Measuring Technical Efficiency of Dairy Farms with Imprecise Data: A Fuzzy Data Envelopment Analysis Approach

This article integrates fuzzy set theory in Data Envelopment Analysis (DEA) framework to compute technical efficiency scores when input and output data are imprecise. The underlying assumption in convectional DEA is that inputs and outputs data are measured with precision. However, production agriculture takes place in an uncertain environment and, in some situations, input and output data may be imprecise. We present an approach of measuring efficiency when data is known to lie within specified intervals and empirically illustrate this approach using a group of 34 dairy producers in Pennsylvania. Compared to the convectional DEA scores that are point estimates, the computed fuzzy efficiency scores allow the decision maker to trace the performance of a decision-making unit at different possibility levels.fuzzy set theory, Data Envelopment Analysis, membership function, α-cut level, technical efficiency, Farm Management, Production Economics, Productivity Analysis, Research Methods/ Statistical Methods, Risk and Uncertainty, D24, Q12, C02, C44, C61,

Orderings of fuzzy sets based on fuzzy orderings. Part I: the basic approach

The aim of this paper is to present a general framework for comparing fuzzy sets with respect to a general class of fuzzy orderings. This approach includes known techniques based on generalizing the crisp linear ordering of real numbers by means of the extension principle, however, in its general form, it is applicable to any fuzzy subsets of any kind of universe for which a fuzzy ordering is known|no matter whether linear or partialPeer Reviewe

A multiple channel queueing model under an uncertain environment with multiclass arrivals for supplying demands in a cement industry

In recent years, cement consumption has increased in most Asian countries, including Malaysia. There are many factors which affect the supply of the increasing order demands in the cement industry, such as traffic congestion, logistics, weather and machine breakdowns. These factors hinder smooth and efficient supply, especially during periods of peak congestion at the main gate of the industry where queues occur as a result of inability to keep to the order deadlines. Basic elements, such as arrival and service rates, that cannot be predetermined must be considered under an uncertain environment. Solution approaches including conventional queueing techniques, scheduling models and simulations were unable to formulate the performance measures of the cement queueing system. Hence, a new procedure of fuzzy subset intervals is designed and embedded in a queuing model with the consideration of arrival and service rates. As a result, a multiple channel queueing model with multiclass arrivals, (M1, M2)/G/C/2Pr, under an uncertain environment is developed. The model is able to estimate the performance measures of arrival rates of bulk products for Class One and bag products for Class Two in the cement manufacturing queueing system. For the (M1, M2)/G/C/2Pr fuzzy queueing model, two defuzzification techniques, namely the Parametric Nonlinear Programming and Robust Ranking are used to convert fuzzy queues into crisp queues. This led to three proposed sub-models, which are sub-model 1, MCFQ-2Pr, sub-model 2, MCCQESR-2Pr and sub-model 3, MCCQ-GSR-2Pr. These models provide optimal crisp values for the performance measures. To estimate the performance of the whole system, an additional step is introduced through the TrMF-UF model utilizing a utility factor based on fuzzy subset intervals and the α-cut approach. Consequently, these models help decision-makers deal with order demands under an uncertain environment for the cement manufacturing industry and address the increasing quantities needed in future

A HIERARCHICAL STRUCTURE FOR SHIP DIESEL ENGINE TROUBLE-SHOOTING PROBLEM USING FUZZY AHP AND FUZZY VIKOR HYBRID METHODS

Although considerable technical preventive measures have been taken in marine diesel engine and auxiliary systems, it is possible to observe unexpected faults in the course of the operating conditions. These faults can become so severe that they can cause losses which can be irreversible. This study aims to present Fuzzy Analytic Hierarchy Process (AHP) and VIKOR (Vise Kriterijumska Optimizacija I Kompromisno Resenje) methods applied for the expert failure detection of marine diesel engine and auxiliary systems. In this study, the failures of marine diesel engine have been revealed and prioritized. Accordingly, the section of the machine from which the failures primarily arise has been determined. At the same time, the importance of the effective use of time in determining and responding to the failures has been indicated. By means of the evaluation of decision-making groups, the system most severely affected by failures has been decided

