Advances in Fuzzy Systems http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Vague Soft Hypergroups and Vague Soft Hypergroup Homomorphism Mon, 31 Mar 2014 08:10:46 +0000 http://www.hindawi.com/journals/afs/2014/758637/ We introduce and develop the initial theory of vague soft hyperalgebra by introducing the novel concept of vague soft hypergroups, vague soft subhypergroups, and vague soft hypergroup homomorphism. The properties and structural characteristics of these concepts are also studied and discussed. Ganeshsree Selvachandran and Abdul Razak Salleh Copyright © 2014 Ganeshsree Selvachandran and Abdul Razak Salleh. All rights reserved. A New Fuzzy TOPSIS-TODIM Hybrid Method for Green Supplier Selection Using Fuzzy Time Function Mon, 17 Mar 2014 16:26:59 +0000 http://www.hindawi.com/journals/afs/2014/841405/ Today green supply chain is considered all around the world and supplier selection has been changed regarding these green and carbon emission criteria, so green supplier selection has been a major problem in this area. In this study we use fuzzy time function to assist managers in green supplier selection under uncertainty and ambiguity. This function will consider derivation from the goal during the time and by using it, and we will be able to have the best supplier in every period after having some modification in legal limitations for green supplier selection criteria. We use a fuzzy TOPSIS to have better initial weighting in TODIM, a discrete multicriteria method based on prospect theory in uncertainty (known as TODIM in Portuguese) decision making method. The results indicated that our proposed approach can easily and effectively accommodate criteria with gains and loss functions during time and also by using this method we will have a more reasonable predict of our suppliers ranking in future and that will help us in future investment in these suppliers. Finally it has been shown in car industries in Iran. Alireza Arshadi Khamseh and Mahdi Mahmoodi Copyright © 2014 Alireza Arshadi Khamseh and Mahdi Mahmoodi. All rights reserved. Fuzzy Methods and Approximate Reasoning in Geographical Information Systems Wed, 12 Mar 2014 09:05:15 +0000 http://www.hindawi.com/journals/afs/2014/840297/ Ferdinando Di Martino, Irina Perfilieva, Salvatore Sessa, and Sabrina Senatore Copyright © 2014 Ferdinando Di Martino et al. All rights reserved. Fuzzy Approach for Group Sequential Test Wed, 19 Feb 2014 10:01:05 +0000 http://www.hindawi.com/journals/afs/2014/896150/ Buckley’s approach (Buckley (2004), (2005), (2006)) uses sets of confidence intervals by taking into consideration both of the uncertainty and impreciseness of concepts that produce triangular shaped fuzzy numbers for the estimator. This approach produces fuzzy test statistics and fuzzy critical values in hypothesis testing. In addition, the sample size is fixed for this test. When data comes sequentially, however, it is not suitable to study with a fixed sample size test. In such cases, sequential and group sequential tests are recommended. Unlike a sequential test, a group of sequential test provides substantial savings in sample and enables us to make decisions as early as possible. This intends paper to combine the benefits of group sequential test and Buckley's approach using -cuts. It attempts to show that using -cuts can be used within the group sequential tests. To illustrate the test more explicitly a numerical example is also given. Duygu İçen, Sevil Bacanlı, and Süleyman Günay Copyright © 2014 Duygu İçen et al. All rights reserved. An Extended Analytical Approach to Evaluating Monotonic Functions of Fuzzy Numbers Tue, 11 Feb 2014 12:22:18 +0000 http://www.hindawi.com/journals/afs/2014/892363/ This paper presents an extended analytical approach to evaluating continuous, monotonic functions of independent fuzzy numbers. The approach is based on a parametric α-cut representation of fuzzy numbers and allows for the inclusion of parameter uncertainties into mathematical models. Arthur Seibel and Josef Schlattmann Copyright © 2014 Arthur Seibel and Josef Schlattmann. All rights reserved. A New Method for Short Multivariate Fuzzy Time Series Based on Genetic Algorithm and Fuzzy Clustering Wed, 18 Dec 2013 13:38:41 +0000 http://www.hindawi.com/journals/afs/2013/494239/ Forecasting activities play an important role in our daily life. In recent years, fuzzy time series (FTS) methods were developed to deal with forecasting problems. FTS attracted researchers because of its ability