The equivalence between fuzzy logic systems and feedforward neural networks

Over the last few decades, fuzzy logic has been shown as a powerful methodology for dealing with imprecision and nonlinearity efficiently. Applications can be found in a wide context ranging from medicine to finance, from human factors to consumer products, from vehicle control to computational linguistics, and so on (Wang 1997; Dubois and Prade 2000; Passino and Yurkovich 1998; Jang et al. 1997; Sugeno 1985; Pedrycz 1993). However, one of the shortcomings of fuzzy logic is the lack of systematic design. To circumvent this problem, fuzzy logic is usually combined with Neural Networks (NNs) by virtue of the learning capability of NNs. NNs are networks of highly interconnected neural computing elements that have the ability of responding to input stimuli and learning to adapt to the environment. Both fuzzy systems and NNs are dynamic and parallel processing systems that estimate input-output functions (Mitra and Hayashi 2000). The merits of both fuzzy and neural systems can be integrated in Fuzzy Neural Networks (FNNs) (Lee and Lee 1974, 1975; Pal and Mitra 1999; Zanchettin and Ludermir 2003). Therefore, the integration of fuzzy and neural systems leads to a symbiotic relationship in which fuzzy systems provide a powerful framework for expert knowledge representation, while NNs provide learning capabilities.

Over the last decade, an extensive research has been carried out in the areas of fuzzy logic and neural networks. Fuzzy logic has emerged as a mathematical tool to deal with the uncertainties in human perception and reasoning. It also provides a framework for an inference mechanism that allows for approximate human reasoning capabilities to be applied to knowledge-based systems. On the other hand, artificial neural networks have emerged as fast computation tools with learning and adaptivity capabilities. Recently, these two fields have been integrated into a new emerging technology called fuzzy neural networks which combines the benefits of each field. The objective of the paper is to establish the similarities and differences between fuzzy systems and neural networks and to discuss possible models for fuzzy neural networks which can be applied to system modeling and control.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Attempts are being made to enhance the drive performance by intelligent control using fuzzy logic (FL) and neural network techniques. One of the frequently discussed applications of artificial intelligence in control is the replacement of a standard proportional plus integral (PI) speed controller with an FL or artificial neural network (ANN) speed controller. Regardless of all the work, it appears that a thorough comparison of the drive behavior under PI, FL, and ANN speed control is necessary. This article attempts to compare PI, fuzzy, and ANN controllers that are implemented in an embedded system for closed-loop speed control of DC drive fed by a buck-type DC–DC power converter. The PI controller is designed based on the small signal modeling of the system. The PI-like fuzzy controller structure is considered for comparison. Two ANN controllers are designed. One controller uses training data obtained from the simulation of a fuzzy controller and the other uses training data from the simulation of a PI controller. The performance of the controllers is studied for a variety of operating conditions, such as step change in speed command and step change in load torque. The parameters selected for the comparison are the steady-state error and the rise time of the response. It is shown that ANN speed controllers provide a superior speed response in terms of rise time and the steady-state error compared to PI and FL controllers. This advantage arises from the fact that the neural network has the property of generalization and the control surface of the neural controller is smooth. The designed neural network controller is simple, with three neurons only, and so it is best suited for embedded system implementation. It is also found that the ANN controller trained with the training data from a PI controller has a better response compared to the ANN controller trained with data from a fuzzy controller.

With the use of fuzzy logic techniques, neural computing can be integrated in symbolic reasoning to solve complex real world problems. In fact, artificial neural networks, expert systems, and fuzzy logic systems, in the context of approximate reasoning, share common features and techniques. A model of Fuzzy Connectionist Expert System is introduced, in which an artificial neural network is designed to construct the knowledge base of an expert system from, training examples (this model can also be used for specifications of rules in fuzzy logic control). Two types of weights are associated with the synaptic connections in an AND-OR structure: primary linguistic weights, interpreted as labels of fuzzy sets, and secondary numerical weights. Cell activation is computed through min-max fuzzy equations of the weights. Learning consists in finding the (numerical) weights and the network topology. This feedforward network is described and first illustrated in a biomedical application (medical diagnosis assistance from inflammatory-syndromes/proteins profiles). Then, it is shown how this methodology can be utilized for handwritten pattern recognition (characters play the role of diagnoses): in a fuzzy neuron describing a number for example, the linguistic weights represent fuzzy sets on cross-detecting lines and the numerical weights reflect the importance (or weakness) of connections between cross-detecting lines and characters.

