Search results for: fuzzy logistic regression

Authors: Georgios Charizanos, Haydar Demirhan, Duygu Icen

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Two of the most impactful issues in classical logistic regression are class imbalance and complete separation. These can result in model predictions heavily leaning towards the imbalanced class on the binary response variable or over-fitting issues. Fuzzy methodology offers key solutions for handling these problems. However, most studies propose the transformation of the binary responses into a continuous format limited within [0,1]. This is called the possibilistic approach within fuzzy logistic regression. Following this approach is more aligned with straightforward regression since a logit-link function is not utilized, and fuzzy probabilities are not generated. In contrast, we propose a method of fuzzifying binary response variables that allows for the use of the logit-link function; hence, a probabilistic fuzzy logistic regression model with the Monte Carlo method. The fuzzy probabilities are then classified by selecting a fuzzy threshold. Different combinations of fuzzy and crisp input, output, and coefficients are explored, aiming to understand which of these perform better under different conditions of imbalance and separation. We conduct numerical experiments using both synthetic and real datasets to demonstrate the performance of the fuzzy logistic regression framework against seven crisp machine learning methods. The proposed framework shows better performance irrespective of the degree of imbalance and presence of separation in the data, while the considered machine learning methods are significantly impacted.

Keywords: fuzzy logistic regression, fuzzy, logistic, machine learning

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Authors: Lavinia B. Dulla

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The exploration study of the fuzzy regression approach attempts to present that fuzzy regression can be used as a possible alternative to classical regression. It likewise seeks to assess the differences and characteristics of simple linear regression and fuzzy regression using the width of prediction interval, mean absolute deviation, and variance of residuals. Based on the simple linear regression model, the fuzzy regression approach is worth considering as an alternative to simple linear regression when the sample size is between 10 and 20. As the sample size increases, the fuzzy regression approach is not applicable to use since the assumption regarding large sample size is already operating within the framework of simple linear regression. Nonetheless, it can be suggested for a practical alternative when decisions often have to be made on the basis of small data.

Keywords: fuzzy regression approach, minimum fuzziness criterion, interval regression, prediction interval

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Authors: Shima Soltanzadeh, Mohammad Hosain Fazel Zarandi, Mojtaba Barzegar Astanjin

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Diagnosis of male infertility by the laboratory tests is expensive and, sometimes it is intolerable for patients. Filling out the questionnaire and then using classification method can be the first step in decision-making process, so only in the cases with a high probability of infertility we can use the laboratory tests. In this paper, we evaluated the performance of four classification methods including naive Bayesian, neural network, logistic regression and fuzzy c-means clustering as a classification, in the diagnosis of male infertility due to environmental factors. Since the data are unbalanced, the ROC curves are most suitable method for the comparison. In this paper, we also have selected the more important features using a filtering method and examined the impact of this feature reduction on the performance of each methods; generally, most of the methods had better performance after applying the filter. We have showed that using fuzzy c-means clustering as a classification has a good performance according to the ROC curves and its performance is comparable to other classification methods like logistic regression.

Keywords: classification, fuzzy c-means, logistic regression, Naive Bayesian, neural network, ROC curve

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Authors: O. Poleshchuk, E. Komarov

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This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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Authors: Shih-Pin Chen, Shih-Syuan You

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Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming

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Authors: Jan Henrik Wosnitza

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The logistic regression has developed into a standard approach for estimating conditional probabilities in a wide range of applications including credit risk prediction. The article at hand contributes to the current literature on logistic regression fourfold: First, it is demonstrated that the binary logistic regression automatically meets its model assumptions under very general conditions. This result explains, at least in part, the logistic regression's popularity. Second, the requirement of homoscedasticity in the context of binary logistic regression is theoretically substantiated. The variances among the groups of defaulted and non-defaulted obligors have to be the same across the level of the aggregated default indicators in order to achieve linear logits. Third, this article sheds some light on the question why nonlinear logits might be superior to linear logits in case of a small amount of data. Fourth, an innovative methodology for estimating correlations between obligor-specific log-odds is proposed. In order to crystallize the key ideas, this paper focuses on the example of credit risk prediction. However, the results presented in this paper can easily be transferred to any other field of application.