A Laplace's principle based approach for solving fuzzy matrix games

We introduce a solution for matrix games with fuzzy payoffs via the α -cuts and the introduction of Nature as a third player expressing the uncertainty involved in the game. The beliefs of players about the behavior of Nature are based on the Laplace’s principle of “insufficient reason”. Moreover, we provide a procedure for computing the introduced solution

Soft computing approaches to uncertainty propagation in environmental risk mangement

Real-world problems, especially those that involve natural systems, are complex and composed of many nondeterministic components having non-linear coupling. It turns out that in dealing with such systems, one has to face a high degree of uncertainty and tolerate imprecision. Classical system models based on numerical analysis, crisp logic or binary logic have characteristics of precision and categoricity and classified as hard computing approach. In contrast soft computing approaches like probabilistic reasoning, fuzzy logic, artificial neural nets etc have characteristics of approximation and dispositionality. Although in hard computing, imprecision and uncertainty are undesirable properties, in soft computing the tolerance for imprecision and uncertainty is exploited to achieve tractability, lower cost of computation, effective communication and high Machine Intelligence Quotient (MIQ). Proposed thesis has tried to explore use of different soft computing approaches to handle uncertainty in environmental risk management. The work has been divided into three parts consisting five papers. In the first part of this thesis different uncertainty propagation methods have been investigated. The first methodology is generalized fuzzy α-cut based on the concept of transformation method. A case study of uncertainty analysis of pollutant transport in the subsurface has been used to show the utility of this approach. This approach shows superiority over conventional methods of uncertainty modelling. A Second method is proposed to manage uncertainty and variability together in risk models. The new hybrid approach combining probabilistic and fuzzy set theory is called Fuzzy Latin Hypercube Sampling (FLHS). An important property of this method is its ability to separate randomness and imprecision to increase the quality of information. A fuzzified statistical summary of the model results gives indices of sensitivity and uncertainty that relate the effects of variability and uncertainty of input variables to model predictions. The feasibility of the method is validated to analyze total variance in the calculation of incremental lifetime risks due to polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/F) for the residents living in the surroundings of a municipal solid waste incinerator (MSWI) in Basque Country, Spain. The second part of this thesis deals with the use of artificial intelligence technique for generating environmental indices. The first paper focused on the development of a Hazzard Index (HI) using persistence, bioaccumulation and toxicity properties of a large number of organic and inorganic pollutants. For deriving this index, Self-Organizing Maps (SOM) has been used which provided a hazard ranking for each compound. Subsequently, an Integral Risk Index was developed taking into account the HI and the concentrations of all pollutants in soil samples collected in the target area. Finally, a risk map was elaborated by representing the spatial distribution of the Integral Risk Index with a Geographic Information System (GIS). The second paper is an improvement of the first work. New approach called Neuro-Probabilistic HI was developed by combining SOM and Monte-Carlo analysis. It considers uncertainty associated with contaminants characteristic values. This new index seems to be an adequate tool to be taken into account in risk assessment processes. In both study, the methods have been validated through its implementation in the industrial chemical / petrochemical area of Tarragona. The third part of this thesis deals with decision-making framework for environmental risk management. In this study, an integrated fuzzy relation analysis (IFRA) model is proposed for risk assessment involving multiple criteria. The fuzzy risk-analysis model is proposed to comprehensively evaluate all risks associated with contaminated systems resulting from more than one toxic chemical. The model is an integrated view on uncertainty techniques based on multi-valued mappings, fuzzy relations and fuzzy analytical hierarchical process. Integration of system simulation and risk analysis using fuzzy approach allowed to incorporate system modelling uncertainty and subjective risk criteria. In this study, it has been shown that a broad integration of fuzzy system simulation and fuzzy risk analysis is possible. In conclusion, this study has broadly demonstrated the usefulness of soft computing approaches in environmental risk analysis. The proposed methods could significantly advance practice of risk analysis by effectively addressing critical issues of uncertainty propagation problem.Los problemas del mundo real, especialmente aquellos que implican sistemas naturales, son complejos y se componen de muchos componentes indeterminados, que muestran en muchos casos una relación no lineal. Los modelos convencionales basados en técnicas analíticas que se utilizan actualmente para conocer y predecir el comportamiento de dichos sistemas