In a recent article in Cancer, Cho and colleagues1 suggested that the Cancer of the Liver Italian Program (CLIP) system was the best prognostic system for predicting the survival of patients with hepatocellular carcinoma (HCC) who were undergoing transcatheter arterial chemoembolization, and further validation studies will be performed. We agree with the authors. Predicting mortality is an important component of the decision-making process, and scoring systems (Child-Pugh, CLIP, Model for Endstage Liver Disease, Barcelona Clinic Liver Cancer, etc) long have been accepted for establishing patient outcomes in HCC. Although these models perform well in predicting the mortality or morbidity in the original cohorts on which the models were developed, they may underestimate or overestimate mortality or morbidity in different populations.1 However, in the midst of such uncertainty, fuzzy logic may play an important role in the decision-making process. Fuzzy logic is the science of reasoning, thinking, and inference that recognizes and uses the real-world phenomenon that everything is a matter of degree. In the simplest terms, fuzzy-logic theory is an extension of binary theory that does not use crisp definitions and distinctions. Instead of assuming that everything must be defined in to black and white (binary view), fuzzy logic is a method that captures and uses the concept of fuzziness in a computationally effective manner. Neural networks and fuzzy logic are 2 complementary technologies. Neural networks can learn (ie, adapt) from data and feedback, but understanding the pattern learned by neural networks is difficult. Conversely, fuzzy rule-based models are easy to comprehend, because they use linguistic terms and the structure of if/then rules. Unlike neural networks, fuzzy logic does not come with a learning algorithm (ie, the system cannot learn from feedback). The combination of neural networks and fuzzy logic has created a new term, a neurofuzzy system. Neural networks, fuzzy systems, and the combination of both already have been applied successfully to computer-aided diagnosis—eg, detection of microcalcification, automatic detection of distorted plethysmogram pulses in neonates and pediatric patients, detection of erythematosquamous diseases, and lung-nodule detection—and have been useful for predicting the presence of prostate cancer.2 In conclusion, slight variations in population characteristics can change predictive values of the scoring systems. However, neurofuzzy systems can incorporate data from many clinical, biologic, and genetic variables and can provide better risk estimations for hepatocellular carcinoma. Mesut Tez MD*, Baris Zulfikaroglu MD , * Gazi University School of Medicine, Department of Surgery, Ankara, Turkey, Ankara Numune Hospital, Department of Fifth Surgery, Ankara, Turkey.

Implementation of fuzzy logic systems and neural networks in industry

The artificial intelligence techniques such as neural networks and fuzzy systems play an important role to disconnect flexion &amp; expansion of the swing leg, the earth response force of the other foot has been redesigned. Underthat paper, we think the fuzzy controller plan issue for yield following flawed genuine investigation of nonlinear systems. For examination, an essential fuzzy control plot has been bristly developed dependent on a current methodology delegate under the field.In this paper, the Feedforward Neural Network has been implemented with integer, fixed point and floating point data representations. Additionally, The Fuzzy Logic Controllers in both analog and digital forms has been implemented in hardware. Both designs use less hardware resources and operate with reasonable speed compared to other existing designs. The digital implementation of Fuzzy Logic Controller has been tested for a simulated first order liquid level process and the performance results have been compared with those of the Matlab version of Fuzzy Logic Controller. Here, Fuzzy Logic Controller is used as the controller and is trained adaptively for the changes in process parameters using recursive k-means clustering algorithm for updating the centers of the hidden layer and Recursive Least Square algorithm for updating the weights of the output layer, the result of the settling time about 20ms and takes 20 iterations, and the squared error reaches zero at approximately 20 µs. Index Terms— Fuzzy Controller, leg interaction force, Prosthetic legs, Human walking, GyroAccelerate,Fuzzy Logic System.

A hybrid fuzzy neural architecture is proposed. The fuzzy neural system is a feedforward network that combines the basic notions of neural networks and fuzzy logic into a common structure. A back-propagation algorithm is used to train the FNS to perform the desired nonlinear mappings. Four simulation examples are presented where the fuzzy neural system is employed as a nonlinear identifier. Finally, comparisons between fuzzy neural systems, backpropagation neural networks and other fuzzy systems are given and discussed.