to predict the future values in some critical situations where most standard forecasting models are doubtfully applicable or produce bad fittings. However, some critical issues in FTS are still open; these issues are often subjective and affect the accuracy of forecasting. In this paper, we focus on improving the accuracy of FTS forecasting methods. The new method integrates the fuzzy clustering and genetic algorithm with FTS to reduce subjectivity and improve its accuracy. In the new method, the genetic algorithm is responsible for selecting the proper model. Also, the fuzzy clustering algorithm is responsible for fuzzifying the historical data, based on its membership degrees to each cluster, and using these memberships to defuzzify the results. This method provides better forecasting accuracy when compared with other extant researches. Kamal S. Selim and Gihan A. Elanany Copyright © 2013 Kamal S. Selim and Gihan A. Elanany. All rights reserved. Mining Linguistic Associations for Emergent Flood Prediction Adjustment Tue, 17 Dec 2013 15:45:48 +0000 http://www.hindawi.com/journals/afs/2013/131875/ Floods belong to the most hazardous natural disasters and their disaster management heavily relies on precise forecasts. These forecasts are provided by physical models based on differential equations. However, these models do depend on unreliable inputs such as measurements or parameter estimations which causes undesirable inaccuracies. Thus, an appropriate data-mining analysis of the physical model and its precision based on features that determine distinct situations seems to be helpful in adjusting the physical model. An application of fuzzy GUHA method in flood peak prediction is presented. Measured water flow rate data from a system for flood predictions were used in order to mine fuzzy association rules expressed in natural language. The provided data was firstly extended by a generation of artificial variables (features). The resulting variables were later on translated into fuzzy GUHA tables with help of Evaluative Linguistic Expressions in order to mine associations. The found associations were interpreted as fuzzy IF-THEN rules and used jointly with the Perception-based Logical Deduction inference method to predict expected time shift of flow rate peaks forecasted by the given physical model. Results obtained from this adjusted model were statistically evaluated and the improvement in the forecasting accuracy was confirmed. Michal Burda, Pavel Rusnok, and Martin Štěpnička Copyright © 2013 Michal Burda et al. All rights reserved. Fuzzy Reliability in Spatial Databases Sun, 15 Dec 2013 14:29:37 +0000 http://www.hindawi.com/journals/afs/2013/107358/ Today it is very difficult to evaluate the quality of spatial databases, mainly for the heterogeneity of input data. We define a fuzzy process for evaluating the reliability of a spatial database: the area of study is partitioned in isoreliable zones, defined as homogeneous zones in terms of data quality and environmental characteristics. We model a spatial database in thematic datasets; each thematic dataset concerns a specific spatial domain and includes a set of layers. We estimate the reliability of each thematic dataset and therefore the overall reliability of the spatial database. We have tested this method on the spatial dataset of the town of Cava de' Tirreni (Italy). Ferdinando Di Martino and Salvatore Sessa Copyright © 2013 Ferdinando Di Martino and Salvatore Sessa. All rights reserved. On Optimal Operator for Combining Left and Right Sole Pressure Data in Biometrics Security Thu, 12 Dec 2013 10:55:42 +0000 http://www.hindawi.com/journals/afs/2013/620312/ This paper describes optimal operator for combining left and right sole pressure data in a personal authentication method by dynamic change of sole pressure distribution while walking. The method employs a pair of right and left sole pressure distribution change data. These data are acquired by a mat-type load distribution sensor. The system extracts features based on shape of sole and weight shift from each sole pressure distribution. We calculate fuzzy degrees of right and left sole pressures for a registered person. Fuzzy if-then rules for each registered person are statistically determined by learning data set. Next, we combine the fuzzy degrees of right and left sole pressure data. In this process, we consider six combination operators. We examine which operator achieves best accuracy for the personal authentication. In the