pueden ser muy complicados e inflexibles cuando se quiere hacer frente a la imprecisión y la complejidad del sistema en un mundo real. El tratamiento de dichos sistemas, supone el enfrentarse a un elevado nivel de incertidumbre así como considerar la imprecisión. Los modelos clásicos basados en análisis numéricos, lógica de valores exactos o binarios, se caracterizan por su precisión y categorización y son clasificados como una aproximación al hard computing. Por el contrario, el soft computing tal como la lógica de razonamiento probabilístico, las redes neuronales artificiales, etc., tienen la característica de aproximación y disponibilidad. Aunque en la hard computing, la imprecisión y la incertidumbre son propiedades no deseadas, en el soft computing la tolerancia en la imprecisión y la incerteza se aprovechan para alcanzar tratabilidad, bajos costes de computación, una comunicación efectiva y un elevado Machine Intelligence Quotient (MIQ). La tesis propuesta intenta explorar el uso de las diferentes aproximaciones en la informática blanda para manipular la incertidumbre en la gestión del riesgo medioambiental. El trabajo se ha dividido en tres secciones que forman parte de cinco artículos. En la primera parte de esta tesis, se han investigado diferentes métodos de propagación de la incertidumbre. El primer método es el generalizado fuzzy α-cut, el cual está basada en el método de transformación. Para demostrar la utilidad de esta aproximación, se ha utilizado un caso de estudio de análisis de incertidumbre en el transporte de la contaminación en suelo. Esta aproximación muestra una superioridad frente a los métodos convencionales de modelación de la incertidumbre. La segunda metodología propuesta trabaja conjuntamente la variabilidad y la incertidumbre en los modelos de evaluación de riesgo. Para ello, se ha elaborado una nueva aproximación híbrida denominada Fuzzy Latin Hypercube Sampling (FLHS), que combina los conjuntos de la teoría de probabilidad con la teoría de los conjuntos difusos. Una propiedad importante de esta teoría es su capacidad para separarse los aleatoriedad y imprecisión, lo que supone la obtención de una mayor calidad de la información. El resumen estadístico fuzzificado de los resultados del modelo generan índices de sensitividad e incertidumbre que relacionan los efectos de la variabilidad e incertidumbre de los parámetros de modelo con las predicciones de los modelos. La viabilidad del método se llevó a cabo mediante la aplicación de un caso a estudio donde se analizó la varianza total en la cálculo del incremento del riesgo sobre el tiempo de vida de los habitantes que habitan en los alrededores de una incineradora de residuos sólidos urbanos en Tarragona, España, debido a las emisiones de dioxinas y furanos (PCDD/Fs). La segunda parte de la tesis consistió en la utilización de las técnicas de la inteligencia artificial para la generación de índices medioambientales. En el primer artículo se desarrolló un Índice de Peligrosidad a partir de los valores de persistencia, bioacumulación y toxicidad de un elevado número de contaminantes orgánicos e inorgánicos. Para su elaboración, se utilizaron los Mapas de Auto-Organizativos (SOM), que proporcionaron un ranking de peligrosidad para cada compuesto. A continuación, se elaboró un Índice de Riesgo Integral teniendo en cuenta el Índice de peligrosidad y las concentraciones de cada uno de los contaminantes en las muestras de suelo recogidas en la zona de estudio. Finalmente, se elaboró un mapa de la distribución espacial del Índice de Riesgo Integral mediante la representación en un Sistema de Información Geográfico (SIG). El segundo artículo es un mejoramiento del primer trabajo. En este estudio, se creó un método híbrido de los Mapas Auto-organizativos con los métodos probabilísticos, obteniéndose de esta forma un Índice de Riesgo Integrado. Mediante la combinación de SOM y el análisis de Monte-Carlo se desarrolló una nueva aproximación llamada Índice de Peligrosidad Neuro-Probabilística. Este nuevo índice es una herramienta adecuada para ser utilizada en los procesos de análisis. En ambos artículos, la viabilidad de los métodos han sido validados a través de su aplicación en el área de la industria química y petroquímica de Tarragona (Cataluña, España). El tercer apartado de esta tesis está enfocado en la elaboración de una estructura metodológica de un sistema de ayuda en la toma de decisiones para la gestión del riesgo medioambiental. En este estudio, se presenta un modelo integrado de análisis de fuzzy (IFRA) para la evaluación del riesgo cuyo resultado depende de múltiples criterios. El modelo es una visión integrada de las técnicas de incertidumbre basadas en diseños de valoraciones múltiples, relaciones fuzzy y procesos analíticos jerárquicos inciertos. La integración de la simulación del sistema y el análisis del riesgo utilizando aproximaciones inciertas permitieron incorporar la incertidumbre procedente del modelo junto con la incertidumbre procedente de la subjetividad de los criterios. En este estudio, se ha demostrado que es posible crear una amplia integración entre la simulación de un sistema incierto y de un análisis de riesgo incierto. En conclusión, este trabajo demuestra ampliamente la utilidad de aproximación Soft Computing en el análisis de riesgos ambientales. Los métodos propuestos podría avanzar significativamente la práctica de análisis de riesgos de abordar eficazmente el problema de propagación de incertidumbre