This paper presents a novel approach to simulate a Knowledge Based System for diagnosis of Breast Cancer using Soft Computing tools like artificial neural networks (ANNs) and Neuro Fuzzy Systems. The feed-forward neural network has been trained using three ANN algorithms, the back propagation algorithm (BPA), the radial basis function (RBF) Networks and the learning vector quantization (LVQ) Networks; and also by adaptive neuro fuzzy inference system (ANFIS). The simulator has been developed using MATLAB and performance is compared by considering the metrics like accuracy of diagnosis, training time, number of neurons, number of epochs etc. The simulation results show that this Knowledge Based Approach can be effectively used for early detection of Breast Cancer to help oncologists to enhance the survival rates significantly.

In 2013 the Editor of Journal of Vibration and Control and SAGE became aware of a peer review ring involving assumed and fabricated identities that appeared to centre around Peter Chen at National Pingtung University of Education, Taiwan (NPUE). SAGE and the Editor then began a complex investigation into the case during the rest of 2013 and 2014. Following an unsatisfactory response from Peter Chen, NPUE was notified. NPUE were serious in addressing the Journal and SAGE’s concerns. NPUE confirmed that the institution was investigating Peter Chen. SAGE subsequently uncovered a citation ring involving the above mentioned author and others. We regret that individual authors have compromised the academic record by perverting the peer review process and apologise to readers. On uncovering problems with peer review and citation SAGE immediately put steps in place to avoid similar vulnerability of the Journal to exploitation in the future. More information may be found at www.sagepub.co.uk/JVC_Statement_2014 . The Journal and SAGE understand from NPUE that Peter Chen has resigned his post at NPUE. The following articles are retracted because after thorough investigation evidence points towards them having at least one author or being reviewed by at least one reviewer who has been implicated in the peer review ring and/or citation ring. All authors have had an opportunity to respond to the allegations and proposed actions. OnlineFirst articles (these articles will not be published in an issue) Chen CY, Chen T-H, Chen Y-H, Yu S-E and Chung P-Y (2013) Information technology system modeling an integrated C-TAM-TPB model to the validation of ocean tidal analyses Journal of Vibration and Control Epub ahead of print 7 May 2013. doi: 10.1177/1077546312472924 Chang R-F, Chen CY, Su F-P and Lin H-C (2013) A two-step approach for broadband digital signal processing technique Journal of Vibration and Control Epub ahead of print 26 April 2013. doi: 10.1177/1077546312472925 Chen TH, Chang CJ, Yu SE, Chung PY and Liu C-K (2013) Nonlinear information analysis and system management technique: the influence of design experience and control complexity Journal of Vibration and Control Epub ahead of print 12 April 2013. doi: 10.1177/1077546312473321 Chen CY, Shih BY, Chen YH, Yu SE and Liu YC (2013) The exploration of a 3T flow model using vibrating NXT: II. Model validation Journal of Vibration and Control Epub ahead of print 10 April 2013. doi: 10.1177/1077546312470481 Chen CY, Shih BY, Chen YH, Yu SE and Liu YC (2013) The exploration of 3T flow model using vibrating NXT: I. model formulation Journal of Vibration and Control Epub ahead of print 6 February 2013. doi: 10.1177/1077546312467360 Lin M-L and Chen C-W (2013) Stability analysis of fuzzy-based NN modeling for ecosystems using fuzzy Lyapunov methods Journal of Vibration and Control Epub ahead of print 6 February 2013. doi: 10.1177/1077546312466687 Chen CY, Chen TH, Chen YH and Chiu J (2012) A multi-stage method for deterministic-statistical analysis: a mathematical case and measurement studies Journal of Vibration and Control Epub ahead of print 20 December 2012. doi: 10.1177/1077546312466579 Shih BY, Lin MC and Chen CY (2012) Autonomous navigation system for radiofrequency identification mobile robot e-book reader Journal of Vibration and Control Epub ahead of print 13 December 2012. doi: 10.1177/1077546312466578 Chang RF, Chen CY, Su FP, Lin HC and Lu C-K (2012) Multiphase SUMO robot based on an agile modeling-driven process for a small mobile robot Journal of Vibration and Control Epub ahead of print 13 December 2012. doi: 10.1177/1077546312464993 Shih B-Y, Lin Y-K, Cheng M-H, Chen C-Y and Chiu C-P (2012) The development of an application program interactive game-based information system Journal of Vibration and Control Epub ahead of print 12 December 2012. doi: 10.1177/1077546312464682 Chen C-Y, Chang C-J and Lin C-H (2012) On dynamic access control in web 2.0 and cloud interactive information hub: technologies Journal of Vibration and Control Epub ahead of print 12 December 2012. doi: 10.1177/1077546312464992 Shin BY, Chen CY and Hsu KH (2012) Robot cross platform system using innovative interactive theory and selection algorithms for Android application Journal of Vibration and Control Epub ahead of print 13 November 2012. doi: 10.1177/1077546312463757 Articles published in an issue Chen C-W (2014) Applications of neural-network-based fuzzy logic control to a nonlinear time-delay chaotic system Journal of Vibration and Control 20 (4): 589-605. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312461370 Chen C-W (2014) A review of intelligent algorithm approaches and neural-fuzzy stability criteria for time-delay tension leg platform systems Journal of Vibration and Control 20 (4): 561-575. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312463759 Chen C-Y, Chang C-J and Lin C-H (2014) On dynamic access control in web 2.0 and cloud interactive information hub: trends and theories Journal of Vibration and Control 20 (4): 548-560. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312463762 Lin M-L and Chen C-W (2014) Stability conditions for ecosystem modeling using the fuzzy Lyapunov method Journal of Vibration and Control 20 (2): 290-302. Epub ahead of print 23 October 2012. doi: 10.1177/1077546312451301 Chen C-H, Kuo C-M, Hsieh S-H and Chen C-Y (2014) Highly efficient very-large-scale integration (VLSI) implementation of probabilistic neural network image interpolator Journal of Vibration and Control 20 (2): 218-224. Epub ahead of print 22 October 2012. doi: 10.1177/1077546312458822 Chen C-Y (2014) Wave vibration and simulation in dissipative media described by irregular boundary surfaces: a mathematical formulation Journal of Vibration and Control 20 (2): 191-203. Epub ahead of print 22 October 2012. doi: 10.1177/1077546312464258 Chen C-H, Yao T-K, Dai J-H and Chen C-Y (2014) A pipelined multiprocessor system- on-a-chip (SoC) design methodology for streaming signal processing Journal of Vibration and Control 20 (2): 163-178. Epub ahead of print 16 October 2012. doi: 10.1177/1077546312458821 Lin M-L and Chen C-W (2014) Fuzzy neural modeling for n-degree ecosystems using the linear matrix inequality approach Journal of Vibration and Control 20 (1): 82-93. Epub ahead of print 8 October 2012. doi: 10.1177/1077546312458533 Chen C-H, Wu W-X and Chen C-Y (2013) Ant-inspired collective problem-solving systems Journal of Vibration and Control 19 (16): 2481-2490. Epub ahead of print 18 September 2012. doi: 10.1177/1077546312456231 Chen C-H, Yao T-K, Kuo C-M and Chen C-Y (2013) Evolutionary design of constructive multilayer feedforward neural network Journal of Vibration and Control 19 (16): 2413-2420. Epub ahead of print 12 September 2012. doi: 10.1177/1077546312456726 Chen C-W (2013) Applications of the fuzzy-neural Lyapunov criterion to multiple time-delay systems Journal of Vibration and Control 19 (13): 2054-2067. Epub ahead of print 16 August 2012. doi: 10.1177/1077546312451034 Chung P-Y, Chen Y-H, Walter L and Chen C-Y (2013) Influence and dynamics of a mobile robot control on mechanical components Journal of Vibration and Control 19 (13): 1923-1935. Epub ahead of print 20 July 2012. doi: 10.1177/1077546312452184 Chen C-W (2013) Neural network-based fuzzy logic parallel distributed compensation controller for structural system Journal of Vibration and Control 19 (11): 1709-1727. Epub ahead of print 22 June 2012. doi: 10.1177/1077546312442233 Chen C-W, Yeh K, Yang H-C, Liu KFR and Liu C-C (2013) A critical review of structural system control by the large-scaled neural network linear-deferential-inclusion-based criterion Journal of Vibration and Control 19 (11): 1658-1673. Epub ahead of print 18 June 2012. doi: 10.1177/1077546312443377 Chen C-H, Kuo C-M, Chen C-Y and Dai J-H (2013) The design and synthesis using hierarchical robotic discrete-event modeling Journal of Vibration and Control 19 (11): 1603-1613. Epub ahead of print 27 June 2012. doi: 10.1177/1077546312449645 Chang CJ, Chen CY and Chou I-T (2013) The design of information and communication technologies: telecom MOD strength machines Journal of Vibration and Control 19 (10): 1499-1513. Epub ahead of print 27 June 2012. doi: 10.1177/1077546312449644 Shih B-Y, Chen C-Y, Li K-H, Wu T-Y, Chen G-Y (2013) A novel NXT control method for implementing force sensing and recycling in a training robot Journal of Vibration and Control 19 (10): 1443-1459. Epub ahead of print 1 June 2012. doi: 10.1177/1077546312446361 Chen C-W, Chen P-C and Chiang W-L (2013) Modified intelligent genetic algorithm-based adaptive neural network control for uncertain structural systems Journal of Vibration and Control 19 (9): 1333-1347. Epub ahead of print 31 May 2012. doi: 10.1177/1077546312442232 Chen C-Y, Shih B-Y, Shih C-H and Wang L-H (2013) Enhancing robust and stability control of a humanoid biped robot: system identification approach. Journal of Vibration and Control 19 (8): 1199-1207. Epub ahead of print 26 April 2012. doi: 10.1177/1077546312442947 Chang C-J, Chen C-Y and Huang C-W (2013) Applications for medical recovery using wireless control of a bluetooth ball with a hybrid G-sensor and human-computer interface technology Journal of Vi