authentication system, we identify the walking persons as a registered person with the highest fuzzy degree. We verify the walking person as the target person when the combined fuzzy degree of the walking person is higher than a threshold. In our experiment, we employed 90 volunteers, and our method obtained higher authentication performance by mean and weighted sum operators. Takahiro Takeda, Kei Kuramoto, Syoji Kobashi, and Yutaka Hata Copyright © 2013 Takahiro Takeda et al. All rights reserved. Hotspots Detection in Spatial Analysis via the Extended Gustafson-Kessel Algorithm Mon, 09 Dec 2013 09:34:16 +0000 http://www.hindawi.com/journals/afs/2013/876073/ We show a new approach for detecting hotspots in spatial analysis based on the extended Gustafson-Kessel clustering method encapsulated in a Geographic Information System (GIS) tool. This algorithm gives (in the bidimensional case) ellipses as cluster prototypes to be considered as hotspots on the geographic map and we study their spatiotemporal evolution. The data consist of georeferenced patterns corresponding to positions of Taliban’s attacks against civilians and soldiers in Afghanistan that happened during the period 2004–2010. We analyze the formation through time of new hotspots, the movement of the related centroids, the variation of the surface covered, the inclination angle, and the eccentricity of each hotspot. Ferdinando Di Martino and Salvatore Sessa Copyright © 2013 Ferdinando Di Martino and Salvatore Sessa. All rights reserved. Usage of Fuzzy Spatial Theory for Modelling of Terrain Passability Thu, 28 Nov 2013 17:39:55 +0000 http://www.hindawi.com/journals/afs/2013/506406/ Geographic support of decision-making processes is based on various geographic products, usually in digital form, which come from various foundations and sources. Each product can be characterized by its quality or by its utility value for the given type of task or group of tasks, for which the product is used. They also usually have different characteristics and thus can very significantly influence the resulting analytical material. The aim of the paper is to contribute to the solution of the question of how it is possible to work with diverse spatial geographic information so that the user has an idea about the resulting product. The concept of fuzzy sets is used for representation of classes, whose boundaries are not clearly (not sharply) set, namely, the fuzzy approach in overlaying operations realized in ESRI ArcGIS environment. The paper is based on a research project which is being solved at the Faculty of Military Technologies of the University of Defence. The research deals with the influence of geographic and climatic factors on the activity of armed forces and the Integrated Rescue System. Alois Hofmann, Sarka Hoskova-Mayerova, and Vaclav Talhofer Copyright © 2013 Alois Hofmann et al. All rights reserved. Fuzzy Functions, Relations, and Fuzzy Transforms 2013 Wed, 06 Nov 2013 13:15:02 +0000 http://www.hindawi.com/journals/afs/2013/296431/ Salvatore Sessa, Ferdinando Di Martino, and Irina G. Perfilieva Copyright © 2013 Salvatore Sessa et al. All rights reserved. A Coupled Fixed Point Theorem in Fuzzy Metric Space Satisfying -Contractive Condition Thu, 03 Oct 2013 19:11:46 +0000 http://www.hindawi.com/journals/afs/2013/826596/ The intent of this paper is to prove a coupled fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous) mappings, satisfying -contractive conditions in a fuzzy metric space. We also furnish some illustrative examples to support our results. B. D. Pant, Sunny Chauhan, Jelena Vujaković, Muhammad Alamgir Khan, and Calogero Vetro Copyright © 2013 B. D. Pant et al. All rights reserved. Extended Tolerance Relation to Define a New Rough Set Model in Incomplete Information Systems Mon, 30 Sep 2013 15:10:54 +0000 http://www.hindawi.com/journals/afs/2013/372091/ This paper discusses and proposes a rough set model for an incomplete information system, which defines an extended tolerance relation using frequency of attribute values in such a system. It first discusses some rough set extensions in incomplete information systems. Next, “probability of matching” is defined from data in information systems and then measures the degree of tolerance. Consequently, a rough set model is developed using a tolerance relation defined with a threshold. The paper discusses the mathematical properties of the newly developed rough set model and also introduces a method to derive reducts and the