On the class of λ-statistically convergent difference sequences of fuzzy numbers

In this study, we introduce the sets $\left[ V,\lambda ,p\right] _{\Updelta }^{{\mathcal{F}}},\left[ C,1,p\right] _{\Updelta }^{{\mathcal{F}}}$ and examine their relations with the classes of $ S_{\lambda }\left( \Updelta ,{\mathcal{F}}\right)$ and $ S_{\mu }\left( \Updelta ,{\mathcal{F}}\right)$ of sequences for the sequences $\left( \lambda _{n}\right)$ and $\left( \mu _{n}\right) , 0<p<\infty $ and difference sequences of fuzzy numbers.     

On λ-statistical convergence of difference sequences of fuzzy numbers

In this paper the concept of strongly -Cesàro summability of a sequence of fuzzy numbers is introduced. Also some inclusion relations between the set of strongly -Cesàro convergent and -statistically convergent sequences of fuzzy numbers are given.     

RM approach for ranking of L–R type generalized fuzzy numbers

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Syst Appl 36:6833–6842, 2009) is incorrect. The main aim of this paper is to propose a new approach for the ranking of L–R type generalized fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as RM approach. The main advantage of the proposed approach is that it provides the correct ordering of generalized and normal fuzzy numbers and it is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets Syst 118:375–385, 2001).     

A new approach for ranking of L–R type generalized fuzzy numbers

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. Cheng (Cheng, C. H. (1998). A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems, 95, 307–317) pointed out that the proof of the statement “Ranking of generalized fuzzy numbers does not depend upon the height of fuzzy numbers” stated by Liou and Wang (Liou, T. S., & Wang, M. J. (1992). Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems, 50, 247–255) is incorrect. In this paper, by giving an alternative proof it is proved that the above statement is correct. Also with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Chen, S. M., & Chen, J. H. (2009). Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Systems with Applications, 36, 6833–6842) is incorrect. The main aim of this paper is to modify the Liou and Wang approach for the ranking of L–R type generalized fuzzy numbers. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of generalized and normal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfy all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Wang, X., & Kerre, E. E. (2001). Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems, 118, 375–385).     

Posture control of robot manipulators with fuzzy voice commands using a fuzzy coach–player system

This paper presents a method of controlling robot manipulators with fuzzy voice commands. Recently, there has been some research on controlling robots using information-rich fuzzy voice commands such as 'go little slowly' and learning from such commands. However, the scope of all those works was limited to basic fuzzy voice motion commands. In this paper, we introduce a method of controlling the posture of a manipulator using complex fuzzy voice commands. A complex fuzzy voice command is composed of a set of fuzzy voice joint commands. Complex fuzzy voice commands can be used for complicated maneuvering of a manipulator, while fuzzy voice joint commands affect only a single joint. Once joint commands are learned, any complex command can be learned as a combination of some or all of them, so that, using the learned complex commands, a human user can control the manipulator in a complicated manner with natural language commands. Learning of complex commands is discussed in the framework of fuzzy coach–player model. The proposed idea is demonstrated with a PA-10 redundant manipulator.     

A new metric for L–R fuzzy numbers and its application in fuzzy linear systems

In this paper, a metric based on modified Euclidean metric on interval numbers, for L–R fuzzy numbers with fixed $L(\cdot)$ and $R(\cdot)$ is introduced. Then, it is applied for solving L–R fuzzy linear system (L–R-FLS) with fuzzy right-hand side, so that L–R-FLS is transformed to the minimization problem. The solution of the mentioned non-linear programming problem is our favorite fuzzy number vector solution. Two constructive Algorithms are proposed in detail and the method is illustrated by solving several numerical examples.     

Robust spatial flood vulnerability assessment for Han River using fuzzy TOPSIS with α-cut level set

This study aims to improve the general flood vulnerability approach using fuzzy TOPSIS based on α-cut level sets which can reduce the uncertainty inherent in even fuzzy multi-criteria decision making process. Since fuzzy TOPSIS leads to a crisp closeness for each alternative, it is frequently argued that fuzzy weights and fuzzy ratings should be in fuzzy relative closeness. Therefore, this study used a modified α-cut level set based fuzzy TOPSIS to develop a spatial flood vulnerability approach for Han River in Korea, considering various uncertainties in weights derivation and crisp data aggregation. Two results from fuzzy TOPSIS and modified fuzzy TOPSIS were compared. Some regions which showed no or small ranking changes have their centro-symmetric distributions, while other regions whose rankings varied dynamically, have biased (anti-symmetric) distributions. It can be concluded that α-cut level set based fuzzy TOPSIS produce more robust prioritization since more uncertainties can be considered. This method can be applied to robust spatial vulnerability or decision making in water resources management.     