Keywords: correlation, credit risk estimation, default correlation, homoscedasticity, logistic regression, nonlinear logistic regression

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Authors: Idrissa Kayijuka

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The logistic regression and Cox regression models (proportional hazard model) at present are being employed in the analysis of prospective epidemiologic research looking into risk factors in their application on chronic diseases. However, a theoretical relationship between the two models has been studied. By definition, Cox regression model also called Cox proportional hazard model is a procedure that is used in modeling data regarding time leading up to an event where censored cases exist. Whereas the Logistic regression model is mostly applicable in cases where the independent variables consist of numerical as well as nominal values while the resultant variable is binary (dichotomous). Arguments and findings of many researchers focused on the overview of Cox and Logistic regression models and their different applications in different areas. In this work, the analysis is done on secondary data whose source is SPSS exercise data on BREAST CANCER with a sample size of 1121 women where the main objective is to show the application difference between Cox regression model and logistic regression model based on factors that cause women to die due to breast cancer. Thus we did some analysis manually i.e. on lymph nodes status, and SPSS software helped to analyze the mentioned data. This study found out that there is an application difference between Cox and Logistic regression models which is Cox regression model is used if one wishes to analyze data which also include the follow-up time whereas Logistic regression model analyzes data without follow-up-time. Also, they have measurements of association which is different: hazard ratio and odds ratio for Cox and logistic regression models respectively. A similarity between the two models is that they are both applicable in the prediction of the upshot of a categorical variable i.e. a variable that can accommodate only a restricted number of categories. In conclusion, Cox regression model differs from logistic regression by assessing a rate instead of proportion. The two models can be applied in many other researches since they are suitable methods for analyzing data but the more recommended is the Cox, regression model.

Keywords: logistic regression model, Cox regression model, survival analysis, hazard ratio

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Authors: Denys Osipenko, Jonathan Crook

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Because of the variety of the card holders’ behaviour types and income sources each consumer account can be transferred to a variety of states. Each consumer account can be inactive, transactor, revolver, delinquent, defaulted and requires an individual model for the income prediction. The estimation of transition probabilities between statuses at the account level helps to avoid the memorylessness of the Markov Chains approach. This paper investigates the transition probabilities estimation approaches to credit cards income prediction at the account level. The key question of empirical research is which approach gives more accurate results: multinomial logistic regression or multistage conditional logistic regression with binary target. Both models have shown moderate predictive power. Prediction accuracy for conditional logistic regression depends on the order of stages for the conditional binary logistic regression. On the other hand, multinomial logistic regression is easier for usage and gives integrate estimations for all states without priorities. Thus further investigations can be concentrated on alternative modeling approaches such as discrete choice models.

Keywords: multinomial regression, conditional logistic regression, credit account state, transition probability

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Authors: Byung Ho Jung, Dong Hoon Lim

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Logistic regression is a statistical method for analyzing a dataset in which there are one or more independent variables that determine an outcome. Logistic regression is used extensively in numerous disciplines, including the medical and social science fields. In this paper, we address the problem of estimating parameters in the logistic regression based on MapReduce framework with RHadoop that integrates R and Hadoop environment applicable to large scale data. There exist three learning algorithms for logistic regression, namely Gradient descent method, Cost minimization method and Newton-Rhapson's method. The Newton-Rhapson's method does not require a learning rate, while gradient descent and cost minimization methods need to manually pick a learning rate. The experimental results demonstrated that our learning algorithms using RHadoop can scale well and efficiently process large data sets on commodity hardware. We also compared the performance of our Newton-Rhapson's method with gradient descent and cost minimization methods. The results showed that our newton's method appeared to be the most robust to all data tested.

Keywords: big data, logistic regression, MapReduce, RHadoop

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Authors: Liang-Hsuan Chen, Sheng-Shing Nien

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This study aims to develop approaches to formulate intuitionistic fuzzy regression (IFR) models for many decision-making applications in the fuzzy environments using intuitionistic fuzzy observations. Intuitionistic fuzzy numbers (IFNs) are used to characterize the fuzzy input and output variables in the IFR formulation processes. A mathematical programming problem (MPP) is built up to optimally determine the IFR parameters. Each parameter in the MPP is defined as a couple of alternative numerical variables with opposite signs, and an intuitionistic fuzzy error term is added to the MPP to characterize the uncertainty of the model. The IFR model is formulated based on the distance measure to minimize the total distance errors between estimated and observed intuitionistic fuzzy responses in the MPP resolution processes. The proposed approaches are simple/efficient in the formulation/resolution processes, in which the sign of parameters can be determined so that the problem to predetermine the sign of parameters is avoided. Furthermore, the proposed approach has the advantage that the spread of the predicted IFN response will not be over-increased, since the parameters in the established IFR model are crisp. The performance of the obtained models is evaluated and compared with the existing approaches.