core. Do Van Nguyen, Koichi Yamada, and Muneyuki Unehara Copyright © 2013 Do Van Nguyen et al. All rights reserved. Generating Suitable Basic Functions Used in Image Reconstruction by F-Transform Wed, 11 Sep 2013 09:36:10 +0000 http://www.hindawi.com/journals/afs/2013/593694/ Image reconstruction technique based on F-transform uses clearly defined basic functions. These functions have strong impact on the quality of reconstruction. We can use some predefined shape and radius, but also we can create a new one from the scratch. The aim of this paper is to analyze the creating process and based on that find best basic function for input set of damaged testing images. Pavel Vlašánek Copyright © 2013 Pavel Vlašánek. All rights reserved. Spatiotemporal Hotspots Analysis for Exploring the Evolution of Diseases: An Application to Oto-Laryngopharyngeal Diseases Wed, 04 Sep 2013 08:52:49 +0000 http://www.hindawi.com/journals/afs/2013/385974/ This paper presents a spatiotemporal analysis of hotspot areas based on the Extended Fuzzy C-Means method implemented in a geographic information system. This method has been adapted for detecting spatial areas with high concentrations of events and tested to study their temporal evolution. The data consist of georeferenced patterns corresponding to the residence of patients in the district of Naples (Italy) to whom a surgical intervention to the oto-laryngopharyngeal apparatus was carried out between the years 2008 and 2012. Ferdinando Di Martino, Roberta Mele, Umberto E. S. Barillari, Maria Rosaria Barillari, Irina Perfilieva, and Sabrina Senatore Copyright © 2013 Ferdinando Di Martino et al. All rights reserved. Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification Wed, 31 Jul 2013 09:15:22 +0000 http://www.hindawi.com/journals/afs/2013/136214/ 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. Oscar Castillo, Juan R. Castro, Patricia Melin, and Antonio Rodriguez-Diaz Copyright © 2013 Oscar Castillo et al. All rights reserved. Theoretical Analysis of the Shaft Wed, 31 Jul 2013 09:08:47 +0000 http://www.hindawi.com/journals/afs/2013/392470/ This paper represents the dynamic response of a steel shaft which is fixed at both ends by bearing. The shaft is subjected to both axial and bending loads. The behavior of the shaft in the presence of two transverse cracks subjected to the same angular position along longitudinal direction is observed by taking basic parameters such as nondimensional depth (), nondimensional length (), and three relative natural frequencies with their relative mode shapes. The compliance matrix is calculated from the stress intensity factor for two degrees of freedom. The dynamic nature of the cracked shaft at two cracked locations at a different depth is observed. The compliance matrix is a function of crack parameters such as depth and location of crack from any one of the bearings. The three relative natural frequencies and their mode shapes at a different location and depth obtained analytical and experimental method. Multiple adaptive neurofuzzy inference system (MANFIS) methodology (an inverse technique) is used for locating the cracks at any depth and location. The input of the MANFIS is provided with the first three natural frequencies and the first three mode shapes obtained from analytical method. The predicted result of the MANFIS (relative crack location and depth) has been validated using the results from the developed experimental setup. Jajneswar Nanda and D. R. Parhi Copyright © 2013 Jajneswar Nanda and D. R. Parhi. All rights reserved. Coding B-Frames of Color Videos with Fuzzy Transforms Mon, 22 Jul 2013 13:00:18 +0000 http://www.hindawi.com/journals/afs/2013/652429/ We use a new method based on discrete fuzzy transforms for coding/decoding frames of color videos in which we determine dynamically the GOP sequences. Frames can be differentiated into intraframes, predictive frames, and bidirectional frames, and we consider particular frames, called Δ-frames (resp., R-frames), for coding P-frames (resp., B-frames) by using two similarity measures based on Lukasiewicz -norm; moreover, a preprocessing phase is proposed to determine similarity thresholds for classifying the above types of frame. The proposed method provides acceptable results in terms of quality of the reconstructed videos to a certain extent if compared with classical-based F-transforms method and the standard MPEG-4. Ferdinando Di Martino and Salvatore Sessa Copyright © 2013 Ferdinando Di Martino