Best Approximation Results for Fuzzy-Number-Valued Continuous Functions

In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then, we prove the existence of the best approximation of a fuzzy-number-valued continuous function to the space of real-valued continuous functions by using the well-known Michael selection theorem

One-Factor ANOVA Model Using Trapezoidal Fuzzy Numbers Through Alpha Cut Interval Method

Most of our traditional tools in descriptive and inferential statistics is based on crispness (preciseness) of data, measurements, random variable, hypotheses, and so on.  By crisp we mean dichotomous that is, yes-or-no type rather than more-or-less type.  But there are many situations in which the above assumptions are rather non-realistic such that we need some new tools to characterize and analyze the problem.  By introducing fuzzy set theory, different branches of mathematics are recently studied.  But probability and statistics attracted more attention in this regard because of their random nature.  Mathematical statistics does not have methods to analyze the problems in which random variables are vague (fuzzy). In this regard, a simple and new technique for testing the hypotheses under the fuzzy environments is proposed.  Here, the employed data are in terms of trapezoidal fuzzy numbers (TFN) which have been transformed into interval data using  interval method and on the grounds of the transformed fuzzy data, the one-factor ANOVA test is executed and decisions are concluded.  This concept has been illustrated by giving two numerical examples. Keywords: Fuzzy set, , Trapezoidal fuzzy number (TFN), Test of hypotheses, One-factor ANOVA model, Upper level data, Lower level data

On improving trapezoidal and triangular approximations of fuzzy numbers

AbstractRecently, various researchers have proved that the approximations of fuzzy numbers may fail to be fuzzy numbers, such as the trapezoidal approximations of fuzzy numbers. In this paper, we show by an example that the weighted triangular approximation of fuzzy numbers, proposed by Zeng and Li, may lead to the same result. For filling the gap, improvements of trapezoidal and triangular approximations are proposed. The formulas for computing the two improved approximations are provided. Some properties of the two improved approximations are also proved

A Comparative Study of Chi-Square Goodness-of-Fit Under Fuzzy Environments

Testing goodness-of-fit plays a vital role in data analysis.  This problem seems to be much more complicated in the presence of vague data.  In this paper, the chi-square goodness-of-fit under trapezoidal fuzzy numbers (tfns.) is proposed using alpha cut interval method.  And the ranking grades of tfns. are also used to compute the chi-square test statistic.  The proposed technique is illustrated with two different numerical examples along with different methods of ranking grades for a concrete comparative study. Keywords: Chi-square Test, Fuzzy Sets, Trapezoidal Fuzzy Numbers, Alpha Cut, Ranking Function, Graded Mean Integration Representation

A parameterized L² metric between fuzzy numbers and its parameter interpretation

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A Comparative Study of Latin Square Design Under Fuzzy Environments Using Trapezoidal Fuzzy Numbers

This paper deals with the problem of Latin Square Design (LSD) test using Trapezoidal Fuzzy Numbers (Tfns.).  The proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation.  Finally a comparative view of the conclusions obtained from various test is given.  Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.   Keywords: LSD, Trapezoidal Fuzzy Numbers, Alpha Cut, Membership Function, Ranking Function, Total Integral Value, Graded Mean Integration Representation.   AMS Mathematics Subject Classification (2010): 62A86, 62F03, 97K8

Ferroelectrics

Ferroelectric materials exhibit a wide spectrum of functional properties, including switchable polarization, piezoelectricity, high non-linear optical activity, pyroelectricity, and non-linear dielectric behaviour. These properties are crucial for application in electronic devices such as sensors, microactuators, infrared detectors, microwave phase filters and, non-volatile memories. This unique combination of properties of ferroelectric materials has attracted researchers and engineers for a long time. This book reviews a wide range of diverse topics related to the phenomenon of ferroelectricity (in the bulk as well as thin film form) and provides a forum for scientists, engineers, and students working in this field. The present book containing 24 chapters is a result of contributions of experts from international scientific community working in different aspects of ferroelectricity related to experimental and theoretical work aimed at the understanding of ferroelectricity and their utilization in devices. It provides an up-to-date insightful coverage to the recent advances in the synthesis, characterization, functional properties and potential device applications in specialized areas

Diagnóstico de fallos en sistemas industriales basado en razonamiento borroso y posibilístico

Esta tesis aborda el diagnóstico de fallos en sistemas industriales por técnicas de Inteligencia Artificial, tratando en particular el razonamiento borroso y posibilístico. Inicialmente, se presentan los problemas a resolver en el diagnóstico de sistemas y después se plantean estrategias para abordarlos a partir de diferentes técnicas de Inteligencia Artificial, en donde destacamos los métodos relacionales borrosos que serán la base para nuestra aportación principal. También se han estudiado los sistemas expertos basados en lógica borrosa y que usan tablas de decisión, los sistemas expertos que combinan lógica borrosa con probabilidad y los sistemas de diagnóstico basados en redes Bayesianas. Se experimenta con varias técnicas de diagnóstico descritas en el estado del arte, haciendo combinaciones entre ellas. Una vez experimentadas y evaluadas las anteriores técnicas, vistos los inconvenientes que surgían, se decidió implementar una nueva metodología que diera una mejor solución al problema del diagnóstico. Esta metodología es el diagnóstico posibilístico borroso visto como un problema de optimización lineal. La metodología convierte los enunciados lingüísticos, que componen una base de reglas de un sistema experto borroso, en un conjunto de ecuaciones lineales a través de técnicas relacionales. Luego, estas ecuaciones se utilizan con algoritmos de programación lineal. Algunas modificaciones requieren programación cuadrática. Los resultados obtenidos en esta última aportación en una aplicación de análisis de aceites fueron satisfactorios, presentando al usuario una salida de diagnóstico fácil de interpretar, suficientemente exacta y teniendo en cuenta la incertidumbre en reglas y medidas.Ramírez Valenzuela, JC. (2007). Diagnóstico de fallos en sistemas industriales basado en razonamiento borroso y posibilístico [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/1922Palanci