Fuzzy Information Theory Research Articles

A Novel Set of Fuzzy f-Divergence Measure-Related Intuitionistic Fuzzy Information Equalities and Inequalities

In the literature on fuzzy information theory, there are numerous divergence metrics and fuzzy information. Disparities are crucial for determining relationships. Here, we'll discuss some fresh information inequalities related to fuzzy measures and how they apply to the detection of patterns. With the aid of the fuzzy f-divergence measure and Jensen's inequality, links between new and well-known fuzzy divergence measures were also created.

Fuzzy correlation entropy-based NSGA-II for energy-efficient hybrid flow-shop scheduling problem

Green scheduling of manufacturing industry with energy saving as the core has been paid more and more attention in academia and industry. As a classic scheduling problem, hybrid flow-shop scheduling problem (HFSP) has been receiving increasing research attention. However, most studies only focus on time-related metrics while neglecting energy consumption. In this article, we studied energy-efficient HFSP and assumed that machines can operate at different speeds. This is an assumption that has been rarely explored but can make the problem more relevant to real-world production. Moreover, the energy-efficient HFSP at a variable machine speed (EHFSP-VMS) was formulated as a multiobjective mathematical optimization model aiming to optimize make-span and total energy consumption simultaneously. As a landmark achievement in the field of multiobjective optimization, non-dominated sorting genetic algorithm-II (NSGA-II) is adopted and improved as the solver, which is called fuzzy correlation entropy (FCE)-based NSGA-II (FCENSGA-II). Firstly, FCE, a fusion of fuzzy mathematics and information theory, is used to describe the difference and the FCE-based crowding distance is proposed for the first time. Its time complexity is lower than the original crowding distance. In addition, a machine learning strategy, namely opposition-based learning (OBL), is used to learn from opposite regions of the search space and increase the exploratory ability of the algorithm and the diversity of solutions. Finally, a critical path knowledge-based energy saving strategy (ESC) is adopted to discover non-dominant solutions by reducing the speed of machines on non-critical paths. A large number of experiments are conducted to test the performance of FCENSGA-II. The results show that in all test instances, the average, best and worst values of the solution obtained by FCENSGA-II are better than the compared state-of-the-art algorithms, and even the worst values obtained by FCENSGA-II in 75% of test instances are better than the best values of compared algorithms, which strongly confirms that FCENSGA-II outperforms the compared state-of-the-art algorithms for solving EHFSP-VMS.

Fuzzy Reasoning based Reliability Fault Prediction of CNC Machine Tools

CNC machine tools are the infrastructure of the manufacturing industry, and many fields cannot do without them. This paper studies the fault data of a series of CNC machine tools, and predicts the fault level based on the activity parameters of Gutenberg Richter curve and fuzzy information theory. Apply the Gutenberg Richter curve model to the reliability analysis of CNC machine tools, and use this model to fit the curves separately. Fit the activity parameters of each stage with curves, and the results show that the b value can reflect the fault activity frequency of CNC machine tools. Due to the correlation and fuzziness between system faults, it is more appropriate to use a fuzzy neural network with strong adaptability and good learning ability, which can easily adjust parameters, and can express a more complex, high-dimensional nonlinear system through fewer conditions. The use of fuzzy reasoning can link the nonlinear relationship between fault level, b-value, and N-value. Analyze the error between the predicted fault level and the original level, and the small error indicates that the model has good predictive ability. Applying this predictive ability to the reliability research of CNC machine tools will yield good results.

Evaluation of Regional Rural e-Commerce Development Potential with Intuitive Fuzzy Information Theory

