ON SOME GENERALIZED DEFERRED STATISTICAL CONVERGENCE OF ORDER αβ FOR FUZZY VARIABLE SEQUENCES IN CREDIBILITY SPACE

In this paper, we investigate the concepts of deferred statistical convergence of order αβ and strongly s-deferred Cesaro summability of order αβ for fuzzy variable sequences in credibility space. Furthermore, the conditions of deferred statistical convergence almost surely of order αβ, deferred statistical convergence in credibility of order αβ, deferred statistical convergence in mean of order αβ, deferred statistical convergence in distribution of order αβ, and deferred statistical convergence uniformly almost surely of order αβ of fuzzy variable sequences have been examined. We have proved relations between these notions

Consistency measurement using the artificial neural network of the results obtained with fuzzy topsis method for the diagnosis of prostate cancer

In recent years great attention has been paid to studies on artificial intelligence since it can be applied easily to several areas like medical diagnosis, engineering and economics, among others. In this paper we present an example in medicine which aims to diagnose the patients with high prostate cancer risk using a multi-criteria decision making method.Our datas set is prostate specific antigen (PSA), free prostate specific antigen (fPSA), prostate volume (PV) and age factors of 78 patients from Necmettin Erbakan University Meram Medicine Faculty. An artificial neural network related to the consistency of convergence coefficients calculated by the Fuzzy TOPSIS method [32] is established.Thus, we understand the accuracy of the results from the Fuzzy TOPSIS method.Publisher's Versio

(R1958) On Deferred Statistical Convergence of Fuzzy Variables

In this paper, within framework credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such as the notion of convergence in credibility, convergence in distribution, convergence in mean, and convergence uniformly virtually certainly via postponed Cesàro mean and a regular matrix are researched using fuzzy variables. We investigate the connections between these concepts. Significant results on deferred statistical convergence for fuzzy variable sequences are thoroughly investigated

ON LACUNARY CONVERGENCE IN CREDIBILITY SPACE

In this paper, we present the notions of lacunary statistically convergent sequence for fuzzy variables, lacunary statistically Cauchy sequence in credibility space, and present a kind of lacunary statistical completeness for credibility space. Also, we present lacunary strong convergence concepts of sequences of fuzzy variables of different types

Solving the linear interval tolerance problem for weight initialization of neural networks

Determining good initial conditions for an algorithm used to train a neural network is considered a parameter estimation problem dealing with uncertainty about the initial weights. Interval Analysis approaches model uncertainty in parameter estimation problems using intervals and formulating tolerance problems. Solving a tolerance problem is defining lower and upper bounds of the intervals so that the system functionality is guaranteed within predefined limits. The aim of this paper is to show how the problem of determining the initial weight intervals of a neural network can be defined in terms of solving a linear interval tolerance problem. The proposed Linear Interval Tolerance Approach copes with uncertainty about the initial weights without any previous knowledge or specific assumptions on the input data as required by approaches such as fuzzy sets or rough sets. The proposed method is tested on a number of well known benchmarks for neural networks trained with the back-propagation family of algorithms. Its efficiency is evaluated with regards to standard performance measures and the results obtained are compared against results of a number of well known and established initialization methods. These results provide credible evidence that the proposed method outperforms classical weight initialization methods

Approximation Theory and Related Applications

In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Monte Carlo and fuzzy interval propagation of hybrid uncertainties on a risk model for the design of a flood protection dike

International audienceA risk model may contain uncertainties that may be best represented by probability distributions and others by possibility distributions. In this paper, a computational framework that jointly propagates probabilistic and possibilistic uncertainties is compared with a pure probabilistic uncertainty propagation. The comparison is carried out with reference to a risk model concerning the design of a flood protection dike