Crisp Inputs Research Articles

A joint chance-constrained data envelopment analysis model with random output data

Data envelopment analysis (DEA) is a mathematical programming approach for evaluating the technical efficiency performances of a set of comparable decision-making units that transform multiple inputs into multiple outputs. The conventional DEA models are based on crisp input and output data, but real-world problems often involve random output data. The main purpose of the paper is to propose a joint chance-constrained DEA model for analyzing a real-world situation characterized by random outputs and crisp inputs. After developing the model, we carry out the following: First, we obtain an upper bound of this stochastic non-linear model deterministically by applying a piecewise linear approximation algorithm based on second-order cone programming; Second, we obtain a lower bound with use of a piecewise tangent approximation algorithm, which is also based on second-order cone programming; and then we use a numerical example to demonstrate the applicability of the proposed joint chance-constrained DEA framework.

Dual possibilistic regression analysis using support vector networks

This study proposes a novel and efficient dual regression model for possibilistic regression analysis that incorporates the principles of support vector machine (SVM) theory. The dual regression model, which comprises an upper model and a lower model, approximates the observed fuzzy phenomena from the outside and inside directions, respectively, such that the inclusion relationship between those two models holds. The proposed dual regression model better explains the inherent vagueness that exists in a given dataset. It provides the outer and inner bounds for the estimated vagueness region, and allows an estimation of the degree of confidence in the predicted fuzzy output. Using the principles for a twin support vector machine (TSVM), the upper- and lower models are estimated by solving two smaller SVM-type quadratic programming problems (QPPs), instead of a single larger QPP. This strategy significantly increases the learning speed for the proposed algorithm. The structural risk minimization principle of SVM makes the proposed method to yield better generalization ability. The kernel function method offers a model-independent framework for the proposed dual regression model. This paper focuses on the class of radial kernels, which enables the proposed method to conquer the problem of increasing spreads. The radial kernel also gives the proposed method a unified framework that allows both crisp and fuzzy inputs. The experimental results verify the effectiveness and efficiency of the proposed method. In comparison with previous SVM-based dual regression model, the proposed approach significantly improves the sparsity, prediction speed, and training speed.

A fuzzy-based career recommender system for senior high school students in K to 12 education

In this paper, a proposed career recommender system was presented which aim to help not only the guidance counselor but most especially the senior high school students to guide them in considering numerous factors associated to their decision on what career they will pursue. In dealing with choosing the student attributes from numerous factors, a feature selection technique is appropriate to use to remove irrelevant features that affect the performance of the proposed fuzzy-based system. In this paper, different filter methods are used to select the best attributes then these attributes are used as crisp inputs. The result of the experiment shows reasonable result for making decisions. It is concluded that the proposed career recommender system for the students is very timely and will be one of the significant research work in the new era of education system in the Philippines.

Formalization of Fuzzy Control in Possibility Theory via Rule Extraction

Possibility system has been recently recognized as a potential foundational theory for fuzzy set theory though the concept of possibility originated from the membership function of fuzzy sets. As an application of fuzzy set theory, fuzzy control has been widely used in engineering practices, where control laws are described by fuzzy if-then rules. This paper intends to formulate fuzzy control in the framework of possibility theory by regarding the fuzzification procedure of fuzzy control as extraction process of the fuzzy variable from crisp input, and the fuzzy if-then rules as extracted rules between fuzzy input/output. Typical procedures of fuzzy control, such as fuzzification, implication, aggregation, and defuzzification, are eventually formulated as a series of conditional possibilities operated by “max-product” operators. The reformulated fuzzy controller has a more general form, which encompasses the Mamdani fuzzy controller as a special case. Some fundamental concepts of possibility theory, such as randomness/fuzziness, possibility, and conditional possibility, are also discussed, which may be helpful for the correct understanding of possibility theory. Efforts have been made to bridge the two systems of possibility theory and fuzzy sets by the derivation of composition rule of fuzzy relations from conditional possibility. All results are derived for both normalized possibility and non-normalized possibility. This paper strengthened the role of possibility theory as a foundation for fuzzy sets, and as a complementary method to probability theory for handling information with fuzzy uncertainty.