In recent years, China’s Internet industry has developed rapidly, and the Internet has penetrated into all aspects of people’s daily lives. As an emerging transaction model, rural e-commerce is an important channel for precise poverty alleviation. To be specific, rural e-commerce can greatly change the lives of rural people in one way or other ways, thus allowing rural consumers to purchase high-quality and inexpensive goods without having to leave home. In other words, the introduction of national e-commerce into rural areas has changed the lifestyle of rural residents, providing them with great convenience in their daily lives. According to statistics, the level of rural e-commerce development in coastal areas is much higher than that in the mainland, while inland areas are hesitant to develop. Rural areas are a crucial component of Chinese society, and the rural economy is also the main driving force of China’s agricultural economy. In an environment where e-commerce is gradually penetrating various fields, the development of rural e-commerce in China has become more urgent with the new and growing rural demand. To be specific, the development of rural e-commerce has become a hot topic in recent years, and it is necessary to gather efforts from all sides to explore and innovate, so as to promote the healthy and orderly growth of rural e-commerce in China. As one of the effective ways to solve the problems of agricultural industry development and farmers’ affluence, rural e-commerce has played an increasingly obvious role in industrial development, poverty alleviation, employment, and solving the problems of selling agricultural products. At the same time, the proportion of national online sales of agricultural products is also increasing year by year. Many rural areas have abundant natural resources, rich history and culture, and a pleasant ecological environment. As a result, a great number of rural areas are well suited for e-commerce development in terms of the overall environment and physical resources. In recent years, the development of rural e-commerce in China has been very rapid, but it has also revealed many problems. Therefore, an in-depth study of the regional factors affecting the development of rural e-commerce is helpful to provide a reference for its better development. Based on the analysis of the current situation of rural e-commerce development, this study collects and organizes the indexes of influencing factors of rural e-commerce. The index system of influencing factors of rural e-commerce development is constructed through data collection and so on. After that, this study adopts the regional fuzzy information theory to evaluate the potential of rural e-commerce development, so as to obtain the main influencing factors of rural e-commerce development.

English Proficiency Evaluation Model of College Students by Using Intuitive Fuzzy Information Theory

English is a required university course in China and is a long-standing and consistent undergraduate-level course in China’s universities. It uses English as the medium and language of instruction to promote general education. As the most important content of undergraduate foreign language education, college English has different characteristics from other courses. It is only when its objectives, content, teaching activities, and assessment system fully reflect its unique requirements that it can truly achieve the ultimate goal of teaching this subject. With the advent of the information age, global economic integration and international exchange are deepening in various industries and fields. It is increasingly common for countries to require professionals to have foreign language skills, especially English as an international language. As a result, the demand for deeper English proficiency has become more prominent. In international communication, the English intercultural communication ability of key personnel directly affects the process of international communication, science and technology exchange, and the smooth transition of cultural conflicts in various fields and even determines the ultimate success of project cooperation. In this context, the effective use of English and cross-cultural communication skills is very important. Therefore, our higher education institutions are mainly responsible for training foreign language talents. However, the core problem facing English teaching in Chinese universities is the teaching value orientation. In particular, it seriously restricts the effectiveness of university English teaching. First, the value orientation of university English teaching deviates from the teaching objectives. It emphasizes the basic knowledge and skills of the English language, which makes teaching mainly stay on the foundation of the language. In other words, it is still limited to learning English for the sake of learning English, and the examination-oriented education is obvious, with a preference for instrumental teaching. Secondly, university English teaching focuses too much on the accumulation of English grammar rules and imitation drills, and the teaching style is dull and the teaching context is empty. This approach deviates from the characteristics of English intercultural communication, which makes the gap between the actual university English teaching and the real intercultural communication more and more obvious. Third, university English teaching lacks integration with other teaching values, especially with the humanistic orientation of university English teaching. Nowadays, a single teaching value orientation dominates university English teaching. As a result, the teaching around various English examinations has become a strange phenomenon in college English teaching.

Fuzzy ensemble of deep learning models using choquet fuzzy integral, coalition game and information theory for breast cancer histology classification

