Application Of Fuzzy Set Theory Research Articles

Examining the Possibility of Fuzzy Set Theory Application in Travel Demand Modelling

Examining the Possibility of Fuzzy Set Theory Application in Travel Demand Modelling

Nurse scheduling using fuzzy modeling approach

Nurse scheduling is a complex scheduling problem and involves generating a schedule for each nurse that consists of shift duties and days off within a short-term planning period. In real world applications, multiple sources of uncertainties are needed to be treated in providing higher quality schedules. This paper presents a seminal research on the application of fuzzy set theory to the nurse scheduling problem (NSP) to treat uncertainties in the target values of the hospital management and nurses’ preferences. More specifically, a new multi-objective integer programming model for the NSP is developed. Then, based on this model three fuzzy goal programming models are developed using different fuzzy solution approaches. A real world application is presented to confirm the viability of the proposed models. Also, to provide the decision maker for a more confident solution set for policy decision making, a sensitivity analysis is performed. Additionally, to show the efficiency of the proposed model, it is applied to several problem instances. The paper contributes to the literature by revealing that fuzzy modeling approaches can effectively be used in the NSP in providing schedules which are more personalized and equitable for nurses, and more satisfying for hospital management.

Stochastic Time-Cost-Resource Utilization Optimization Using Nondominated Sorting Genetic Algorithm and Discrete Fuzzy Sets

In a construction project, the cost and duration of activities could change due to different uncertain variables such as weather, resource availability, etc. Resource leveling and allocation strategies also influence total time and costs of projects. In this paper, two concepts of time-cost trade-off and resource leveling and allocation have been embedded in a stochastic multiobjective optimization model which minimizes the total project time, cost, and resource moments. In the proposed time-cost-resource utilization optimization (TCRO) model, time and cost variables are considered to be fuzzy, to increase the flexibility for decision makers when using the model outputs. Application of fuzzy set theory in this study helps managers/planners to take these uncertainties into account and provide an optimal balance of time, cost, and resource utilization during the project execution. The fuzzy variables are discretized to represent different options for each activity. Nondominated sorting genetic algorithm (NSGA-II) has been used to solve the optimization problem. Results of the TCRO model for two different case studies of construction projects are presented in the paper. Total time and costs of the two case studies in the Pareto front solutions of the TCRO model cover more than 85% of the ranges of total time and costs of solutions of the biobjective time-cost optimization (TCO) model. The results show that adding the resource leveling capability to the previously developed TCO models provides more practical solutions in terms of resource allocation and utilization, which makes this research relevant to both industry practitioners and researchers.

Fuzzy Based Solid Waste Management Method

Fuzzy-based Solid Waste Management involves the application of fuzzy set theory to formulate a solid waste management algorithm by taking into account a large criterion set and an extensive number of alternatives for various levels of uncertainty in Solid Waste Management. Fuzzy method of solid waste management allows consideration of multicriteria to better manage the inherent uncertainties. The fuzzy-based approach involve determination of solid waste management alternatives, selection of basic criteria, assignment of linguistic variables, construction of membership functions, assignment of membership degree values to each criterion, determination of the best criteria combination for alternatives and the choice of the best alternative. The result shows that alternative 2 has highest degree of membership function to the decision function and therefore is the chosen option.

Comparison between a Soft and Crisp Geographic Boundary of the Soil Texture Component in Hydrologic Models

This note is based on the generally accepted fact that soil boundaries are usually gradual rather than abrupt, and this is followed by an application of fuzzy set theory to what are already known to be diffuse boundaries. Sediment yield measurements are used to describe the control condition against which the fuzzy and conventional boundaries are assessed. In terms of the K factor, the fuzzy boundary representation showed less difference (up to 16.8%). The Nash–Sutcliff coefficient of efficiency and the root mean square error for the fuzzy boundary are 0.96 and 1.3× 10−3 , respectively, whereas those for the conventional boundary are 0.76 and 3.4× 10−3 , respectively. The estimation by the soil erosion model shows that the fuzzy representation of geographic boundary is more accurate than the conventional method. But the difference between erosion predictions using conventional boundaries and fuzzy boundaries is relatively small.