A fuzzy logic-based expert system for substrate selection for soil construction in land reclamation

Abstract The mining industry can be one of the most impacting human activities. In the southern region of Santa Catarina (Brazil), open pit coal mining has left an extensive environmental impact. Since there was no topsoil in the abandoned open pit sites, it is necessary to provide a substrate for vegetation growth. However, the selection of the best substrate between multiple options is difficult. Thus, a fuzzy logic-based model is proposed. The proposed model was compared to reference models and to experts’ knowledge. Statistical analysis and validation were carried out with a correlation coefficient, a Kappa coefficient, along with the Accuracy, Precision, Sensibility Specificity, F-Score and Mathews correlation coefficients. The data set used to assess the proposed model presented a wide range of data, but for values such as aluminum saturation, higher values were common. The fuzzy logic-based expert system presented better results when assessing the behavior of the defuzzified output values with the crisp input values. The fuzzy model also followed the trend of the reference models (with R2 between 0.3639 and 0.5250). The comparison to the experts’ opinion demonstrated that agreement comes easily with extreme values (such as not suitable and suitable). However, using a Winner-Takes-All approach, the proposed fuzzy model had high scores for suitable soils for land reclamation’s soil construction. The proposed model can be used to define the best substrate for land reclamation. Some improvements, such as different parameters and increases in the number of interviews rounds, should be also tested.

Diagnostic methods and risk analysis based on fuzzy soft information

In our daily life problem we face uncertainties in making right decisions. In this study, we propose two different decision-making problems in medical field. The first problem is fever diagnosing and second problem is mouth cancer risk analysis. In the first problem, we use fuzzy soft similarity measures and fuzzy soft matrix operations to diagnose the type of fever. We consider a hypothetical case study and manipulate similarity measures on it. Our work diagnoses different patients having similar symptoms. We also develop a small application using JAVA. In the second problem, we perform risk analysis of mouth cancer. The proposed fuzzy soft expert system takes two biochemical parameters as inputs that is, serum total malondialdehyde (MDA), and serum proton donors capacity (donors_protons) and determines the risk of mouth cancer. Our study facilitates doctors by diagnosing mouth cancer at its earlier stages. There are four main components of our fuzzy soft expert system. The first component is named as fuzzification which converts crisp input into linguistic variables and formulates fuzzy sets. The second component transforms fuzzy sets into their respective fuzzy soft sets. The third component determines indispensable parameters and performs parameter reduction. The fourth component performs risk analysis by using algorithm. We use exemplary dataset and run all the components of fuzzy soft expert system to compute cancer risk.

Deep Crisp Boundaries: From Boundaries to Higher-Level Tasks.

Edge detection has made significant progress with the help of deep convolutional networks (ConvNet). These ConvNet-based edge detectors have approached human level performance on standard benchmarks. We provide a systematical study of these detectors' outputs. We show that the detection results did not accurately localize edge pixels, which can be adversarial for tasks that require crisp edge inputs. As a remedy, we propose a novel refinement architecture to address the challenging problem of learning a crisp edge detector using ConvNet. Our method leverages a top-down backward refinement pathway, and progressively increases the resolution of feature maps to generate crisp edges. Our results achieve superior performance, surpassing human accuracy when using standard criteria on BSDS500, and largely outperforming the state-of-the-art methods when using more strict criteria. More importantly, we demonstrate the benefit of crisp edge maps for several important applications in computer vision, including optical flow estimation, object proposal generation, and semantic segmentation.

Interval linear programming under transformations: optimal solutions and optimal value range

Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb independently within the given lower and upper bounds. However, contrarily to classical linear programming, an interval program cannot always be converted into a desired form without affecting its properties, due to the so-called dependency problem. In this paper, we discuss the common transformations used in linear programming, such as imposing non-negativity on free variables or splitting equations into inequalities, and their effects on interval programs. Specifically, we examine changes in the set of all optimal solutions, optimal values and the optimal value range. Since some of the considered properties do not holds in the general case, we also study a special class of interval programs, in which uncertainty only affects the objective function and the right-hand-side vector. For this class, we obtain stronger results.

CLUS-MCDA: A novel framework based on cluster analysis and multiple criteria decision theory in a supplier selection problem

Abstract In past recent years, by increasing in the considerations on the significance of data science many studies have been developed concerning the big data structured problems. Along with the information science, in the field of decision science, multi-attribute decision-making (MADM) approaches have been considerably applied in research studies. One of the most important procedures in supply chain management is selecting the optimal supplier to maintain the long-term productivity of the supply chain. There has been a vast amount of research which utilized MADM approaches to tackle the supplier selection problems, but only a few of these research considered big data structured problems. The current study presents a comprehensive novel approach for improving Multiple Criteria Decision Analysis (MCDA) based on cluster analysis considering crisp big data structure input which is called CLUS-MCDA (Cluster analysis for improving Multiple Criteria Decision Analysis) algorithm. The proposed method is based on consolidating a data mining technique i.e. k -means clustering method and a MADM approach which is MULTIMOORA method. CLUS-MCDA method is a fast and practical approach which has been developed in this research which is implied in a supplier selection problem considering crisp big data structured input. A real-world case study in MAMUT multi-national corporation has been presented to show the validity and practicality of the CLUS-MCDA approach which calculated considering the business areas and criteria based on expert comments of mentioned organizations and previous literature on supplier selection problem.

A New Fuzzy Regression Model by Mixing Fuzzy and Crisp Inputs

A New Fuzzy Regression Model by Mixing Fuzzy and Crisp Inputs Magda M. M. Haggag Abstract This paper proposes a new form of the multiple regression model (mixed model) based on adding both fuzzy and crisp input data. The least squares approach of the proposed multiple regression parameters are derived in different cases. This derivation is based on the fact that each fuzzy datum is a nonempty compact interval of the real line. The main contribution is to mix both fuzzy and crisp predictors in the linear regression model. The mixed fuzzy crisp model will be introduced mathematically and by coded via R-language. The least squares of the regression parameters will be derived and evaluated using distance measures. Numerical examples using generated data showed best results for the mixed fuzzy crisp multiple regression models compared to the multiple fuzzy models. Full Text: PDF DOI: 10.15640/arms.v6n2a2

A Similarity Based Fuzzy System as a Function Approximator

In this paper, an attempt is made to prove that some similarity based fuzzy systems can be found to behave as function approximators. A typical similarity based fuzzy system is proposed and its behaviour is shown to have the said property. It elucidates the connection between similarity relation and similarity measure of fuzzy sets to fuzzy inference methodology. The concept of similarity relation is used in fuzzification of crisp input values. Similarity index is used in measuring approximate equality of fuzzy sets over a given universe of discourse of a linguistic variable. The similarity between the observation(s) and the antecedent of a rule is used in selecting rule(s) for possible firing and also in modifying the relation between the antecedent and consequent of the rule based on the specific observation. Inference is drawn through the usual composition and subsequently by projecting the modified fuzzy restriction acting on the variables of interest on the universe of the linguistic variable in the consequent of the rule. A specificity based defuzzification scheme is proposed for multiple-rule firing. It has been proved systematically that such a similarity based fuzzy system can uniformly approximate continuous functions to any desired degree of accuracy on a closed and bounded interval. Simulation results are presented for the well-known dc-motor problem. A comparative study is made to establish the validity and efficiency of the proposed similarity based fuzzy system.

Minimum Entropy Active Fault Tolerant Control of the Non-Gaussian Stochastic Distribution System Subjected to Mean Constraint

Stochastic distribution control (SDC) systems are a group of systems where the outputs considered is the measured probability density function (PDF) of the system output whilst subjected to a normal crisp input. The purpose of the active fault tolerant control of such systems is to use the fault estimation information and other measured information to make the output PDF still track the given distribution when the objective PDF is known. However, if the target PDF is unavailable, the PDF tracking operation will be impossible. Minimum entropy control of the system output can be considered as an alternative strategy. The mean represents the center location of the stochastic variable, and it is reasonable that the minimum entropy fault tolerant controller can be designed subjected to mean constraint. In this paper, using the rational square-root B-spline model for the shape control of the system output probability density function (PDF), a nonlinear adaptive observer based fault diagnosis algorithm is proposed to diagnose the fault. Through the controller reconfiguration, the system entropy subjected to mean restriction can still be minimized when fault occurs. An illustrative example is utilized to demonstrate the use of the minimum entropy fault tolerant control algorithms.

A Position Controller Model on Color-Based Object Tracking using Fuzzy Logic

Robotics vision is applying technology on the camera to view the environmental conditions as well as the function of the human eye. Colour object tracking system is one application of robotics vision technology with the ability to follow the object being detected. Several methods have been used to generate a good response position control, but most are still using conventional control approach. Fuzzy logic which includes several step of which is to determine the value of crisp input must be fuzzification. The output of fuzzification is forwarded to the process of inference in which there are some fuzzy logic rules. The inference output forwarded to the process of defuzzification to be transformed into outputs (crisp output) to drive the servo motors on the X-axis and Y-axis. Fuzzy logic control is applied to the color-based object tracking system, the system is successful to follow a moving object with average speed of 7.35 cm/s in environments with 117 lux light intensity.

Accurate density prediction for aqueous Na-K-Mg-Ca-Li-Cl-Br-SO4 solution at high-pressure and high-temperature conditions

Knowledge of water volumetric properties is considered of extreme value in many disciplines of science and engineering, especially those seeking effective management of water resources. This knowledge is normally gathered through experimentation in laboratories within a wide span of time. Traditional methods have already been employed in integrating databases, but these are either afflicted by their limited accuracies or restricted in their applicability ranges. In this communication, density of aqueous electrolyte solution was estimated using adaptive network-based fuzzy inference system. Subtractive clustering was employed to transform crisp input data into fuzzy sets and radius of the clusters were tuned using a hybrid of particle swarm optimization and pattern search algorithms. Results of constructed model were compared to experimental data and excellent accordance was observed yielding an adjusted total correlation coefficient (R2) of 0.9847 and RMSE of 0.0003569. The model was also found to outperform a previously developed multiple regression model. Moreover, using the method of leverage value statistics, suspected outliers were diagnosed from the bulk of data. Results indicate that the model presented in this study can successfully be used for predicting saline water densities for Na-K-Mg-Ca-Li-Cl-Br-SO4-H2O system at temperatures ranging from −20 to 200°C, and pressures ranging from 1.013 to 684bars with acceptable degree of accuracy.

A new robust DEA model and super-efficiency measure

Applications of traditional data envelopments analysis (DEA) models require knowledge of crisp input and output data. However, the real-world problems often deal with imprecise or ambiguous data. In this paper, the problem of considering uncertainty in the equality constraints is analyzed and by using the equivalent form of CCR model, a suitable robust DEA model is derived in order to analyze the efficiency of decision-making units (DMUs) under the assumption of uncertainty in both input and output spaces. The new model based on the robust optimization approach is suggested. Using the proposed model, it is possible to evaluate the efficiency of the DMUs in the presence of uncertainty in a fewer steps compared to other models. In addition, using the new proposed robust DEA model and envelopment form of CCR model, two linear robust super-efficiency models for complete ranking of DMUs are proposed. Two different case studies of different contexts are taken as numerical examples in order to compare the proposed model with other approaches. The examples also illustrate various possible applications of new models.

Fuzzy Logic-Based Operation of Battery Energy Storage Systems (BESSs) for Enhancing the Resiliency of Hybrid Microgrids

The resiliency of power systems can be enhanced during emergency situations by using microgrids, due to their capability to supply local loads. However, precise prediction of disturbance events is very difficult rather the occurrence probability can be expressed as, high, medium, or low, etc. Therefore, a fuzzy logic-based battery energy storage system (BESS) operation controller is proposed in this study. In addition to BESS state-of-charge and market price signals, event occurrence probability is taken as crisp input for the BESS operation controller. After assessing the membership levels of all the three inputs, BESS operation controller decides the operation mode (subservient or resilient) of BESS units. In subservient mode, BESS is fully controlled by an energy management system (EMS) while in the case of resilient mode, the EMS follows the commands of the BESS operation controller for scheduling BESS units. Therefore, the proposed hybrid microgrid model can operate in normal, resilient, and emergency modes with the respective objective functions and scheduling horizons. Due to the consideration of resilient mode, load curtailment can be reduced during emergency operation periods. Numerical simulations have demonstrated the effectiveness of the proposed strategy for enhancing the resiliency of hybrid microgrids.