Stabilization of Rössler chaotic dynamical system using fuzzy logic control algorithm

This paper proposes a fuzzy logic control algorithm (FLCA) to stabilize the Rössler chaotic dynamical system. The fuzzy logic control system is based on a Takagi-Sugeno-Kang inference engine and the stability analysis in the sense of Lyapunov is carried out using Lyapunov’s direct method. The new FLCA is formulated to offer sufficient inequality stability conditions. The asymptotic complexity of our algorithm is analyzed and proved to be lower in comparison with that of linear matrix inequality-based FLCAs. A set of simulation results illustrates the effectiveness of the proposed FLCA.     

Study of the potential of alternative crops by integration of multisource data using a neuro‐fuzzy technique

This work proposes a neuro‐fuzzy method for suggesting alternative crop production over a region using integrated data obtained from land‐survey maps as well as satellite imagery. The methodology proposed here uses an artificial neural network (multilayer perceptron, MLP) to predict alternative crop production. For each pixel, the MLP takes vector input comprising elevation, rainfall and goodness values of different existing crops. The first two components of the aforementioned input, that is, elevation and rainfall, are determined from contour information of land‐survey maps. The other components, such as goodness values of different existing crops, are based on the productivity estimates of soil determined by fuzzyfication and expert opinion (on soil) along with production quality by the Normalized Difference Vegetation Index (NDVI) obtained from satellite imagery. The methodology attempts to ensure that the suggested crop will also be a high productivity crop for that region.     

Detection of phishing attacks in Iranian e-banking using a fuzzy–rough hybrid system

Phishing is a method of stealing electronic identity in which social engineering and website forging methods are used in order to mislead users and reveal confidential information having economic value. Destroying the trust between users in business network, phishing has a negative effect on the budding area of e-commerce. Developing countries such as Iran have been recently facing Internet threats like phishing, whose methods, regarding the social differences, may be different from other experiences. Thus, it is necessary to design a suitable detection method for these deceits. The aim of current paper is to provide a phishing detection system to be used in e-banking system in Iran. Identifying the outstanding features of phishing is one of the important prerequisites in design of an accurate system; therefore, in first step, to identify the influential features of phishing that best fit the Iranian bank sites, a list of 28 phishing indicators was prepared. Using feature selection algorithm based on rough sets theory, six main indicators were identified as the most effective factors. The fuzzy expert system was designed using these indicators, afterwards. The results show that the proposed system is able to determine the Iranian phishing sites with a reasonable speed and precision, having an accuracy of 88%.     

Image segmentation using Atanassov’s intuitionistic fuzzy sets

The problem of segmentation in spite of all the work over the last decades, is still an important research field and also a critical preprocessing step for image processing, mostly due to the fact that finding a global optimal threshold that works well for all kind of images is indeed a very difficult task that, probably, will never be accomplished.During the past years, fuzzy logic theory has been successfully applied to image thresholding. In this paper we describe a thresholding technique using Atanassov’s intuitionistic fuzzy sets (A-IFSs). This approach uses Atanassov’s intuitionistic index values for representing the hesitance of the expert in determining whether the pixel belongs to the background or that it belongs to the object. First, we describe the general framework of this approach to bi-level thresholding. Then we present its natural extension to multilevel thresholding. This multilevel threshold methodology segments the image into several distinct regions which correspond to a background and several objects.Segmentation experimental results and comparison with Otsu’s multilevel thresholding algorithm for the calculation of two and three thresholds are presented.     

WEEE treatment strategies’ evaluation using fuzzy LINMAP method

Electrical and electronic equipments (EEE) have already begun to be accumulated at the garbage dumps. This garbage accumulation brings big danger to the environment and human health. That’s why one should look for exploring the ways to dispose of these wastes and emphasize the waste treatment strategies. Waste treatment strategies also contribute either to local or global economies by creating a new sector and employment opportunities, and by reducing use of scarce resources. In this paper, a linear programming technique for multidimensional analysis of preference (LINMAP) method for solving multi-attribute group decision making (MAGDM) problems with preference information on alternatives in fuzzy environment is developed. The aim is to develop a fuzzy LINMAP model for evaluation and select of a waste treatment strategy for EEE. Thus, three treatment strategy alternatives and eight criteria are determined. The best strategy is selected and the key criterion is found accordingly. The best alternative is found to be treating waste electrical and electronic equipments (WEEE) by reuse and recycling methods.     