Keywords: fuzzy sets, intuitionistic fuzzy number, intuitionistic fuzzy regression, mathematical programming method

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Authors: Entisar A. Elgmati

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Recurrent infant diarrhea is studied using daily data collected in Salvador, Brazil over one year and three months. A logistic regression model is fitted instead of Aalen's additive model using the same covariates that were used in the analysis with the additive model. The model gives reasonably similar results to that using additive regression model. In addition, the problem with the estimated conditional probabilities not being constrained between zero and one in additive model is solved here. Also martingale residuals that have been used to judge the goodness of fit for the additive model are shown to be useful for judging the goodness of fit of the logistic model.

Keywords: additive model, cumulative probabilities, infant diarrhoea, recurrent event

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Authors: Shih-Pin Chen, Shih-Syuan You

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This study proposes a regression model with flexible spreads for fuzzy input-output data to cope with the situation that the existing measures cannot reflect the actual estimation error. The main idea is that a dissemblance index (DI) is carefully identified and defined for precisely measuring the actual estimation error. Moreover, the graded mean integration (GMI) representation is adopted for determining more representative numeric regression coefficients. Notably, to comprehensively compare the performance of the proposed model with other ones, three different criteria are adopted. The results from commonly used test numerical examples and an application to Taiwan's business monitoring indicator illustrate that the proposed dissemblance index method not only produces valid fuzzy regression models for fuzzy input-output data, but also has satisfactory and stable performance in terms of the total estimation error based on these three criteria.

Keywords: dissemblance index, forecasting, fuzzy sets, linear regression

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Authors: Chen Li-Ching

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The multinomial logistic regression model is used popularly for inferring the relationship of risk factors and disease with multiple categories. This study based on the discrepancy between the nonparametric maximum likelihood estimator and semiparametric maximum likelihood estimator of the cumulative distribution function to propose a Kolmogorov-Smirnov type test statistic to assess adequacy of the multinomial logistic regression model for case-control data. A bootstrap procedure is presented to calculate the critical value of the proposed test statistic. Empirical type I error rates and powers of the test are performed by simulation studies. Some examples will be illustrated the implementation of the test.

Keywords: case-control studies, goodness-of-fit test, Kolmogorov-Smirnov test, multinomial logistic regression

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Authors: Arindam Chaudhuri

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The research presents epsilon- hierarchical fuzzy twin support vector regression (epsilon-HFTSVR) based on epsilon-fuzzy twin support vector regression (epsilon-FTSVR) and epsilon-twin support vector regression (epsilon-TSVR). Epsilon-FTSVR is achieved by incorporating trapezoidal fuzzy numbers to epsilon-TSVR which takes care of uncertainty existing in forecasting problems. Epsilon-FTSVR determines a pair of epsilon-insensitive proximal functions by solving two related quadratic programming problems. The structural risk minimization principle is implemented by introducing regularization term in primal problems of epsilon-FTSVR. This yields dual stable positive definite problems which improves regression performance. Epsilon-FTSVR is then reformulated as epsilon-HFTSVR consisting of a set of hierarchical layers each containing epsilon-FTSVR. Experimental results on both synthetic and real datasets reveal that epsilon-HFTSVR has remarkable generalization performance with minimum training time.

Keywords: regression, epsilon-TSVR, epsilon-FTSVR, epsilon-HFTSVR

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Authors: Bader Alkandari, Jamal Y. Madouh, Ahmad M. Alkandari, Anwar A. Alnaqi

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A new formulation of fuzzy linear estimation problem is presented. It is formulated as a linear programming problem. The objective is to minimize the spread of the data points, taking into consideration the type of the membership function of the fuzzy parameters to satisfy the constraints on each measurement point and to insure that the original membership is included in the estimated membership. Different models are developed for a fuzzy triangular membership. The proposed models are applied to different examples from the area of fuzzy linear regression and finally to different examples for estimating the electrical load on a busbar. It had been found that the proposed technique is more suited for electrical load estimation, since the nature of the load is characterized by the uncertainty and vagueness.