Retraction notice

Many bridges in Taiwan have been in use from the period that Taiwan was governed by the Japanese, over 50 years ago, which is the average ultimate usable lifetime of such structures. Three-quarters of the bridges on major highways have been in use for more than 20 years and numerous bridges on country roads have also been in use for more than 20 years. In other words, most of the bridges in Taiwan are aging and may require repair or replacement. Ambient vibration tests are utilized to measure the response of old bridges, which are difficult to equip with accelerometers. The Fourier transform method is traditionally used to gain important information about ambient vibration records. However, the development of information technology over the last 20 years has meant that there are more kinds of signal management technologies, including the wavelet and Hilbert—Huang transform (HHT) methods. In this study we investigate the characteristics of aging bridges by comparison with their structural properties. We analyze their ambient vibration, and discuss the possible influence of the frequency function. Long-term environmental impacts create many structural problems, but with traditional methods examination of bridge health is difficult. Therefore, in our HHT management system, we examine destroyed bridges. The characteristics and behavior of bridges subjected to random loading can be understood by analysis with the random decrement technique and the frequency response function method.

Retraction notice

Introduction: This paper presents a novel approach for classifying different types of steel rods using a combination of pre-trained convolutional neural networks (CNNs) and fuzzy logic systems. We utilize VGG16, ResNet50, and InceptionV3 models to extract features from grayscale images of steel rods, which are then classified using Support Vector Machines (SVM). Furthermore, we incorporate a fuzzy logic system to improve the final classification accuracy by combining the individual accuracies of each CNN model. Experimental results demonstrate the effectiveness of our approach in achieving high classification accuracy compared to traditional methods. Objectives: This research presents a novel multi-model approach for steel rod classification utilizing three distinct fuzzy logic systems: Fuzzy Recurrent Neural Network (RNN), Fuzzy Convolutional Neural Network (CNN), and Fuzzy Neural Network. The proposed system addresses the critical challenge of accurate defect detection and classification in steel manufacturing processes. By combining these complementary approaches, we achieve enhanced feature extraction capabilities and improved classification accuracy. Experimental results demonstrate that our multi-model system achieves a classification accuracy of 97.8%, surpassing single-model approaches by an average of 8.2%. The system successfully identifies surface defects, structural anomalies, and dimensional variations with high precision, making it suitable for real-time industrial applications. Methods: This paper introduces a novel approach for the feature extraction and classification of steel rods by integrating multiple models and utilizing fuzzy logic systems. The methodology leverages pre-trained convolutional neural networks (CNNs) for extracting comprehensive feature representations from steel rod images. These extracted features are then combined and integrated using fuzzy logic to enhance classification accuracy and reliability. By addressing the limitations of traditional manual inspection methods and single-model approaches, this integrated multi-model system offers a robust solution for real-time industrial implementation. The proposed system aims to improve the efficiency and effectiveness of quality control processes in steel rod manufacturing, ensuring consistent and accurate classification even under varying conditions and complexities. This innovative approach paves the way for more advanced and adaptable automated inspection systems in the industry. Results: The paper aims to develop an integrated multi-model system that combines three distinct fuzzy logic approaches to enhance feature extraction capabilities through complementary