and Salvatore Sessa. All rights reserved. A Fuzzy Inference System for the Conjunctive Use of Surface and Subsurface Water Thu, 18 Jul 2013 11:53:56 +0000 http://www.hindawi.com/journals/afs/2013/128393/ This study develops the water resources management model for conjunctive use of surface and subsurface water using a fuzzy inference system (FIS). The study applies the FIS to allocate the demands of surface and subsurface water. Subsequently, water allocations in the surface water system are simulated by using linear programming techniques, and the responses of subsurface water system with respect to pumping are forecasted by using artificial neural networks. The operating rule for the water systems is that the more abundant water system supplies more water. By using the fuzzy rule, the FIS conjunctive use model easily incorporates expert knowledge and operational polices into water resources management. The result indicates that the FIS model is more effective and efficient when compared with the decoupled conjunctive use and simulation-optimization models. Furthermore, the FIS model is an alternative way to obtain the conjunctive use policies between surface and subsurface water. Liang-Cheng Chang, Hone-Jay Chu, and Yi-Wen Chen Copyright © 2013 Liang-Cheng Chang et al. All rights reserved. Innovative Strategy to Improve Precision and to Save Power of a Real-Time Control Process Using an Online Adaptive Fuzzy Logic Controller Mon, 01 Jul 2013 11:01:58 +0000 http://www.hindawi.com/journals/afs/2013/658145/ The main objective of this paper is to prove the great advantage that brings our novel approach to the intelligent control area. A set of various types of intelligent controllers have been designed to control the temperature of a room in a real-time control process in order to compare the obtained results with each other. Through a training board that allows us to control the temperature, all the used algorithms should present their best performances in this control process; therefore, our self-organized and online adaptive fuzzy logic controller (FLC) will be required to present great improvements in the control task and a real high control performance. Simulation results can show clearly that the new approach presented and tested in this work is very efficient. Thus, our adaptive and self-organizing FLC presents the best accuracy compared with the remaining used controllers, and, besides that, it can guarantee an important reduction of the power consumption during the control process. R. Lasri, I. Rojas, H. Pomares, and O. Valenzuela Copyright © 2013 R. Lasri et al. All rights reserved. Real-Life Applications of Fuzzy Logic Wed, 26 Jun 2013 10:07:34 +0000 http://www.hindawi.com/journals/afs/2013/581879/ Harpreet Singh, Madan M. Gupta, Thomas Meitzler, Zeng-Guang Hou, Kum Kum Garg, Ashu M. G. Solo, and Lotfi A. Zadeh Copyright © 2013 Harpreet Singh et al. All rights reserved. Fuzzy Logic Applications in Control Theory and Systems Biology Wed, 19 Jun 2013 09:45:09 +0000 http://www.hindawi.com/journals/afs/2013/504728/ Sendren Sheng-Dong Xu, Hao Ying, Pablo Carbonell, Ching-Hung Lee, and Wei-Sheng Wu Copyright © 2013 Sendren Sheng-Dong Xu et al. All rights reserved. Fuzzy Algorithm for Power Transformer Diagnostics Tue, 18 Jun 2013 15:59:19 +0000 http://www.hindawi.com/journals/afs/2013/421621/ Dissolved gas analysis (DGA) of transformer oil has been one of the most reliable techniques to detect the incipient faults. Many conventional DGA methods have been developed to interpret DGA results obtained from gas chromatography. Although these methods are widely used in the world, they sometimes fail to diagnose, especially when DGA results fall outside conventional methods codes or when more than one fault exist in the transformer. To overcome these limitations, the fuzzy inference system (FIS) is proposed. Two hundred different cases are used to test the accuracy of various DGA methods in interpreting the transformer condition. Nitin K. Dhote and Jagdish B. Helonde Copyright © 2013 Nitin K. Dhote and Jagdish B. Helonde. All rights reserved. A Study on Multiattribute Aggregation Approaches to Product Recommendation Mon, 17 Jun 2013 15:16:45 +0000 http://www.hindawi.com/journals/afs/2013/806749/ In today’s increasingly competitive market, consumers usually have to face a huge number of products with different designs but having the same use. Therefore, an important problem for manufacturers is to attract consumers by special designs of the