Keywords: fuzzy regression, load estimation, fuzzy linear parameters, electrical load estimation

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Authors: Retius Chifurira

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Logistic regression model is the most used regression model to predict meteorological drought probabilities. When the dependent variable is extreme, the logistic model fails to adequately capture drought probabilities. In order to adequately predict drought probabilities, we use the generalized linear model (GLM) with the quantile function of the generalized extreme value distribution (GEVD) as the link function. The method maximum likelihood estimation is used to estimate the parameters of the generalized extreme value (GEV) regression model. We compare the performance of the logistic and the GEV regression models in predicting drought probabilities for Zimbabwe. The performance of the regression models are assessed using the goodness-of-fit tests, namely; relative root mean square error (RRMSE) and relative mean absolute error (RMAE). Results show that the GEV regression model performs better than the logistic model, thereby providing a good alternative candidate for predicting drought probabilities. This paper provides the first application of GLM derived from extreme value theory to predict drought probabilities for a drought-prone country such as Zimbabwe.

Keywords: generalized extreme value distribution, general linear model, mean annual rainfall, meteorological drought probabilities

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Authors: P. S. Jagadeesh Kumar, Mingmin Pan, Xianpei Li, Yanmin Yuan, Tracy Lin Huan

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Researchers are doing enchanting research into the inherited features of Alzheimer’s disease and probable consistent therapies. In Alzheimer’s, memories are extinct in reverse order; memories formed lately are more transitory than those from formerly. Reminiscence therapy includes the conversation of past actions, trials and knowledges with another individual or set of people, frequently with the help of perceptible reminders such as photos, household and other acquainted matters from the past, music and collection of tapes. In this manuscript, the competence of reminiscence therapy for Alzheimer’s disease is measured using logistic regression based linear bootstrap aggregating. Logistic regression is used to envisage the experiential features of the patient’s memory through various therapies. Linear bootstrap aggregating shows better stability and accuracy of reminiscence therapy used in statistical classification and regression of memories related to validation therapy, supportive psychotherapy, sensory integration and simulated presence therapy.

Keywords: Alzheimer’s disease, linear bootstrap aggregating, logistic regression, reminiscence therapy

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Authors: Tahmidul Islam

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Propensity Score Matching (PSM) technique has been widely used for estimating causal effect of treatment in observational studies. One major step of implementing PSM is estimating the propensity score (PS). Logistic regression model with additive linear terms of covariates is most used technique in many studies. Logistics regression model is also used with cubic splines for retaining flexibility in the model. However, choosing the functional form of the logistic regression model has been a question since the effectiveness of PSM depends on how accurately the PS been estimated. In many situations, the linearity assumption of linear logistic regression may not hold and non-linear relation between the logit and the covariates may be appropriate. One can estimate PS using machine learning techniques such as random forest, neural network etc for more accuracy in non-linear situation. In this study, an attempt has been made to compare the efficacy of Generalized Additive Model (GAM) in various linear and non-linear settings and compare its performance with usual logistic regression. GAM is a non-parametric technique where functional form of the covariates can be unspecified and a flexible regression model can be fitted. In this study various simple and complex models have been considered for treatment under several situations (small/large sample, low/high number of treatment units) and examined which method leads to more covariate balance in the matched dataset. It is found that logistic regression model is impressively robust against inclusion quadratic and interaction terms and reduces mean difference in treatment and control set equally efficiently as GAM does. GAM provided no significantly better covariate balance than logistic regression in both simple and complex models. The analysis also suggests that larger proportion of controls than treatment units leads to better balance for both of the methods.

Keywords: accuracy, covariate balances, generalized additive model, logistic regression, non-linearity, propensity score matching

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Authors: Sami Mestiri, Abdeljelil Farhat

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The aim of this current paper is to predict the credit risk of banks in Tunisia, over the period (2000-2005). For this purpose, two methods for the estimation of the logistic regression model with random effects: Penalized Quasi Likelihood (PQL) method and Gibbs Sampler algorithm are applied. By using the information on a sample of 528 Tunisian firms and 26 financial ratios, we show that Bayesian approach improves the quality of model predictions in terms of good classification as well as by the ROC curve result.

