• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1041-1043
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• 1993

Fuzzy logic based Control Theory has gained much interest in the industrial world, thanks to its ability to formalize and solve in a very natural way many problems that are very difficult to quantify at an analytical level. This paper shows a solution for treating membership function inside hardware circuits. The proposed hardware structure optimizes the memoried size by using particular form of the vectorial representation. The process of memorizing fuzzy sets, i.e. their membership function, has always been one of the more problematic issues for the hardware implementation, due to the quite large memory space that is needed. To simplify such an implementation, it is commonly [1,2,8,9,10,11] used to limit the membership functions either to those having triangular or trapezoidal shape, or pre-definite shape. These kinds of functions are able to cover a large spectrum of applications with a limited usage of memory, since they can be memorized by specifying very few parameters ( ight, base, critical points, etc.). This however results in a loss of computational power due to computation on the medium points. A solution to this problem is obtained by discretizing the universe of discourse U, i.e. by fixing a finite number of points and memorizing the value of the membership functions on such points [3,10,14,15]. Such a solution provides a satisfying computational speed, a very high precision of definitions and gives the users the opportunity to choose membership functions of any shape. However, a significant memory waste can as well be registered. It is indeed possible that for each of the given fuzzy sets many elements of the universe of discourse have a membership value equal to zero. It has also been noticed that almost in all cases common points among fuzzy sets, i.e. points with non null membership values are very few. More specifically, in many applications, for each element u of U, there exists at most three fuzzy sets for which the membership value is ot null [3,5,6,7,12,13]. Our proposal is based on such hypotheses. Moreover, we use a technique that even though it does not restrict the shapes of membership functions, it reduces strongly the computational time for the membership values and optimizes the function memorization. In figure 1 it is represented a term set whose characteristics are common for fuzzy controllers and to which we will refer in the following. The above term set has a universe of discourse with 128 elements (so to have a good resolution), 8 fuzzy sets that describe the term set, 32 levels of discretization for the membership values. Clearly, the number of bits necessary for the given specifications are 5 for 32 truth levels, 3 for 8 membership functions and 7 for 128 levels of resolution. The memory depth is given by the dimension of the universe of the discourse (128 in our case) and it will be represented by the memory rows. The length of a world of memory is defined by: Length = nem (dm(m)＋dm(fm) Where: fm is the maximum number of non null values in every element of the universe of the discourse, dm(m) is the dimension of the values of the membership function m, dm(fm) is the dimension of the word to represent the index of the highest membership function. In our case then Length=24. The memory dimension is therefore 128*24 bits. If we had chosen to memorize all values of the membership functions we would have needed to memorize on each memory row the membership value of each element. Fuzzy sets word dimension is 8*5 bits. Therefore, the dimension of the memory would have been 128*40 bits. Coherently with our hypothesis, in fig. 1 each element of universe of the discourse has a non null membership value on at most three fuzzy sets. Focusing on the elements 32,64,96 of the universe of discourse, they will be memorized as follows: The computation of the rule weights is done by comparing those bits that represent the index of the membership function, with the word of the program memor . The output bus of the Program Memory (μCOD), is given as input a comparator (Combinatory Net). If the index is equal to the bus value then one of the non null weight derives from the rule and it is produced as output, otherwise the output is zero (fig. 2). It is clear, that the memory dimension of the antecedent is in this way reduced since only non null values are memorized. Moreover, the time performance of the system is equivalent to the performance of a system using vectorial memorization of all weights. The dimensioning of the word is influenced by some parameters of the input variable. The most important parameter is the maximum number membership functions (nfm) having a non null value in each element of the universe of discourse. From our study in the field of fuzzy system, we see that typically nfm 3 and there are at most 16 membership function. At any rate, such a value can be increased up to the physical dimensional limit of the antecedent memory. A less important role n the optimization process of the word dimension is played by the number of membership functions defined for each linguistic term. The table below shows the request word dimension as a function of such parameters and compares our proposed method with the method of vectorial memorization[10]. Summing up, the characteristics of our method are: Users are not restricted to membership functions with specific shapes. The number of the fuzzy sets and the resolution of the vertical axis have a very small influence in increasing memory space. Weight computations are done by combinatorial network and therefore the time performance of the system is equivalent to the one of the vectorial method. The number of non null membership values on any element of the universe of discourse is limited. Such a constraint is usually non very restrictive since many controllers obtain a good precision with only three non null weights. The method here briefly described has been adopted by our group in the design of an optimized version of the coprocessor described in [10].

