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Neural networks (NNs), type-1 fuzzy logic systems (T1FLSs), and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be universal approximators, which means that they can approximate any nonlinear continuous function. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of nonlinear complex systems, especially when handling imperfect or incomplete information. In this paper we show, based on the Stone-Weierstrass theorem, that an interval type-2 fuzzy neural network (IT2FNN) is a universal approximator, which uses a set of rules and interval type-2 membership functions (IT2MFs) for this purpose. Simulation results of nonlinear function identification using the IT2FNN for one and three variables and for the Mackey-Glass chaotic time series prediction are presented to illustrate the concept of universal approximation.

Fuzzy set theory, rough set theory, and soft set theory are three effective mathematical tools for dealing with uncertainties and have many wide applications both in theory and practise. Meng et al. (2011) introduced the notion of soft fuzzy rough sets by combining fuzzy sets, rough sets, and soft sets all together. The aim of this paper is to study the parameter reduction of fuzzy soft sets based on soft fuzzy rough approximation operators. We propose some concepts and conditions for two fuzzy soft sets to generate the same lower soft fuzzy rough approximation operators and the same upper soft fuzzy rough approximation operators. The concept of reduct of a fuzzy soft set is introduced and the procedure to find a reduct for a fuzzy soft set is given. Furthermore, the concept of exclusion of a fuzzy soft set is introduced and the procedure to find an exclusion for a fuzzy soft set is given.

A minimax estimation fusion in distributed multisensor systems is proposed, which aims to minimize the worst-case squared estimation error when the cross-covariances between local sensors are unknown and the normalized estimation errors of local sensors are norm bounded. The proposed estimation fusion is called as the Chebyshev fusion estimation (CFE) because its geometrical interpretation is in coincidence with the Chebyshev center, which is a nonlinear combination of local estimates. Theoretically, the CFE is better than any local estimator in the sense of the worst-case squared estimation error and is robust to the choice of the supporting bound. The simulation results illustrate that the proposed CFE is a robust fusion in localization and tracking and more accurate than the previous covariance intersection (CI) method.

Rainfall observed on the ground is dependent on the four dimensional radar observations. Least Squares Approximations (LSA) method is a parametric method that is going to be used. The performance of the LSA based rainfall estimation is subject to many factors such as the representativeness and sufficiency of the dataset, the seasonal changes, and regional changes. The goal of the present paper is to estimate rainfall based on adaptive empirical formulas using radar reflectivity and rain measurements. Data from Melbourne- Florida NEXRAD ground radar (KMLB) and Houston–Texas NEXRAD radar (KHGX) over different years along with rain gauge measurements are used to develop this method. The nonlinear relationship is derived directly from a dataset consisting of radar measurements and rain gauge measurements. A direct gauge comparison study is done to demonstrate the improvement brought in by the method of Least Squares Approximations to show the feasibility of this system in real life. هطول الأمطار الملاحظ على الأرض يعتمد على مشاهدات الرادار الرباعية الأبعاد. طريقة التقريب باستخدام مربعات الخطأ الأقل (LSA) و هي أسلوب حدودي تعتبر الطريقة الأساسية التي تستخدم في هذا البحث. أداء تقدير الأمطار باستخدام (LSA) يخضع لعوامل كثيرة مثل التمثيل و الاكتفاء من مجموعة البيانات، التغيرات الموسمية، و التغيرات الإقليمية. الهدف من هذه الورقة هو تقدير هطول الأمطار على أساس صيغ تجريبية قابلة للتغير و التكيف و ذلك من خلال قراءات رادار أرضي تسمى الانعكاسية و قياسات المطر. البيانات المستخدمة مأخوذة من أمريكا من رادرين أرضيين واحد في مدينة ملبورن في ولاية فلوريدا يمسى (KMLB)، و الآخر في مدينة هيوستن في ولاية تكساس و يسمى (KHGX). البيانات مأخوذة على مجى سنوات مختلفة جنبا إلى جنب مع قياسات مقياس المطر حتى نتمكن من اشتقاق العلاقة غير الخطية بين قياسات الرادار (الانعاكسية) و مقياس المطر. سيتم إجراء مقارنة مباشرة بين قيم المطر المقدرة و القيم الحقيقية المأخوذة من مقياس المطر للتأكيد على دقة و إمكانية و فاعلية الطريقة المستخدمة و ذلك لإظهار جدوى هذه الطريقة في الحياة العملية.

In this paper, we have discussed and investigated an extended PR-CG method which uses function and gradient values. The new method involves the extended CGmethods and have the sufficient descent and globally convergence properties under certain conditions. We have got some important numerical results by improving a standard computer program compared with Wu and Chen (2010) method in this field.

In this paper, we present a modified algorithm with curve search rule for unconstrained minimization problems. At each iteration, the next iterative point is determined by means of a curve search rule. That the search direction and the step-size are particularly determined simultaneously at each iteration of the new algorithm.