Keywords: forecasting, credit risk, Penalized Quasi Likelihood, Gibbs Sampler, logistic regression with random effects, curve ROC

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Authors: Encarnación Álvarez, Rosa M. García-Fernández, Juan F. Muñoz, Francisco J. Blanco-Encomienda

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The problem of estimating a proportion has important applications in the field of economics, and in general, in many areas such as social sciences. A common application in economics is the estimation of the headcount index. In this paper, we define the general headcount index as a proportion. Furthermore, we introduce a new quantitative method for estimating the headcount index. In particular, we suggest to use the logistic regression estimator for the problem of estimating the headcount index. Assuming a real data set, results derived from Monte Carlo simulation studies indicate that the logistic regression estimator can be more accurate than the traditional estimator of the headcount index.

Keywords: poverty line, poor, risk of poverty, Monte Carlo simulations, sample

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Authors: Ehsan Mehryaar, Seyed Armin Motahari Tabari

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Without a doubt, soil shear strength is the most important property of the soil. The majority of fatal and catastrophic geological accidents are related to shear strength failure of the soil. Therefore, its prediction is a matter of high importance. However, acquiring the shear strength is usually a cumbersome task that might need complicated laboratory testing. Therefore, prediction of it based on common and easy to get soil properties can simplify the projects substantially. In this paper, A hybrid model based on the classification and regression tree algorithm and logistic regression is proposed where each leaf of the tree is an independent regression model. A database of 189 points for clay soil, including Moisture content, liquid limit, plastic limit, clay content, and shear strength, is collected. The performance of the developed model compared to the existing models and equations using root mean squared error and coefficient of correlation.

Keywords: model tree, CART, logistic regression, soil shear strength

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Authors: Suzan Anwar, Utkarsh Goyal

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Heart rate (HR) is a predictor of cardiovascular, cerebrovascular, and all-cause mortality in the general population, as well as in patients with cardio and cerebrovascular diseases. Machine learning (ML) significantly improves the accuracy of cardiovascular risk prediction, increasing the number of patients identified who could benefit from preventive treatment while avoiding unnecessary treatment of others. This research examines relationship between the individual's various heart health inputs like age, sex, cp, trestbps, thalach, oldpeaketc, and the likelihood of developing heart disease. Machine learning techniques like logistic regression and decision tree, and Python are used. The results of testing and evaluating the model using the Heart Failure Prediction Dataset show the chance of a person having a heart disease with variable accuracy. Logistic regression has yielded an accuracy of 80.48% without data handling. With data handling (normalization, standardscaler), the logistic regression resulted in improved accuracy of 87.80%, decision tree 100%, random forest 100%, and SVM 100%.

Keywords: heart rate, machine learning, SVM, decision tree, logistic regression, random forest

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Authors: Y. H. Wu, Ji-Yuan Lin, Yu-Ming Liou

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This study aims to set up the landslide susceptibility map of County Route 89 at Ren-Ai Township in Nantou County using the Instability Index Method and Logistic regression. Seven susceptibility factors including Slope Angle, Aspect, Elevation, Distance to fold, Distance to River, Distance to Road and Accumulated Rainfall were obtained by GIS based on the Typhoon Toraji landslide area identified by Industrial Technology Research Institute in 2001. To calculate the landslide percentage of each factor and acquire the weight and grade the grid by means of Instability Index Method. In this study, landslide susceptibility can be classified into four grades: high, medium high, medium low and low, in order to determine the advantages and disadvantages of the two models. The precision of this model is verified by classification error matrix and SRC curve. These results suggest that the logistic regression model is a preferred method than instability index in the assessment of landslide susceptibility. It is suitable for the landslide prediction and precaution in this area in the future.

Keywords: instability index method, logistic regression, landslide susceptibility, SRC curve

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Authors: Ali Koam, Ismail Ibedou, S. E. Abbas

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In this paper, it is introduced the notion of r-fuzzy ideal separation axioms Tᵢi = 0; 1; 2 based on a fuzzy ideal I on a fuzzy topological space (X; τ). An r-fuzzy ideal connectedness related to the fuzzy ideal I is introduced which has relations with a previous r-fuzzy fuzzy connectedness. An r-fuzzy ideal compactness related to Ι is introduced which has also relations with many other types of fuzzy compactness.