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.489-491
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• 1993

Many optimization problem or multiple attribute, multiple alternative decision making problem may have fuzzy evaluation factors. In this case, fuzzy number operation technique is needed to evaluate and compare object functions which become fuzzy sets. Generally, fuzzy number operations can be defined by extension principle of fuzzy set theory, but it is tedious to do fuzzy number operations by using extension principle when the membership functions are defined by complex functions. Many fast methods which approximate the membership functions such as triangle, trapezoidal, or L-R type functions are proposed. In this paper, a fast fuzzy number operation method is proposed which do not simplify the membership functions of fuzzy numbers.

• Journal of Electrical Engineering and Technology
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• v.13 no.2
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• pp.969-980
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• 2018

This paper aims to design of the neutrosophic fuzzy-PID controller and it has been compared with the conventional fuzzy-PID controller for position tracking control in terms of robustness. In the neutrosophic fuzzy-PID controller, error (e) and change of error (ce) were assessed separately on two fuzzy inference systems (FISs). In this study, the designed method is different from the conventional fuzzy logic controller design, membership degrees of antecedent variables were determined by using the T(true), I(indeterminacy), and F(false) membership functions. These membership functions are grouped on the universe of discourse with the neutrosophic set approach. These methods were tested on three-dimensional (3-D) position-tracking control application of a spherical robot manipulator in the MATLAB Simulink. In all tests, reference trajectory was defined for movements of all axes of the robot manipulator. According to the results of the study, when the moment of inertia of the rotor is changed, less overshoot ratio and less oscillation are obtained in the neutrosophic fuzzy-PID controller. Thus, our suggested method is seen to be more robust than the fuzzy-PID controllers.

• Proceedings of the KSRS Conference
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• 1999.11a
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• pp.48-53
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• 1999

The paper presents an automated method for generating fuzzy rules and fuzzy membership functions for pattern classification from training sets of examples and an application to the land-cover classification. Initially, fuzzy subspaces are created from the partitions formed by the minimum and maximum of individual feature values of each class. The initial membership functions are determined according to the generated fuzzy partitions. The fuzzy subspaces are further iteratively partitioned if the user-specified classification performance has not been archived on the training set. Our classifier was trained and tested on patterns consisting of the DN of each band, (XS1, XS2, XS3), extracted from KITSAT-3 multispectral scene. The result represents that our classification method has higher generalization power.

• Journal of the Korean Society of Safety
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• v.8 no.4
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• pp.82-90
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• 1993

Manual lifting, as a part of Manual Materials Handling Activities, is recognized by authorities in the field of occupational health and safety as a major hazard to industrial workers. The most important problem in applying fuzzy model of manual materials lifting is the decision of membership functions on each approaches. : Biomechanical, Physiological, Psychophysical. The primary objectives of this paper suggests to process deciding the most acceptable membership functions for establishing permissible weights on manual lifting activities using fuzzy sets.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.1 no.1
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• pp.1-5
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• 2001

In this paper, we propose a fuzzy traffic controller that is able to cope with traffic congestion appropriately. In order to consider such situation as loss of green time caused by spillback of upper crossroad, it imports a degree of traffic congestion of upper roads which vehicles on a crossroad are to proceed to. We constructed the equal-partitioned fuzzy traffic controller that uses the membership functions of the same size and shape, and modified the size and shape, and modified the size and shape of its membership functions by the membership function modification algorithm. In experiment, we compared and analyzed the fixed signal controller, the fuzzy traffic controller with the membership of the same size and shape, and the modified fuzzy traffic controller by using the delay time, the proportion of entered vehicles to occurred vehicles and the proportion of passed vehicles to entered vehicles. As a result of experiment, the modified fuzzy controller showed more enhanced performance than others.