methodologies. By improving the classification accuracy and reliability, the system addresses the limitations of existing methods. The goal is to create a robust and adaptable system that is suitable for real-time industrial implementation for steel rod analysis and classification. This comprehensive approach leverages the strengths of multiple models and fuzzy logic techniques, ensuring accurate and efficient classification processes, even under complex and varying conditions. The proposed multi model system is designed to meet the stringent quality control requirements of industrial applications, ultimately improving productivity and product quality through reliable automated inspection and classification for steel rod with accuracy of 97.80%, precision of 97.30% and recall 97.50%. Conclusions: This paper presents a novel approach for the classification of steel rods using a combination of pre-trained CNN models and fuzzy logic systems. The experimental results demonstrate the effectiveness of our method in achieving high classification accuracy. This research demonstrates the effectiveness of a multi-model fuzzy logic approach for steel rod classification. The system achieves significant improvements over single-model approaches while maintaining real-time processing capabilities. Our approach provides a foundation for further research and development in automated industrial image classification.

These papers are originally published in the proceedings of Korea fuzzy logic and intelligent systems society (KFIS) fall conference in 1999. Eight papers are selected for this special issue. Major topics of them are fuzzy theory, neural network, inference system, intelligent controller, etc. In this issue, Seihwan Park and Hyung Lee-Kwang extend the concept of fuzzy hypergraph to type-2 fuzzy hypergraph using type-2 fuzzy sets. It has not only the same properties of hypergraphs but also the extended properties of them. It is also shown that interval valued fuzzy hypergraph is a special case of type-2 fuzzy hypergraph. Jung-Heum Yon, Yong-Taek Kim, Jae-Yong Seo and Hong-Tae Jeon design an efficient neural network called dynamic multidimensional wavelet neural network. It can perform an effective dynamic mapping with less dimensions of the input signal. These features show one way to compensate the weakness of the diagonal recurrent neural network and feedforward wavelet neural network. Yigon Kim, Yang Hee Jung and Young Chel Bae propose a new method for diagnosis of insulation aging using wavelet. It measures the partial discharge on-line from data acquisition system and analyses it using wavelet to acquire 21) patterns. They design a neuro-fuzzy model that diagnoses an electrical equipment using the data. Byung-Jae Choi, Seong-Woo Kwak and Byung Kook Kim develop an adaptive fuzzy logic controller. A sole input fuzzy variable is used to simplify the design procedure and the switching hyperplane of sliding mode control is used to improve the adaptability. Myung-Geun Chun, Keun-Chang Kwak and Jeong-Woong Ryu show an efficient fuzzy rule generation scheme for adaptive network-based fuzzy inference system using the conditional fuzzy c-means and fuzzy equalization methods. They apply this method to the truck backer-upper control and Box-Jenkins modeling problem. Daijin Kim proposes a new data classification method based on the tolerant rough set that extends the existing equivalent rough set. Twostage classification method is used. All data are classified by using the lower approximation at the first stage and then the non-classified data at the first stage are classified again by using the rough membership functions obtained from the upper approximation set. Min-Soeng Kim, Sun-Gi Hong and Ju-Jang Lee incorporate the Q-learning algorithm into the fuzzy logic controller. Modified fuzzy rule is used for the incorporation. As a result, a fuzzy logic controller is obtained that can learn through experience. Dong Hwa Kim designs a new 2-DOF PID controller and applies it to the operating data based transfer function of Gun-san Gas turbine in Korea. We hope that this issue can be helpful to readers and we appreciate professor Kaoru Hirota for his interest and support for the publication.