Keywords: fuzzy ideal, fuzzy separation axioms, fuzzy compactness, fuzzy connectedness

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Authors: Osamu Komori, Shinto Eguchi, Hiroshi Okamura, Momoko Ichinokawa

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The long time-series data on population assessments are essential for global ecosystem assessment because the temporal change of biomass in such a database reflects the status of global ecosystem properly. However, the available assessment data usually have limited sample sizes and the ratio of populations with low abundance of biomass (collapsed) to those with high abundance (non-collapsed) is highly imbalanced. To allow for the imbalance and uncertainty involved in the ecological data, we propose a binary regression model with mixed effects for inferring ecosystem status through an asymmetric logistic model. In the estimation equation, we observe that the weights for the non-collapsed populations are relatively reduced, which in turn puts more importance on the small number of observations of collapsed populations. Moreover, we extend the asymmetric logistic regression model using propensity score to allow for the sample biases observed in the labeled and unlabeled datasets. It robustified the estimation procedure and improved the model fitting.

Keywords: double robust estimation, ecological binary data, mixed effect logistic regression model, propensity score

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Authors: S. Benchelha, H. C. Aoudjehane, M. Hakdaoui, R. El Hamdouni, H. Mansouri, T. Benchelha, M. Layelmam, M. Alaoui

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The logistic regression (LR) and multivariate adaptive regression spline (MarSpline) are applied and verified for analysis of landslide susceptibility map in Oudka, Morocco, using geographical information system. From spatial database containing data such as landslide mapping, topography, soil, hydrology and lithology, the eight factors related to landslides such as elevation, slope, aspect, distance to streams, distance to road, distance to faults, lithology map and Normalized Difference Vegetation Index (NDVI) were calculated or extracted. Using these factors, landslide susceptibility indexes were calculated by the two mentioned methods. Before the calculation, this database was divided into two parts, the first for the formation of the model and the second for the validation. The results of the landslide susceptibility analysis were verified using success and prediction rates to evaluate the quality of these probabilistic models. The result of this verification was that the MarSpline model is the best model with a success rate (AUC = 0.963) and a prediction rate (AUC = 0.951) higher than the LR model (success rate AUC = 0.918, rate prediction AUC = 0.901).

Keywords: landslide susceptibility mapping, regression logistic, multivariate adaptive regression spline, Oudka, Taounate

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Authors: Ekele Alih, Enejo Jalija

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Female Genital Mutilation (FGM) is made up of three types namely: Clitoridectomy, Excision and Infibulation. In this study, we examine the factors responsible for FGM in order to identify the causality variables in a logistic regression approach. From the result of the survey conducted by the Public Health Division, Nigeria Institute of Medical Research, Yaba, Lagos State, the tau statistic, τ was used to screen 9 factors that causes FGM in order to select few of the predictors before multiple regression equation is obtained. The need for this may be that the sample size may not be able to sustain having a regression with all the predictors or to avoid multi-collinearity. A total of 300 respondents, comprising 150 adult males and 150 adult females were selected for the household survey based on the multi-stage sampling procedure. The tau statistic,

Keywords: female genital mutilation, logistic regression, tau statistic, African society

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Authors: S. H. Nasseri, A. Ebrahimnejad

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Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.

Keywords: fuzzy linear programming, fuzzy numbers, duality, sensitivity analysis

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Authors: Encarnación Álvarez, Rosa M. García-Fernández, Juan F. Muñoz

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Estimation of a proportion has many applications in economics and social studies. A common application is the estimation of the low income proportion, which gives the proportion of people classified as poor into a population. In this paper, we present this poverty indicator and propose to use the logistic regression estimator for the problem of estimating the low income proportion. Various sampling designs are presented. Assuming a real data set obtained from the European Survey on Income and Living Conditions, Monte Carlo simulation studies are carried out to analyze the empirical performance of the logistic regression estimator under the various sampling designs considered in this paper. Results derived from Monte Carlo simulation studies indicate that the logistic regression estimator can be more accurate than the customary estimator under the various sampling designs considered in this paper. The stratified sampling design can also provide more accurate results.

Keywords: poverty line, risk of poverty, auxiliary variable, ratio method

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Authors: G. S. Thakur

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In this paper, four new operators (O1, O2, O3, O4) are proposed, defined and considered to study the new properties and identities on hesitant fuzzy sets. These operators are useful for different operation on hesitant fuzzy sets. The various theorems are proved using the new operators. The study of the proposed new operators has opened a new area of research and applications.

Keywords: vague sets, hesitant fuzzy sets, intuitionistic fuzzy set, fuzzy sets, fuzzy multisets

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