products. This paper aims at the improvement of a consumer-oriented approach in recommending products, and proposing a recommendation system for Japanese traditional crafts based on target-oriented fuzzy method and ontological engineering. Specifically, a target-oriented fuzzy method is used for measuring the fitness of a selected attribute to a certain object. Two aggregation models for dealing with a multiattribute evaluation and ranking are introduced; four ranking methods are also examined for getting a recommendation list. To test the aggregation models and the ranking methods, a recommendation system was developed and a comparison test was conducted. Jing-Zhong Jin, Yoshiteru Nakamori, and Andrzej P. Wierzbicki Copyright © 2013 Jing-Zhong Jin et al. All rights reserved. Image Matching by Using Fuzzy Transforms Tue, 04 Jun 2013 14:57:55 +0000 http://www.hindawi.com/journals/afs/2013/760704/ We apply the concept of Fuzzy Transform (for short, F-transform) for improving the results of the image matching based on the Greatest Eigen Fuzzy Set (for short, GEFS) with respect to max-min composition and the Smallest Eigen Fuzzy Set (for short, SEFS) with respect to min-max composition already studied in the literature. The direct F-transform of an image can be compared with the direct F-transform of a sample image to be matched and we use suitable indexes to measure the grade of similarity between the two images. We make our experiments on the image dataset extracted from the well-known Prima Project View Sphere Database, comparing the results obtained with this method with that one based on the GEFS and SEFS. Other experiments are performed on frames of videos extracted from the Ohio State University dataset. Ferdinando Di Martino and Salvatore Sessa Copyright © 2013 Ferdinando Di Martino and Salvatore Sessa. All rights reserved. The Parameter Reduction of Fuzzy Soft Sets Based on Soft Fuzzy Rough Sets Wed, 29 May 2013 19:24:33 +0000 http://www.hindawi.com/journals/afs/2013/197435/ 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. Zhiming Zhang Copyright © 2013 Zhiming Zhang. All rights reserved. Fuzzy TOPSIS for Multiresponse Quality Problems in Wafer Fabrication Processes Sun, 12 May 2013 11:54:53 +0000 http://www.hindawi.com/journals/afs/2013/496158/ The quality characteristics in the wafer fabrication process are diverse, variable, and fuzzy in nature. How to effectively deal with multiresponse quality problems in the wafer fabrication process is a challenging task. In this study, the fuzzy technique for order preference by similarity to an ideal solution (TOPSIS), one of the fuzzy multiattribute decision-analysis (MADA) methods, is proposed to investigate the fuzzy multiresponse quality problem in integrated-circuit (IC) wafer fabrication process. The fuzzy TOPSIS is one of the effective fuzzy MADA methods for dealing with decision-making problems under uncertain environments. First, a fuzzy TOPSIS methodology is developed by considering the ambiguity between quality characteristics. Then, a detailed procedure for the developed fuzzy TOPSIS approach is presented to show how the fuzzy wafer fabrication quality problems can be solved. Real-world data is collected from an IC semiconductor company and the developed fuzzy TOPSIS approach is applied to find an optimal combination of parameters. Results of this study show that the developed approach provides a satisfactory solution to the wafer fabrication multiresponse problem. This developed approach can be also applied to other industries for investigating multiple quality characteristics problems. Chiun-Ming Liu, Mei-Yu Ji, and Wen-Chieh Chuang Copyright © 2013 Chiun-Ming Liu et al. All rights reserved. Approximate Fixed Point Theorems in Fuzzy Norm Spaces for an Operator Tue, 30 Apr 2013 11:28:04 +0000 http://www.hindawi.com/journals/afs/2013/613604/ We define approximate fixed point and fuzzy diameter in fuzzy norm spaces. We prove theorems for various types of well-known generalized contractions on fuzzy norm spaces with the use of two general lemmas that are given regarding approximate fixed points of operators on fuzzy norm spaces. S. A. M. Mohsenalhosseini and H. Mazaheri Copyright © 2013 S. A. M. Mohsenalhosseini and H. Mazaheri. All rights reserved. Erratum to “Multiaspect Soft Sets” Sun, 21 Apr 2013 10:57:15 +0000 http://www.hindawi.com/journals/afs/2013/410956/ Nor Hashimah Sulaiman and Daud Mohamad Copyright © 2013 Nor Hashimah Sulaiman and Daud Mohamad. All rights reserved.