MEMBERSHIP FUNCTION based on probability density FUNCTIONچندین روش به منظور برآورد تابع چگالی احتمال وجود دارد. از سوی دیگر، در نظریه مجموعه هایفازی یکی از روش های ساختن تابع عضویت بر پایه ی مجموعه داده، روش مبتنی بر تابع چگالی احتمال است.با توجه به روش های متداول در برآورد تابع چگالی، این مسئله می تواند به محاسبه انواع تابع عضویت بر پایهیک مجموعه داده منجر شود. در این مقاله، برخی از این روش ها بیان و با مثال عددی تشریح می شوند..

In this paper, by means of fuzzy approaches, an accurate method is introduced for edging of color photographs. The difference between our method with other similar methods is the use of a morphological operation to think or thick the obtained edges. In this proposed method, a 3×3 window is dragged on the photo. For each block, 12 point sets will be defined, each including two non-overlapping point sets. Then, a fuzzy MEMBERSHIP FUNCTION will be designed for each point sets according to data of contrast. At last, the range of MEMBERSHIP contrast degree for the points of second point sets will be assessed. A comparison of MEMBERSHIP degree of second point sets with a pre-defined threshold indicates whether central point of window is bordered or non-bordered. The method was performed on some reference images and the results were compared with common edging methods. The results show that proposed method has a high capability to edge photographs.

A new hybrid framework is proposed for optimization of orderable search spaces. It is based on fuzzy-MEMBERSHIP of design variable alternatives to the optimal solution. The method has DYNAMIC behavior since the MEMBERSHIP values are assigned as any solution candidates arises during the search and they are summed based on their overlaps in the alternatives scope. A trail matrix is also utilized to indirectly share values of the fuzzy MEMBERSHIPs further ranked regarding closeness of an individual to the optimal solution both in the objective FUNCTION and in the design space scope. The method takes benefit of different random, vector-sum and probability-based walks to move new solutions toward the global optimum. Utilizing a generalized cooling procedure, the related thresholds are tuned to choose between different walk types in searching the design space and also a search refinement strategy is developed. Two variants of such a framework is then proposed and compared with each other in addition to some well-known procedures including genetic algorithm and particle swarm optimization. Test results with some treated problems, reveals the superior performance of the proposed algorithm and its special feature in adaptive tuning the diversity index during the search.

In this paper, a new approach is proposed in order to select an optimal MEMBERSHIP FUNCTION for inputs of wind speed prediction system. Then using a fuzzy method and the stochastic characteristics of wind speed in the previous year, the wind speed modeling is performed and the wind speed for the future year will be predicted. In this proposed method, the average and the standard deviation of inputs data are calculated. The MEMBERSHIP FUNCTION shape and the domain intervals are evaluated using the variance of system. This technique prevents from trial and error method for defining the shape and domain intervals of optimal MEMBERSHIP FUNCTION and helps to achieve the desired prediction in a quick way. The wind speed is estimated in the fuzzy inference system and simulated with the fuzzy logic. The sensitivity analyses are performed by changing the input parameters and MEMBERSHIP FUNCTIONs shape and the results are compared. The results demonstrate that this new prediction method is a fast and applicable method compared to the other methods since the calculated error will be more than the error of this method if the shape and domain interval of MEMBERSHIP FUNCTION are changed.

Groundwater is one of the most important sources of drinking, industrial, and agricultural water in arid and semi-arid regions, where the occurrence of droughts, rapid population growth, and the corresponding increase in water demand threaten groundwater resources. Over-exploitation and mismanagement of groundwater resources result in environmental problems such as subsidence and saltwater intrusion in coastal aquifers. The risk of saltwater intrusion threatens the Urmia aquifer due to the proximity of the aquifer to Lake Urmia and severe groundwater decline. This study evaluates the vulnerability of saltwater intrusion by the GALDIT framework. The results show the conservative vulnerability index with low efficiency, where vulnerable areas are limited to a narrow strip near the coastline. Fuzzy MEMBERSHIP FUNCTIONs were employed within the GALDIT framework to increase efficiency. The results of the modified GALDIT resolve the weakness of presenting conservative results in the basic GALDIT framework.

Fuzzification of support vector machine has been utilized to deal with outlier and noise problem. This importance is achieved, by the means of fuzzy MEMBERSHIP FUNCTION, which is generally built based on the distance of the points to the class centroid. The focus of this research is twofold. Firstly, by taking the advantage of robust statistics in the fuzzy SVM, more emphasis on reducing the impact of outliers on the generalizability of SVM has been placed. Moreover, the variety of MEMBERSHIP FUNCTION for the elliptical data has been designated, based on the classic and robust Mahalanobis distance. Minimum covariance determinant and orthogonalised Gnanadesikan Kettenring estimators are employed in the structure of the robust– fuzzy SVM. By implementing the new MEMBERSHIP FUNCTION, the disadvantages of the traditional fuzzy MEMBERSHIP FUNCTION has been rectified. Simulated and real benchmarking data set confirm the effectiveness of the proposed methods. Compared with the traditional SVM and fuzzy SVM, these methods give a better performance on reducing the effects of outliers and significantly improves the classification accuracy and generalization.

Data envelopment analysis (DEA) is a method to evaluate the relative efficiency of decision making units (DMUs). In this method, the issue has always been to determine a set of weights for each DMU which often caused many problems. Since the DEA models also have the multi-objective linear programming (MOLP) problems nature, a rational relationship can be established between MOLP and DEA problems to overcome the problem of determining weights. In this study, a MEMBERSHIP FUNCTION was defined base on the results of CCR model and cross efficiency, and by using this MEMBERSHIP FUNCTION in a proposed model, we obtained a common set of weights for all DMUs. Finally, by solving a sample problem, the proposed algorithm was explained.

This paper presents a new Neuro-fuzzy control system to control rigid-flexible manipulators. Enhancing the performance of fuzzy controller and intelligence in fuzzy and non-fuzzy units is the goal of this research. Proposed control system includes a fuzzy controller in the feedback and a neural network is the feed-forward. The network has the responsibility of estimating the inverse DYNAMIC of device and then, the production of control command. Updating weighting coefficients of network is done online using the fuzzy controller output. On the other hand, two DYNAMIC recurrent neural networks are used for making fuzzy unit intelligent. Networks are responsible for regulating the main factors of MEMBERSHIP FUNCTIONs in the fuzzy controller. The input of these networks is error and error change rate and their weights are done by using an error back-propagation algorithm. To verify the effectiveness of the proposed method, simulation is conducted for skilled manipulators with three interfaces where the end interface is flexible. System responses to step input and sinusoidal input are separately obtained for fuzzy controllers and proposed controller and compared. Comparison and studies indicate the effectiveness of the provided method.