Application of Fuzzy Set Theory to Rock Engineering Classification Systems: An Illustration of the Rock Mass Excavability Index

The characterization of rock masses is one of the integral aspects of rock engineering. Over the years, many classification systems have been developed for characterization and design purposes in mining and civil engineering practices. However, the strength and weak points of such rating-based classifications have always been questionable. Such classification systems assign quantifiable values to predefined classified geotechnical parameters of rock mass. This results in subjective uncertainties, leading to the misuse of such classifications in practical applications. Fuzzy set theory is an effective tool to overcome such uncertainties by using membership functions and an inference system. This study illustrates the potential application of fuzzy set theory in assisting engineers in the rock engineering decision processes for which subjectivity plays an important role. So, the basic principles of fuzzy set theory are described and then it was applied to rock mass excavability (RME) classification to verify the applicability of fuzzy rock engineering classifications. It was concluded that fuzzy set theory has an acceptable reliability to be employed for all rock engineering classification systems.

Assessing supply side risk in supply chain with pattern matching

The paper discusses potential application of fuzzy set theory, more specifically, pattern matching for assessing risk in supply chain. Risk factors have been evaluated using linguistic representations of the extent of risk characteristics involved, their frequency of occurrence, severity of its impact and the uncertainty involved in its control mechanism if any. For each linguistic value, there is corresponding membership function ranging over a universe of discourse. The risk characteristics having highest degree of featural value are taken as the known pattern. Each sample pattern of the other risk characteristics with their known featural values are then matched with the known pattern. The concept of multi-feature pattern matching based on fuzzy logic is used to derive the rank ordering of risk characteristics. A methodology has been developed and the same exemplified by presenting a case example with limited number of risk characteristics.

A supply chain application of fuzzy set theory to inventory control models – DRP system analysis

As competition abounds, the efficient solution on inventory control of a DRP’s (Distribution Requirement Planning) supply chain management is a vital success factor for companies in today’s business world. A stochastic program of market distribution and its deterministic equivalent control program is approximated by a multi-echelon lot-sizing model based on “risk inflated effective demands”. The DRP-decomposition of this approximate model, which can be used with allocation application of Fuzzy Set Theory, is then introduced. The aim of this paper is to find methods to address traditional DRP’s weaknesses and to improve the performances of DRP systems. In this paper, the field of continuous review model will be focused in, and a new method on the model with triangular fuzzy numbers (input data) will be presented. By using the method, the maximum of order quantity under a minimum of total cost can be obtained. In many previous research, authors take a precise number approximately as the representative of a fuzzy number. But the precise number can not reflect the property of fuzzy inventory control number fully. Therefore, in a numerical example of this paper, in addition to providing a transformation for reducing a fuzzy number into a closed interval by introducing the interval mean value concept proposed by Dubios and Prude, this fuzzy system can be transformed into a more precise diagnosis system for channel members in the supply chain distribution organization.

Fuzzy logic for process safety analysis

Fuzzy logic deals with uncertainty and imprecision, and is an efficient tool for solving problems where knowledge uncertainty may occur. Such situations frequently arise in a quantitative fault and event tree analysis in safety and risk assessment of different processes. The lack of detailed data on failure rates, uncertainties in available data, imprecision and vagueness may lead to uncertainty in results, thus producing an underestimated or overestimated process risk level. This paper explores the application of fuzzy sets theory for basic tools used in process safety analysis such as fault and event tree methods which can be further used in the “bow-tie” approach for accident scenario risk assessment. In the traditional fault and event tree analyses, the input variables are treated as exact values and the exact outcome data are received by an appropriate mathematical approach. In the fuzzy method, all variables are replaced by fuzzy numbers in the process of fuzzification and subsequently using fuzzy arithmetic, fuzzy probability of the top event for fault tree, and fuzzy outcome probabilities for event tree are calculated. A single value for each of the outcome event result is obtained with the use of one of the defuzzification methods. A typical case study comprising a fault tree for rupture of the isobutane storage tank and the event tree for its consequences is performed and a comparison between the traditional approach and fuzzy method is made.