Probability representations of fuzzy systems

1 Background of birth of fuzzy systems As is well-known, just considering the great uncertainties of many systems, Zadeh put forward the notion of fuzzy sets and advanced the idea of the fuzzy reasoning by means of fuzzy sets which could describe a system approximately[1]. Those systems that are constructed on the basis of fuzzy reasoning are called fuzzy systems in general[2―4]. The research on fuzzy systems has attracted broad attention[5―7]. For instance, universal ap- proximation proper…     

The Geometric Continuity of Rational Bezler Triangular Surfaces

The problems of geometric continuity for rational Bezier surfaces are discussed.Concise conditions of first order and second order geometric continuity for rational triangular bezier surfaces are given.Meanwhile,a geometric condition for smoothness between adjacent rational bezier surfaces and the transformation formulae between rational triangular patches and rational rectangular patches are obtained.     

The Geometric Continuity of Rational Bezler Triangular Surfaces

The problems of geometric continuity for rational Bezter surfaces are discussed. Concise conditionsof first order and second order geometric continuity for rational triangular Bézier surfaces are given.Meanwhile,a geometric condition for smoothness between adjacent rational Bézier surfaces andthe transformation formulae between rational triangular patches and rational rectangular patches areobtained.     

Similarity–divergence intuitionistic fuzzy decision using particle swarm optimization

Many existing intuitionistic fuzzy (IF) decision methods focus on a reasonable ranking for alternatives under unknown weight information. Traditionally, the weight information is usually determined from a multiobjective optimization model based on real-valued measures such as IF distance or similarity measures, which may lose divergence information. In this paper, we propose one new type of optimization model for determining the weights based on a fuzzy measure called the similarity–divergence measure (S–D measure). First, we develop similarity and divergence measures of IF sets respectively, and a 2-tuple consisting of similarity and divergence is defined as a S–D measure. This measure is further proven to be an IF similarity degree and has practical semantics of similarity and divergence features in human’s cognition. Second, we utilize such measure to calculate fuzzy similarities of each alternative and construct a nonlinear optimization model to determine the weights. Third, we design an algorithm for solving the model with the aid of particle swarm optimization and thus develop an IF decision method. Finally, two examples are given to demonstrate our method and then it is compared with existing methods to explain its effectiveness and superiority.     

A Type of Triangular Ball Surface and its Properties

1IntroductionIntheCONSURFsystemll--3]developedbyA.A.Ball,thebasisfunctionsforcubicpolynomialsweredefinedbyandhencecubicBallcurveswithcontrolpointsPi(i=0,1,2,3)canberepresentedasp(u)=Z?=.B!(u)Pi,0Su51.TwotypesofhigherdegreegeneralizedBallbasisfunctionsandcorrespondingcurveshavebeenderivedbyWangl4]andSaidls]independently.InWang'spaper,generalizedBailbasisfunctionsofarbitrarydegreeweredefinedasfollows'.ifnisanevennumber.ifnisanoddnumberwherew~2u(1--u),05u51.Aparametriccurveofdegreentcall…     

An efficient diagnosis system for detection of Parkinson’s disease using fuzzy k-nearest neighbor approach

In this paper, we present an effective and efficient diagnosis system using fuzzy k-nearest neighbor (FKNN) for Parkinson’s disease (PD) diagnosis. The proposed FKNN-based system is compared with the support vector machines (SVM) based approaches. In order to further improve the diagnosis accuracy for detection of PD, the principle component analysis was employed to construct the most discriminative new feature sets on which the optimal FKNN model was constructed. The effectiveness of the proposed system has been rigorously estimated on a PD data set in terms of classification accuracy, sensitivity, specificity and the area under the receiver operating characteristic (ROC) curve (AUC). Experimental results have demonstrated that the FKNN-based system greatly outperforms SVM-based approaches and other methods in the literature. The best classification accuracy (96.07%) obtained by the FKNN-based system using a 10-fold cross validation method can ensure a reliable diagnostic model for detection of PD. Promisingly, the proposed system might serve as a new candidate of powerful tools for diagnosing PD with excellent performance.