• Journal of Power Electronics
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• v.12 no.5
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• pp.830-841
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• 2012

Active power filters (APF) can be employed for harmonic compensation in power systems. In this paper, a fuzzy based method is proposed for identification of probable APF nodes of a radial distribution system. The modified adaptive particle swarm optimization (MAPSO) technique is used for final selection of the APFs size. A combination of Fuzzy-MAPSO method is implemented to determine the optimal allocation and size of APFs. New fuzzy membership functions are formulated where the harmonic current membership is an exponential function of the nodal injecting harmonic current. Harmonic voltage membership has been formulated as a function of the node harmonic voltage. The product operator shows better performance than the AND operator because all harmonics are considered in computing membership function. For evaluating the proposed method, it has been applied to the 5-bus and 18-bus test systems, respectively, which the results appear satisfactorily. The proposed membership functions are new at the APF placement problem so that weighting factors can be changed proportional to objective function.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.3
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• pp.1205-1223
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• 2018

Image enhancement is an emerging method for analyzing the images clearer for interpretation and analysis in the spatial domain. The goal of image enhancement is to serve an input image so that the resultant image is more suited to the particular application. In this paper, a novel method is proposed based on Mamdani fuzzy inference system (FIS) using multiple fuzzy membership functions. It is observed that the shape of membership function while converting the input image into the fuzzy domain is the essential important selection. Then, a set of fuzzy If-Then rule base in fuzzy domain gives the best result in image contrast enhancement. Based on a different combination of membership function shapes, a best predictive solution can be determined which can be suitable for different types of the input image as per application requirements. Our result analysis shows that the quality attributes such as PSNR, Index of Fuzziness (IOF) parameters give different performances with a selection of numbers and different sized membership function in the fuzzy domain. To get more insight, an optimization algorithm is proposed to identify the best combination of the fuzzy membership function for best image contrast enhancement.

• Journal of Digital Convergence
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• v.12 no.8
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• pp.321-327
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• 2014

Feature selection is the technique to improve the classification performance by using a minimal set by removing features that are not related with each other and characterized by redundancy. This study proposed new feature selection using the distance between the center of gravity of the bounded sum of weighted fuzzy membership functions (BSWFMs) provided by the neural network with weighted fuzzy membership functions (NEWFM) in order to improve the classification performance. The distance-based feature selection selects the minimum features by removing the worst features with the shortest distance between the center of gravity of BSWFMs from the 24 initial features one by one, and then 22 minimum features are selected with the highest performance result. The proposed methodology shows that sensitivity, specificity, and accuracy are 97.7%, 99.7%, and 98.7% with 22 minimum features, respectively.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.380-383
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• 2003

In this paper, we propose a fuzzy group decision making method for multiple decision maker-multiple objective programming problems to obtain the agreeable solution. In the proposed method, considering the vague nature of human subjective judgement it is assumed that each of multiple decision makers has a fuzzy goal for each of his/her own objective functions. After eliciting the membership functions from the decision makers for their fuzzy goals, total M-Pareto optimal solution concept is defined in membership spaces in order to deal with multiple decision maker-multiple objective programming problems. For generating a candidate of the agreeable solution which is total M-Pareto optimal, the extended weighted minimax problem is formulated and solved for some weighting vector which is specified by the decision makers in their subjective manner, Given the total M-Pareto optimal solution, each of the derision makers must either be satisfied with the current values of the membership functions, or update his/her weighting vector, However, in general, it seems to be very difficult to find the agreeable solution with which all of the decision makers are satisfied perfectly because of the conflicts between their membership functions. In the proposed method, each of the decision makers is requested to estimate the degree of satisfaction for the candidate of the agreeable solution. Using the estimated values or satisfaction of each of the decision makers, the core concept is desnfied, which is a set of undominated candidates. The interactive algorithm is developed to obtain the agreeable solution which satisfies core conditions.