Application of Fuzzy Set Theory to Evaluate the Effect of Pore Pressure Build-Up on the Seismic Stability of Karkheh Dam, Iran

It is a current practice to employ composite clay—a mixture of clay and aggregates that float within the clayey matrix—as the core of embankment dams that have classically been constructed from pure clays. Experience has shown that significant pore pressures could build up during cyclic undrained loading in composite clays. This may threaten dam stability during earthquake loading. However, it is difficult to attribute a single value to excess pore pressure in conventional seismic stability analysis because of the random nature of earthquake loading, leading to uncertainty in the evaluation of factor of safety against sliding. This article evaluates the importance of pore pressure build-up in composite clays on the seismic behavior of Karkheh embankment dam in Iran and then documents a quantitative scheme using fuzzy set analysis to evaluate the failure potential of the dam.

Hybrid GPS/GSM Positioning Systems Design with Fuzzy Logic

Global Positioning System (GPS) is based on a satellite system. Much work has been carried out on a non-satellite positioning systems using the existing Global System of Mobile Communications (GSM) infrastructure. This leads to a hybrid GPS/GSM positioning systems in the paper. We purpose to adopt GSM for positioning via an integrated switch design with fuzzy logic, if GPS lose efficacy. This induces four main research features in this paper. (1) Designs with optimal-based Fourier analyzer to achieve error of GPS decrease is presented. (2) New applications of fuzzy set theory are presented to solve the problem of GPS accuracy. (3) An integrated switch of fuzzy logic is designed for selecting GPS or GSM positioning systems. (4) Discussions on various GSM positioning methods are adopted with different error and location parameters of environment.

Efficiency measures for SOC concepts

This paper discusses efficiency measures for the evaluation of high performance systems on a chip (SOC), considering a throughput rate R, chip size A, power dissipation P, and a flexibility criterion F. Based on the analysis of recently published multimedia chips, the paper shows equivalences between the ratio of R over AP, a weighted sum on 1/R, A, P, and a fuzzy multicriteria analysis on R, A, P. The paper indicates the fuzzy multicriteria analysis as generalization of the other efficiency measures, which can be easily extended to multiple cost and performance criteria. Because of the application of fuzzy set theory, the multicriteria approach supports quantitative criteria with a physical background as well as qualitative criteria by linguistic variables. Uncertainties at early conceptual phases are considered by a possibilistic measure, which is based on fuzzy set theory.

Fuzzy Logic with Applications to Hybrid GPS/GSM Positioning System Design

Global Positioning System (GPS) is based on a satellite system. Much work has been carried out on a non-satellite positioning systems using the existing Global System of Mobile Communications (GSM) infrastructure. This leads to a hybrid GPS/GSM positioning systems in the paper. We purpose to adopt GSM for positioning via an integrated switch design with fuzzy logic, if GPS lose efficacy. This induces four main research features in this paper: (1) Designs with optimal-based Fourier analyzer to achieve error of GPS decrease is presented. (2) New applications of fuzzy set theory are presented to solve the problem of GPS accuracy. (3) An integrated switch of fuzzy logic is designed for selecting GPS or GSM positioning systems. (4) Discussions on various GSM positioning methods are adopted with different error and location parameters of environment.

Exploring Multi-Dimensional Wellbeing and Remittances in El Salvador

El Salvador has experienced high and increasing migration outflows during the last three decades, fuelled by the civil war in the 1980s and currently by a lack of economic opportunities. In parallel, family remittances have grown to represent 16.1 percent of GDP in 2004. In this context, it is relevant to explore the wellbeing of individuals in households receiving remittances. In this paper, we propose an alternative measure of multi-dimensional wellbeing based on the capability approach that focuses on functionings or achievements of individuals in valuable dimensions of life, such as ���life and physical health�۝ and ���social relations�۝. From the multipurpose household survey (EHPM), we select feasible indicators for these dimensions which we aggregated using the Fuzzy Sets theory. We analyse wellbeing of different population groups in the selected dimensions of life. We find interesting differences in wellbeing between urban and rural households and male and female headed households. Finally, we analyse wellbeing for individuals in households depending on migration and remittances status. Households that receive remittances do show higher wellbeing, and those that are non-poor and receive remittances perform better than all other groups. The difference is higher in the dimensions of ���security, shelter and environment�۝ and in social relations�۝. This is the first application of Fuzzy Sets theory to measure multi-dimensional wellbeing in El Salvador, based on the EHPM. We recommend the inclusion of additional indicators in the questionnaire and a further exploration of this method to assess wellbeing of different population groups in order to support a more precise definition of social protection policies. Keywords: wellbeing, capabilities and functionings, migration, remittances, fuzzy sets JEL codes: F22, I31, I32, R20

Statistical confidence intervals for fuzzy data

The application of fuzzy sets theory to statistical confidence intervals for unknown fuzzy parameters is proposed in this paper by considering fuzzy random variables. In order to obtain the belief degrees under the sense of fuzzy sets theory, we transform the original problem into the optimization problems. We provide the computational procedure to solve the optimization problems. A numerical example is also provided to illustrate the possible application of fuzzy sets theory to statistical confidence intervals.