Decision Support System for Managing Reverse Supply Chain

Reverse logistics are becoming more and more important in the overall Industry area because of the environment and business factors. Planning and implementing a suitable reverse logistics network could bring more profit, customer satisfaction, and an excellent social picture for companies. But, most of the logistics networks are not equipped to handle the return products in reverse channels. Reverse logistics processes and plans rely heavily on reversing the supply chain so that companies can correctly identify and categorize returned products for disposition, an area that offers many opportunities for additional revenue. The science of reverse logistics includes return policy administration, product recall protocols, repairs processing, product repackaging, parts management, recycling, product disposition management, maximizing liquidation values and much more. The focus of this project is to develop a reverse logistics management system/ tools (RLMS). The proposed tools are demonstrated in the following order. First, we identify the risks involved in the reverse supply chain. Survey tool is used to collect data and information required for analysis. The methodologies that are used to identify key risks are the six sigma tools, namely Define, Measure, Analyse, Improve and Control (DMAIC), SWOT analysis, cause and effect, and Risk Mapping. An improved decision-making method using fuzzy set theory for converting linguistic data into numeric risk ratings has been attempted. In this study, the concept of ‘Left and Right dominance approach’(Chen and Liu, 2001) and Method of ‘In center of centroids’ (Thoran et al., 2012a,b) for generalized trapezoidal fuzzy numbers has been used to quantify the ‘degree of risk’ in terms of crisp ratings. After the analysis, the key risks are identified are categorized, and an action requirement plan suggested for providing guidelines for the managers to manage the risk successfully in the context of reverse logistics. Next, from risk assessment findings, information technology risk presents the highest risk impact on the performance of the reverse logistics, especially lack of use of a decision support system (DSS). We propose a novel multi-attribute decision (MADM) support tool that can categorizes return products and make the best alternative selection of recovery and disposal option using carefully considered criteria using MADM decision making methodologies such as fuzzy MOORA and VIKOR. The project can be applied to all types of industries. Once the returned products are collected and categorized at the retailers/ Points of return (PoR), an optimized network is required to determine the number of reprocessing centres to be opened and the optimized optimum material flow between retailers, reprocessing, recycling and disposal centers at minimum costs. The research develops a mixed integer linear programming model for two scenarios, namely considering direct shipping from retailer/ PoR to the respective reprocessing centers and considering the use of centralized return centers (CRC). The models are solved using LINGO 15 software and excel solver tools respectively. The advantage of the implementation of our solution is that it will help improve performance and reduce time. This benefits the company by having a reduction in their cost due to uncertainties and also contributes to better customer satisfaction. Implementation of these tools at ABZ computer distributing company demonstrates how the reverse logistics management tools can used in order to be beneficial to the organization. The tool is designed to be easily implemented at minimal cost and serves as a valuable tool for personnel faced with significant and costly decisions regarding risk assessment, decision making and network optimization in the reverse supply chain practices

Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately