Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1506

Search results for: interval type-2 fuzzy rough set

1506 Single Valued Neutrosophic Hesitant Fuzzy Rough Set and Its Application

Authors: K. M. Alsager, N. O. Alshehri


In this paper, we proposed the notion of single valued neutrosophic hesitant fuzzy rough set, by combining single valued neutrosophic hesitant fuzzy set and rough set. The combination of single valued neutrosophic hesitant fuzzy set and rough set is a powerful tool for dealing with uncertainty, granularity and incompleteness of knowledge in information systems. We presented both definition and some basic properties of the proposed model. Finally, we gave a general approach which is applied to a decision making problem in disease diagnoses, and demonstrated the effectiveness of the approach by a numerical example.

Keywords: single valued neutrosophic fuzzy set, single valued neutrosophic fuzzy hesitant set, rough set, single valued neutrosophic hesitant fuzzy rough set

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1505 A Fuzzy Nonlinear Regression Model for Interval Type-2 Fuzzy Sets

Authors: O. Poleshchuk, E. Komarov


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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1504 Using Genetic Algorithms and Rough Set Based Fuzzy K-Modes to Improve Centroid Model Clustering Performance on Categorical Data

Authors: Rishabh Srivastav, Divyam Sharma


We propose an algorithm to cluster categorical data named as ‘Genetic algorithm initialized rough set based fuzzy K-Modes for categorical data’. We propose an amalgamation of the simple K-modes algorithm, the Rough and Fuzzy set based K-modes and the Genetic Algorithm to form a new algorithm,which we hypothesise, will provide better Centroid Model clustering results, than existing standard algorithms. In the proposed algorithm, the initialization and updation of modes is done by the use of genetic algorithms while the membership values are calculated using the rough set and fuzzy logic.

Keywords: categorical data, fuzzy logic, genetic algorithm, K modes clustering, rough sets

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1503 Application of Interval Valued Picture Fuzzy Set in Medical Diagnosis

Authors: Palash Dutta


More frequently uncertainties are encountered in medical diagnosis and therefore it is the most important and interesting area of applications of fuzzy set theory. In this present study, an attempt has been made to extend Sanchez’s approach for medical diagnosis via interval valued picture fuzzy sets and exhibit the technique with suitable case studies. In this article, it is observed that a refusal can be expressed in the databases concerning the examined objects. The technique is performing diagnosis on the basis of distance measures and as a result, this approach makes it possible to introduce weights of all symptoms and consequently patient can be diagnosed directly.

Keywords: medical diagnosis, uncertainty, fuzzy set, picture fuzzy set, interval valued picture fuzzy set

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1502 Group Decision Making through Interval-Valued Intuitionistic Fuzzy Soft Set TOPSIS Method Using New Hybrid Score Function

Authors: Syed Talib Abbas Raza, Tahseen Ahmed Jilani, Saleem Abdullah


This paper presents interval-valued intuitionistic fuzzy soft sets based TOPSIS method for group decision making. The interval-valued intuitionistic fuzzy soft set is a mutation of an interval-valued intuitionistic fuzzy set and soft set. In group decision making problems IVIFSS makes the process much more algebraically elegant. We have used weighted arithmetic averaging operator for aggregating the information and define a new Hybrid Score Function as metric tool for comparison between interval-valued intuitionistic fuzzy values. In an illustrative example we have applied the developed method to a criminological problem. We have developed a group decision making model for integrating the imprecise and hesitant evaluations of multiple law enforcement agencies working on target killing cases in the country.

Keywords: group decision making, interval-valued intuitionistic fuzzy soft set, TOPSIS, score function, criminology

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1501 Application of IF Rough Data on Knowledge Towards Malaria of Rural Tribal Communities in Tripura

Authors: Chhaya Gangwal, R. N. Bhaumik, Shishir Kumar


Handling uncertainty and impreciseness of knowledge appears to be a challenging task in Information Systems. Intuitionistic fuzzy (IF) and rough set theory enhances databases by allowing it for the management of uncertainty and impreciseness. This paper presents a new efficient query optimization technique for the multi-valued or imprecise IF rough database. The usefulness of this technique was illustrated on malaria knowledge from the rural tribal communities of Tripura where most of the information is multi-valued and imprecise. Then, the querying about knowledge on malaria is executed into SQL server to make the implementation of IF rough data querying simpler.

Keywords: intuitionistic fuzzy set, rough set, relational database, IF rough relational database

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1500 Multi-Criteria Test Case Selection Using Ant Colony Optimization

Authors: Niranjana Devi N.


Test case selection is to select the subset of only the fit test cases and remove the unfit, ambiguous, redundant, unnecessary test cases which in turn improve the quality and reduce the cost of software testing. Test cases optimization is the problem of finding the best subset of test cases from a pool of the test cases to be audited. It will meet all the objectives of testing concurrently. But most of the research have evaluated the fitness of test cases only on single parameter fault detecting capability and optimize the test cases using a single objective. In the proposed approach, nine parameters are considered for test case selection and the best subset of parameters for test case selection is obtained using Interval Type-2 Fuzzy Rough Set. Test case selection is done in two stages. The first stage is the fuzzy entropy-based filtration technique, used for estimating and reducing the ambiguity in test case fitness evaluation and selection. The second stage is the ant colony optimization-based wrapper technique with a forward search strategy, employed to select test cases from the reduced test suite of the first stage. The results are evaluated using the Coverage parameters, Precision, Recall, F-Measure, APSC, APDC, and SSR. The experimental evaluation demonstrates that by this approach considerable computational effort can be avoided.

Keywords: ant colony optimization, fuzzy entropy, interval type-2 fuzzy rough set, test case selection

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1499 Behind Fuzzy Regression Approach: An Exploration Study

Authors: Lavinia B. Dulla


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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1498 Interval Type-2 Fuzzy Vibration Control of an ERF Embedded Smart Structure

Authors: Chih-Jer Lin, Chun-Ying Lee, Ying Liu, Chiang-Ho Cheng


The main objective of this article is to present the semi-active vibration control using an electro-rheological fluid embedded sandwich structure for a cantilever beam. ER fluid is a smart material, which cause the suspended particles polarize and connect each other to form chain. The stiffness and damping coefficients of the ER fluid can be changed in 10 micro seconds; therefore, ERF is suitable to become the material embedded in the tunable vibration absorber to become a smart absorber. For the ERF smart material embedded structure, the fuzzy control law depends on the experimental expert database and the proposed self-tuning strategy. The electric field is controlled by a CRIO embedded system to implement the real application. This study investigates the different performances using the Type-1 fuzzy and interval Type-2 fuzzy controllers. The Interval type-2 fuzzy control is used to improve the modeling uncertainties for this ERF embedded shock absorber. The self-tuning vibration controllers using Type-1 and Interval Type-2 fuzzy law are implemented to the shock absorber system. Based on the resulting performance, Internal Type-2 fuzzy is better than the traditional Type-1 fuzzy control for this vibration control system.

Keywords: electro-rheological fluid, semi-active vibration control, shock absorber, type 2 fuzzy control

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1497 From Type-I to Type-II Fuzzy System Modeling for Diagnosis of Hepatitis

Authors: Shahabeddin Sotudian, M. H. Fazel Zarandi, I. B. Turksen


Hepatitis is one of the most common and dangerous diseases that affects humankind, and exposes millions of people to serious health risks every year. Diagnosis of Hepatitis has always been a challenge for physicians. This paper presents an effective method for diagnosis of hepatitis based on interval Type-II fuzzy. This proposed system includes three steps: pre-processing (feature selection), Type-I and Type-II fuzzy classification, and system evaluation. KNN-FD feature selection is used as the preprocessing step in order to exclude irrelevant features and to improve classification performance and efficiency in generating the classification model. In the fuzzy classification step, an “indirect approach” is used for fuzzy system modeling by implementing the exponential compactness and separation index for determining the number of rules in the fuzzy clustering approach. Therefore, we first proposed a Type-I fuzzy system that had an accuracy of approximately 90.9%. In the proposed system, the process of diagnosis faces vagueness and uncertainty in the final decision. Thus, the imprecise knowledge was managed by using interval Type-II fuzzy logic. The results that were obtained show that interval Type-II fuzzy has the ability to diagnose hepatitis with an average accuracy of 93.94%. The classification accuracy obtained is the highest one reached thus far. The aforementioned rate of accuracy demonstrates that the Type-II fuzzy system has a better performance in comparison to Type-I and indicates a higher capability of Type-II fuzzy system for modeling uncertainty.

Keywords: hepatitis disease, medical diagnosis, type-I fuzzy logic, type-II fuzzy logic, feature selection

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1496 A New Aggregation Operator for Trapezoidal Fuzzy Numbers Based On the Geometric Means of the Left and Right Line Slopes

Authors: Manju Pandey, Nilay Khare, S. C. Shrivastava


This paper is the final in a series, which has defined two new classes of aggregation operators for triangular and trapezoidal fuzzy numbers based on the geometrical characteristics of their fuzzy membership functions. In the present paper, a new aggregation operator for trapezoidal fuzzy numbers has been defined. The new operator is based on the geometric mean of the membership lines to the left and right of the maximum possibility interval. The operator is defined and the analytical relationships have been derived. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TrFN aggregates have also been computed.

Keywords: LR fuzzy number, interval fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, apex angle, left apex angle, right apex angle, aggregation operator, arithmetic and geometric mean

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1495 A Fuzzy-Rough Feature Selection Based on Binary Shuffled Frog Leaping Algorithm

Authors: Javad Rahimipour Anaraki, Saeed Samet, Mahdi Eftekhari, Chang Wook Ahn


Feature selection and attribute reduction are crucial problems, and widely used techniques in the field of machine learning, data mining and pattern recognition to overcome the well-known phenomenon of the Curse of Dimensionality. This paper presents a feature selection method that efficiently carries out attribute reduction, thereby selecting the most informative features of a dataset. It consists of two components: 1) a measure for feature subset evaluation, and 2) a search strategy. For the evaluation measure, we have employed the fuzzy-rough dependency degree (FRFDD) of the lower approximation-based fuzzy-rough feature selection (L-FRFS) due to its effectiveness in feature selection. As for the search strategy, a modified version of a binary shuffled frog leaping algorithm is proposed (B-SFLA). The proposed feature selection method is obtained by hybridizing the B-SFLA with the FRDD. Nine classifiers have been employed to compare the proposed approach with several existing methods over twenty two datasets, including nine high dimensional and large ones, from the UCI repository. The experimental results demonstrate that the B-SFLA approach significantly outperforms other metaheuristic methods in terms of the number of selected features and the classification accuracy.

Keywords: binary shuffled frog leaping algorithm, feature selection, fuzzy-rough set, minimal reduct

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1494 Fuzzy Population-Based Meta-Heuristic Approaches for Attribute Reduction in Rough Set Theory

Authors: Mafarja Majdi, Salwani Abdullah, Najmeh S. Jaddi


One of the global combinatorial optimization problems in machine learning is feature selection. It concerned with removing the irrelevant, noisy, and redundant data, along with keeping the original meaning of the original data. Attribute reduction in rough set theory is an important feature selection method. Since attribute reduction is an NP-hard problem, it is necessary to investigate fast and effective approximate algorithms. In this paper, we proposed two feature selection mechanisms based on memetic algorithms (MAs) which combine the genetic algorithm with a fuzzy record to record travel algorithm and a fuzzy controlled great deluge algorithm to identify a good balance between local search and genetic search. In order to verify the proposed approaches, numerical experiments are carried out on thirteen datasets. The results show that the MAs approaches are efficient in solving attribute reduction problems when compared with other meta-heuristic approaches.

Keywords: rough set theory, attribute reduction, fuzzy logic, memetic algorithms, record to record algorithm, great deluge algorithm

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1493 Knowledge Representation Based on Interval Type-2 CFCM Clustering

Authors: Lee Myung-Won, Kwak Keun-Chang


This paper is concerned with knowledge representation and extraction of fuzzy if-then rules using Interval Type-2 Context-based Fuzzy C-Means clustering (IT2-CFCM) with the aid of fuzzy granulation. This proposed clustering algorithm is based on information granulation in the form of IT2 based Fuzzy C-Means (IT2-FCM) clustering and estimates the cluster centers by preserving the homogeneity between the clustered patterns from the IT2 contexts produced in the output space. Furthermore, we can obtain the automatic knowledge representation in the design of Radial Basis Function Networks (RBFN), Linguistic Model (LM), and Adaptive Neuro-Fuzzy Networks (ANFN) from the numerical input-output data pairs. We shall focus on a design of ANFN in this paper. The experimental results on an estimation problem of energy performance reveal that the proposed method showed a good knowledge representation and performance in comparison with the previous works.

Keywords: IT2-FCM, IT2-CFCM, context-based fuzzy clustering, adaptive neuro-fuzzy network, knowledge representation

Procedia PDF Downloads 241
1492 Using Gene Expression Programming in Learning Process of Rough Neural Networks

Authors: Sanaa Rashed Abdallah, Yasser F. Hassan


The paper will introduce an approach where a rough sets, gene expression programming and rough neural networks are used cooperatively for learning and classification support. The Objective of gene expression programming rough neural networks (GEP-RNN) approach is to obtain new classified data with minimum error in training and testing process. Starting point of gene expression programming rough neural networks (GEP-RNN) approach is an information system and the output from this approach is a structure of rough neural networks which is including the weights and thresholds with minimum classification error.

Keywords: rough sets, gene expression programming, rough neural networks, classification

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1491 Using Interval Type-2 Fuzzy Controller for Diabetes Mellitus

Authors: Nafiseh Mollaei, Reihaneh Kardehi Moghaddam


In case of Diabetes Mellitus the controlling of insulin is very difficult. This illness is an incurable disease affecting millions of people worldwide. Glucose is a sugar which provides energy to the cells. Insulin is a hormone which supports the absorption of glucose. Fuzzy control strategy is attractive for glucose control because it mimics the first and second phase responses that the pancreas beta cells use to control glucose. We propose two control algorithms a type-1 fuzzy controller and an interval type-2 fuzzy method for the insulin infusion. The closed loop system has been simulated for different patients with different parameters, in present of the food intake disturbance and it has been shown that the blood glucose concentrations at a normoglycemic level of 110 mg/dl in the reasonable amount of time. This paper deals with type 1 diabetes as a nonlinear model, which has been simulated in MATLAB-SIMULINK environment. The novel model, termed the Augmented Minimal Model is used in the simulations. There are some uncertainties in this model due to factors such as blood glucose, daily meals or sudden stress. In addition to eliminate the effects of uncertainty, different control methods may be utilized. In this article, fuzzy controller performance were assessed in terms of its ability to track a normoglycemic set point (110 mg/dl) in response to a [0-10] g meal disturbance. Finally, the development reported in this paper is supposed to simplify the insulin delivery, so increasing the quality of life of the patient.

Keywords: interval type-2, fuzzy controller, minimal augmented model, uncertainty

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1490 Combination of Topology and Rough Set for Analysis of Power System Control

Authors: M. Kamel El-Sayed


In this research, we have linked the concept of rough set and topological structure to the creation of a new topological structure that assists in the analysis of the information systems of some electrical engineering issues. We used non-specific information whose boundaries do not have an empty set in the top topological structure is rough set. It is characterized by the fact that it does not contain a large number of elements and facilitates the establishment of rules. We used this structure in reducing the specifications of electrical information systems. We have provided a detailed example of this method illustrating the steps used. This method opens the door to obtaining multiple topologies, each of which uses one of the non-defined groups (rough set) in the overall information system.

Keywords: electrical engineering, information system, rough set, rough topology, topology

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1489 Power Quality Improvement Using Interval Type-2 Fuzzy Logic Controller for Five-Level Shunt Active Power Filter

Authors: Yousfi Abdelkader, Chaker Abdelkader, Bot Youcef


This article proposes a five-level shunt active power filter for power quality improvement using a interval type-2 fuzzy logic controller (IT2 FLC). The reference compensating current is extracted using the P-Q theory. The majority of works previously reported are based on two-level inverters with a conventional Proportional integral (PI) controller, which requires rigorous mathematical modeling of the system. In this paper, a IT2 FLC controlled five-level active power filter is proposed to overcome the problem associated with PI controller. The IT2 FLC algorithm is applied for controlling the DC-side capacitor voltage as well as the harmonic currents of the five-level active power filter. The active power filter with a IT2 FLC is simulated in MATLAB Simulink environment. The simulated response shows that the proposed shunt active power filter controller has produced a sinusoidal supply current with low harmonic distortion and in phase with the source voltage.

Keywords: power quality, shunt active power filter, interval type-2 fuzzy logic controller (T2FL), multilevel inverter

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1488 Fuzzy Ideal Topological Spaces

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


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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1487 Fuzzy Time Series Forecasting Based on Fuzzy Logical Relationships, PSO Technique, and Automatic Clustering Algorithm

Authors: A. K. M. Kamrul Islam, Abdelhamid Bouchachia, Suang Cang, Hongnian Yu


Forecasting model has a great impact in terms of prediction and continues to do so into the future. Although many forecasting models have been studied in recent years, most researchers focus on different forecasting methods based on fuzzy time series to solve forecasting problems. The forecasted models accuracy fully depends on the two terms that are the length of the interval in the universe of discourse and the content of the forecast rules. Moreover, a hybrid forecasting method can be an effective and efficient way to improve forecasts rather than an individual forecasting model. There are different hybrids forecasting models which combined fuzzy time series with evolutionary algorithms, but the performances are not quite satisfactory. In this paper, we proposed a hybrid forecasting model which deals with the first order as well as high order fuzzy time series and particle swarm optimization to improve the forecasted accuracy. The proposed method used the historical enrollments of the University of Alabama as dataset in the forecasting process. Firstly, we considered an automatic clustering algorithm to calculate the appropriate interval for the historical enrollments. Then particle swarm optimization and fuzzy time series are combined that shows better forecasting accuracy than other existing forecasting models.

Keywords: fuzzy time series (fts), particle swarm optimization, clustering algorithm, hybrid forecasting model

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1486 Iraqi Short Term Electrical Load Forecasting Based on Interval Type-2 Fuzzy Logic

Authors: Firas M. Tuaimah, Huda M. Abdul Abbas


Accurate Short Term Load Forecasting (STLF) is essential for a variety of decision making processes. However, forecasting accuracy can drop due to the presence of uncertainty in the operation of energy systems or unexpected behavior of exogenous variables. Interval Type 2 Fuzzy Logic System (IT2 FLS), with additional degrees of freedom, gives an excellent tool for handling uncertainties and it improved the prediction accuracy. The training data used in this study covers the period from January 1, 2012 to February 1, 2012 for winter season and the period from July 1, 2012 to August 1, 2012 for summer season. The actual load forecasting period starts from January 22, till 28, 2012 for winter model and from July 22 till 28, 2012 for summer model. The real data for Iraqi power system which belongs to the Ministry of Electricity.

Keywords: short term load forecasting, prediction interval, type 2 fuzzy logic systems, electric, computer systems engineering

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1485 Effect of Genuine Missing Data Imputation on Prediction of Urinary Incontinence

Authors: Suzan Arslanturk, Mohammad-Reza Siadat, Theophilus Ogunyemi, Ananias Diokno


Missing data is a common challenge in statistical analyses of most clinical survey datasets. A variety of methods have been developed to enable analysis of survey data to deal with missing values. Imputation is the most commonly used among the above methods. However, in order to minimize the bias introduced due to imputation, one must choose the right imputation technique and apply it to the correct type of missing data. In this paper, we have identified different types of missing values: missing data due to skip pattern (SPMD), undetermined missing data (UMD), and genuine missing data (GMD) and applied rough set imputation on only the GMD portion of the missing data. We have used rough set imputation to evaluate the effect of such imputation on prediction by generating several simulation datasets based on an existing epidemiological dataset (MESA). To measure how well each dataset lends itself to the prediction model (logistic regression), we have used p-values from the Wald test. To evaluate the accuracy of the prediction, we have considered the width of 95% confidence interval for the probability of incontinence. Both imputed and non-imputed simulation datasets were fit to the prediction model, and they both turned out to be significant (p-value < 0.05). However, the Wald score shows a better fit for the imputed compared to non-imputed datasets (28.7 vs. 23.4). The average confidence interval width was decreased by 10.4% when the imputed dataset was used, meaning higher precision. The results show that using the rough set method for missing data imputation on GMD data improve the predictive capability of the logistic regression. Further studies are required to generalize this conclusion to other clinical survey datasets.

Keywords: rough set, imputation, clinical survey data simulation, genuine missing data, predictive index

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1484 A New Approach to Interval Matrices and Applications

Authors: Obaid Algahtani


An interval may be defined as a convex combination as follows: I=[a,b]={x_α=(1-α)a+αb: α∈[0,1]}. Consequently, we may adopt interval operations by applying the scalar operation point-wise to the corresponding interval points: I ∙J={x_α∙y_α ∶ αϵ[0,1],x_α ϵI ,y_α ϵJ}, With the usual restriction 0∉J if ∙ = ÷. These operations are associative: I+( J+K)=(I+J)+ K, I*( J*K)=( I*J )* K. These two properties, which are missing in the usual interval operations, will enable the extension of the usual linear system concepts to the interval setting in a seamless manner. The arithmetic introduced here avoids such vague terms as ”interval extension”, ”inclusion function”, determinants which we encounter in the engineering literature that deal with interval linear systems. On the other hand, these definitions were motivated by our attempt to arrive at a definition of interval random variables and investigate the corresponding statistical properties. We feel that they are the natural ones to handle interval systems. We will enable the extension of many results from usual state space models to interval state space models. The interval state space model we will consider here is one of the form X_((t+1) )=AX_t+ W_t, Y_t=HX_t+ V_t, t≥0, where A∈ 〖IR〗^(k×k), H ∈ 〖IR〗^(p×k) are interval matrices and 〖W 〗_t ∈ 〖IR〗^k,V_t ∈〖IR〗^p are zero – mean Gaussian white-noise interval processes. This feeling is reassured by the numerical results we obtained in a simulation examples.

Keywords: interval analysis, interval matrices, state space model, Kalman Filter

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1483 A Mixed Expert Evaluation System and Dynamic Interval-Valued Hesitant Fuzzy Selection Approach

Authors: Hossein Gitinavard, Mohammad Hossein Fazel Zarandi


In the last decades, concerns about the environmental issues lead to professional and academic efforts on green supplier selection problems. In this sake, one of the main issues in evaluating the green supplier selection problems, which could increase the uncertainty, is the preferences of the experts' judgments about the candidate green suppliers. Therefore, preparing an expert system to evaluate the problem based on the historical data and the experts' knowledge can be sensible. This study provides an expert evaluation system to assess the candidate green suppliers under selected criteria in a multi-period approach. In addition, a ranking approach under interval-valued hesitant fuzzy set (IVHFS) environment is proposed to select the most appropriate green supplier in planning horizon. In the proposed ranking approach, the IVHFS and the last aggregation approach are considered to margin the errors and to prevent data loss, respectively. Hence, a comparative analysis is provided based on an illustrative example to show the feasibility of the proposed approach.

Keywords: green supplier selection, expert system, ranking approach, interval-valued hesitant fuzzy setting

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1482 Thermal Contact Resistance of Nanoscale Rough Surfaces

Authors: Ravi Prasher


In nanostructured material thermal transport is dominated by contact resistance. Theoretical models describing thermal transport at interfaces assume perfectly flat surface whereas in reality surfaces can be rough with roughness ranging from sub-nanoscale dimension to micron scale. Here we introduce a model which includes both nanoscale contact mechanics and nanoscale heat transfer for rough nanoscale surfaces. This comprehensive model accounts for the effect of phonon acoustic mismatch, mechanical properties, chemical properties and randomness of the rough surface.

Keywords: adhesion and contact resistance, Kaptiza resistance of rough surfaces, nanoscale thermal transport

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1481 Fuzzy-Machine Learning Models for the Prediction of Fire Outbreak: A Comparative Analysis

Authors: Uduak Umoh, Imo Eyoh, Emmauel Nyoho


This paper compares fuzzy-machine learning algorithms such as Support Vector Machine (SVM), and K-Nearest Neighbor (KNN) for the predicting cases of fire outbreak. The paper uses the fire outbreak dataset with three features (Temperature, Smoke, and Flame). The data is pre-processed using Interval Type-2 Fuzzy Logic (IT2FL) algorithm. Min-Max Normalization and Principal Component Analysis (PCA) are used to predict feature labels in the dataset, normalize the dataset, and select relevant features respectively. The output of the pre-processing is a dataset with two principal components (PC1 and PC2). The pre-processed dataset is then used in the training of the aforementioned machine learning models. K-fold (with K=10) cross-validation method is used to evaluate the performance of the models using the matrices – ROC (Receiver Operating Curve), Specificity, and Sensitivity. The model is also tested with 20% of the dataset. The validation result shows KNN is the better model for fire outbreak detection with an ROC value of 0.99878, followed by SVM with an ROC value of 0.99753.

Keywords: Machine Learning Algorithms , Interval Type-2 Fuzzy Logic, Fire Outbreak, Support Vector Machine, K-Nearest Neighbour, Principal Component Analysis

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1480 Improving Load Frequency Control of Multi-Area Power System by Considering Uncertainty by Using Optimized Type 2 Fuzzy Pid Controller with the Harmony Search Algorithm

Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar


This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.

Keywords: load frequency control, fuzzy-pid controller, type 2 fuzzy system, harmony search algorithm

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1479 Formulating Rough Approximations in Information Tables with Possibilistic Information

Authors: Michinori Nakata, Hiroshi Sakai


A rough set, which consists of lower and upper approximations, is formulated in information tables containing possibilistic information. First, lower and upper approximations on the basis of possible world semantics in the same way as Lipski did in the field of incomplete databases are shown in order to clarify fundamentals of rough sets under possibilistic information. Possibility and necessity measures are used, as is done in possibilistic databases. As a result, each object has certain and possible membership degrees to lower and upper approximations, which degrees are the lower and upper bounds. Therefore, the degree that the object belongs to lower and upper approximations is expressed by an interval value. And the complementary property linked with the lower and upper approximations holds, as is valid under complete information. Second, the approach based on indiscernibility relations, which is proposed by Dubois and Prade, are extended in three cases. The first case is that objects used to approximate a set of objects are characterized by possibilistic information. The second case is that objects used to approximate a set of objects with possibilistic information are characterized by complete information. The third case is that objects that are characterized by possibilistic information approximate a set of objects with possibilistic information. The extended approach create the same results as the approach based on possible world semantics. This justifies our extension.

Keywords: rough sets, possibilistic information, possible world semantics, indiscernibility relations, lower approximations, upper approximations

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1478 Sensitivity Analysis in Fuzzy Linear Programming Problems

Authors: S. H. Nasseri, A. Ebrahimnejad


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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1477 A New Concept for Deriving the Expected Value of Fuzzy Random Variables

Authors: Liang-Hsuan Chen, Chia-Jung Chang


Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

Keywords: fuzzy random variables, distance measure, expected value, descriptive parameters

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