An application of fuzzy set theory for supply chain coordination

One of the important issues in supply chain management is the coordination among different members of the supply chain. In this paper, we have studied a two-stage supply chain coordination problem under uncertain cost and demand information. The aim of the paper is to design a coordination mechanism through quantity discount policy under asymmetric information environment that allows the system to perform as closely as that of under complete information. Fuzzy set theory is applied to estimate the uncertainty associated with the input parameters and triangular membership function has been used to analyze the model. Finally, the model is illustrated with a suitable numerical example.

Supply chain management: a modular Fuzzy Inference System approach in supplier selection for new product development

The critical objectives of purchasing departments include obtaining the product requested, at the right cost, in the right quantity, with the best quality, at the right time, from the right supplier. These goals require effective decisions concerning supplier selection at the early stage of product development. This work provides an application of fuzzy set theory in supply chain management, specifically in supplier selection for new product development. Here, a Fuzzy Inference System is proposed as an alternative approach to handle effectively the impreciseness and uncertainty that are normally found in supplier selection processes. This paper also shows that the proposed decision-making model is applicable to any supply chain system.

REPRESENTABILITY IN INTERVAL-VALUED FUZZY SET THEORY

Interval-valued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0,1]-valued membership degrees are replaced by intervals in [0,1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended setting, it is both natural and appropriate to "reuse" ingredients from classical fuzzy set theory. In this paper, we compare different ways of representing operations on interval-valued fuzzy sets by corresponding operations on fuzzy sets, study their intuitive semantics, and relate them to an existing, purely order-theoretical approach. Our approach reveals, amongst others, that subtle differences in the representation method can have a major impact on the properties satisfied by the generated operations, and that contrary to popular perception, interval-valued fuzzy set theory hardly corresponds to a mere twofold application of fuzzy set theory. In this way, by making the mathematical machinery behind the interval-valued fuzzy set model fully transparent, we aim to foster new avenues for its exploitation by offering application developers a much more powerful and elaborate mathematical toolbox than existed before.

Uma aplicação de conjuntos difusos na otimização do prognóstico de consenso sazonal de chuva no Nordeste do Brasil

Esse estudo apresenta a aplicação da teoria de conjuntos difusos como ferramenta para otimizar a previsão de consenso (PC) sazonal de chuva da Região Semi-Árida do Nordeste do Brasil (RSANEB) para o período de 1985-1996. Foram utilizados como variáveis de entrada parâmetros termodinâmicos sobre e nos Oceanos Atlântico e Pacífico Tropicais. Os resultados mostraram que qualitativamente, na escala interanual, o resultado determinístico dessa técnica aplicada a PC foi capaz de prever pelo menos uma das categorias da variável de saída (total de chuva de fevereiro a maio da RSANEB). Quantitativamente, os menores erros foram observados para os anos classificados na variável de saída nas categorias de Normal (N), Chuvoso (C), e Muito Chuvoso (MC), com correlações que variam de 0,8 a 0,85, dependendo do método de desfuzificação usado. Esta técnica permite unificar em um resultado determinístico todas as informações climáticas usadas na previsão sazonal de chuva da RSANEB, possibilitando seu prognóstico em mais de uma categoria, informando a mais provável a vir a ocorrer em função do seu nível de pertinência.

A Measurement-Theoretic Axiomatization of Trapezoidal Membership Functions

In many applications of fuzzy set theory, the membership of an object is not defined directly. One of its attributes (like height, age, weight, etc.) is first mapped to a real number (often by means of a physical instrument) and a parametric function then maps this real number to a membership degree in some fuzzy set (like "tall," "old," "heavy," etc.). A very common parametric function is the trapezoidal one. This paper presents some conditions guaranteeing the existence of such a trapezoidal membership function representing the knowledge of an expert. Further experimental research is needed for testing whether these conditions are satisfied by human agents