o imprecisa asociada a los parámetros del modelo. Se considera la posibilidad de que la importancia relativa que tienen los criterios del problema para los decisores se representa mediante intervalos de valores o información ordinal o mediante números borrosos trapezoidales. Adicionalmente, se considera que los decisores tienen derecho a veto sobre los valores de los criterios bajo consideración, pero solo un subconjunto de ellos es efectivo, teniéndose el resto solo en cuenta de manera parcial. ABSTRACT In most decision-making problems, the best choice is unclear because of their complexity. This complexity is mainly associated with the existence of multiple conflicting objectives. Besides, there is, in many cases, only incomplete or inaccurate information on the various decision model parameters. Alternatively, the decision-making process may be performed by a group. Consequently, the model must account for individual preferences for each decision-maker (DM), which have to be aggregated to reach a final consensus. This makes the decision process even more difficult. The decision analysis (DA) methodology is a systematic and logical procedure for structuring and simplifying the decision-making task. It takes advantage of existing information, collected data, models and professional opinions to quantify the probability of the alternative values or impacts and utility theory to quantify the DM’s preferences concerning the possible alternative values. This PhD. thesis focuses on developing extensions for a multicriteria additive utility model for group decision-making accounting for vetoes based on DA and on the concept of dominance intensity in order to exploit incomplete or imprecise information associated with the parameters of the decision-making model. We consider the possibility of the relative importance of criteria for DMs being represented by intervals or ordinal information, or by trapezoidal fuzzy numbers. Additionally, we consider that DMs are allowed to provide veto values for the criteria under consideration, of which only a subset are effective, whereas the remainder are only partially taken into account.

Procedure of Formalization of the Indices of Banks’ Stable Functioning in Comparative Estimates of Their Development

The advisability of analyzing the banks liquidity and profitability as the key factor when building the comparative estimate of their functioning is considered. The procedure of formal description of the bank stable functioning indices is substantiated. Fuzzy interpretation of the bank management efficiency estimation is offered. The possibility to formalize the bank functioning estimates on the basis of the corresponding fuzzy set levels hierarchy is analyzed. The comparative estimate of different bank systems functioning is given.

Service bid comparisons by fuzzy ranking in open railway market timetabling

In an open railway access market, the Infrastructure Provider (IP), upon the receipts of service bids from the Train Service Providers (TSPs), assigns track access rights according to its own business objectives and the merits of the bids; and produces the train service timetable through negotiations. In practice, IP chooses to negotiate with the TSPs one by one in such a sequence that IP optimizes its objectives. The TSP bids are usually very complicated, containing a large number of parameters in different natures. It is a difficult task even for an expert to give a priority sequence for negotiations from the contents of the bids. This study proposes the application of fuzzy ranking method to compare and prioritize the TSP bids in order to produce a negotiation sequence. The results of this study allow investigations on the behaviors of the stakeholders in bid preparation and negotiation, as well as evaluation of service quality in the open railway market.