Anterior osteoporosis classification in cervical vertebrae using fuzzy decision tree

Anterior Osteoporosis (AOs) in the cervical vertebrae is an osteoporosis complication and a common condition of vertebral irregularity caused by a decrease in bone density and strength, which can lead to fragile bone and fractures. Consequently, it is crucial to detect the AOs irregularity early so that appropriate pharmacological intervention can be done to reduce further complications. To do so via a computer approach, an efficient method that can provide high classification rate is required. Basing on the fuzzy logic theory, this article affords a new method for AOs (classes and severity) classification of the cervical radiography by designing a fuzzy decision tree (FDT) model. The method involves two main processed, namely i) segmentation process which employs the active shape model (ASM) based on the 9-anatomical points representation (9-APR) to segment the cervical vertebra shape boundary (C-VSB) and ii) fuzzy based feature extraction and classifier development, known as FDT method. The fuzzy set along with its membership functions are derived from the resulting C-VSB segment. It operates by extracting a specific angle descriptor (horizontal, vertical, and corner) as crisp input to the fuzzification inter-face to produce reasonable key indexing to the fuzzy interface system. Then, the defuzzification interface converts it into a crisp output that adequately represents the degree of AOs class and severity as appraisal values. The resulting fuzzy then acts as input to a basic concept of if-then rules called FDT to recognise and distinguish between vertebrae presented with/without AOs. Receiver operating characteristic (ROC) and area under curve (AUC) index evaluation methods are examined to offer quantitative evaluation between the medical ground truth versus FDT classifier predicted results. Results obtained on a set of 400 cervical vertebrae images indicate superb classification rate (R > 90 %) which suggest that the proposed FDT as an appropriate solution to AOs classification process for reliable vertebral fracture diagnosis. In summary, the findings confirmed the effectiveness of FDT as an excellent classifier to recognize and differentiate AOs classes and severity thus, able to provide important basis for pathology.

A Position Controller Model on Color-Based Object Tracking using Fuzzy Logic

Robotics vision is applying technology on the camera to view the environmental conditions as well as the function of the human eye. Colour object tracking system is one application of robotics vision technology with the ability to follow the object being detected. Several methods have been used to generate a good response position control, but most are still using conventional control approach. Fuzzy logic which includes several step of which is to determine the value of crisp input must be fuzzification. The output of fuzzification is forwarded to the process of inference in which there are some fuzzy logic rules. The inference output forwarded to the process of defuzzification to be transformed into outputs (crisp output) to drive the servo motors on the X-axis and Y-axis. Fuzzy logic control is applied to the color- based object tracking system, the system is successful to follow a moving object with average speed of 7.35 cm/s in environments with 117 lux light intensity.

Fuzzy Parameters Estimation via Hybrid Methods

Fuzzy regression analysis is one of the most widely used statistical techniques which represents the relation between variables. In this paper, the crisp inputs and the symmetrical triangular fuzzy output are considered. Two hybrid algorithms are considered to fit the fuzzy regression model. In this study, algorithms are based on adaptive neuro-fuzzy inference system. The results are derived based on the $V$-fold cross validation, so that the validity and quality of the suggested methods can be guaranteed. Finally, using the numerical examples, the performance of the suggested methods are compared with the other ones, such as linear programming (LP) and quadratic programming (QP). Based on examples, hybrid methods are verified for the prediction.

Solving generalized fuzzy data envelopment analysis model: a parametric approach

Data envelopment analysis (DEA) is a non-parametric technique to assess the performance of a set of homogeneous decision making units (DMUs) with common crisp inputs and outputs. Regarding the problems that are modelled out of the real world, the data cannot constantly be precise and sometimes they are vague or fluctuating. So in the modelling of such data, one of the best approaches is using the fuzzy numbers. Substituting the fuzzy numbers for the crisp numbers in DEA, the traditional DEA problem transforms into a fuzzy data envelopment analysis (FDEA) problem. Different methods have been suggested to compute the efficiency of DMUs in FDEA models so far but the most of them have limitations such as complexity in calculation, non-contribution of decision maker in decision making process, utilizable for a specific model of FDEA and using specific group of fuzzy numbers. In the present paper, to overcome the mentioned limitations, a new approach is proposed. In this approach, the generalized FDEA problem is transformed into a parametric programming, in which, parameter selection depends on the decision maker’s ideas. Two numerical examples are used to illustrate the approach and to compare it with some other approaches.