Millions of women, worldwide, suffer from breast cancer and a large number of them succumb to death. In recent years, computer-aided diagnosis (CAD) systems are being developed for the detection of Breast Cancer. A number of fusion techniques have been proposed in this domain, but none of them take into consideration the decisions taken by a subset of classifiers during fusion. Our method, which uses Choquet Integral, considers subsets of classifiers and is thus stronger than the existing methods and beat all of these existing fusion methods in terms of accuracy. This however poses a significant challenge in terms of complexity, since the calculation of the fuzzy measures is a complicated and complex task, which we have dealt with using a novel heuristic method by employing Coalition Game, Information Theory, and by defining a novel mathematical function. In the present work, we have fused VGG16, VGG19, Xception, Inception V3, and InceptionResnet V2 for the classification of breast cancer histology images using a Choquet integral, Coalition game theory, and Information theory. The dataset used for evaluating the proposed model is the ICIAR 2018 Grand Challenge on Breast Cancer Histology (popularly known as BACH) images, which consist of 2-class and 4-class problems. To the best of our knowledge, our experimental results outperform almost all the state-of-the-art methods. For the two-class problem, the best test accuracy among the five deep learning models was achieved by Xception and it was 95% while the Fusion method has a test accuracy of 96%. For the four-class problem, Xception and InceptionResnet V2 have achieved the best test accuracy and both have a test accuracy of 91% while the Fusion method has a test accuracy of 95%. Again, in the case of the two-class problem the best precision and recall by the deep learning models are 0.95 and 0.95 respectively, while the precision and recall for after fusion are 0.96 and 0.96 respectively which is an increase of .01. In the case of the four-class problem, the best precision and recall by the deep learning models are 0.91 and 0.91 respectively, while the precision and recall after fusion are 0.95 and 0.95 respectively which is a very significant increase of .04. The source code for this project can be accessed at https://github.com/subhankar01/fuzzyBACH

Many-objective Particle Swarm Optimization Algorithm Based on New Fitness Allocation and Multiply Cooperative Strategies

Many-objective optimization problems (MaOPs) refer to those multi-objective problems (MOPs) withmore than three objectives. In order to solve MaOPs, a multi-objective particle swarm optimization algorithm based on new fitness assignment and multi cooperation strategy(FAMSHMPSO) is proposed. Firstly, this paper proposes a new fitness allocation method based on fuzzy information theory to enhance the convergence of the algorithm. Then a new multi criteria mutation strategy is introduced to disturb the population and improve the diversity of the algorithm. Finally, the external files are maintained by the three-point shortest path method, which improves the quality of the solution. The performance of FAMSHMPSO algorithm is evaluated by evaluating the mean value, standard deviation and IGD+ index of the target value on dtlz test function set of different targets of FAMSHMPSO algorithm and other five representative multi-objective evolutionary algorithms. The experimental results show that FAMSHMPSO algorithm has obvious performance advantages in convergence, diversity and robustness.

Many-Objective Particle Swarm Optimization Algorithm Based on New Fitness Allocation and Multiple Cooperative Strategies

Many-objective optimization problems (MaOPs) refer to those multi-objective problems (MOPs) withmore than three objectives. In order to solve MaOPs, a multi-objective particle swarm optimization algorithm based on new fitness assignment and multi cooperation strategy(FAMSHMPSO) is proposed. Firstly, this paper proposes a new fitness allocation method based on fuzzy information theory to enhance the convergence of the algorithm. Then a new multi criteria mutation strategy is introduced to disturb the population and improve the diversity of the algorithm. Finally, the external files are maintained by the three-point shortest path method, which improves the quality of the solution. The performance of FAMSHMPSO algorithm is evaluated by evaluating the mean value, standard deviation and IGD+ index of the target value on dtlz test function set of different targets of FAMSHMPSO algorithm and other five representative multi-objective evolutionary algorithms. The experimental results show that FAMSHMPSO algorithm has obvious performance advantages in convergence, diversity and robustness.

A New Fuzzy Information Inequalities and its Applications in Establishing Relation among Fuzzy $f$-Divergence Measures

There are many fuzzy information and divergence measures exist in the literature of fuzzy Information Theory. Inequalities play important role for finding the relations. Here, we will introduce some new information inequalities on fuzzy measures and their applications in pattern recognition. Also established relations between new and well known fuzzy divergence measures with help of the fuzzy $f$-divergence measure and jensen’s inequality.

Maximum Fuzzy Correntropy Kalman Filter and Its Application to Bearings-Only Maneuvering Target Tracking

In this paper, a novel maximum fuzzy correntropy Kalman filter (MFC-KF) algorithm is proposed to solve the problem that the effect of different samples on state estimation is uncertain in common correntropy. In the proposed algorithm, a new optimization criterion—the maximum fuzzy correntropy criterion with fuzzy correntropy based on fuzzy information theory—is used to optimize the Kalman filter, by reducing the effect of the common correntropy applying the same weight for all samples. Moreover, to apply the MFC-KF algorithm to bearings-only maneuvering target tracking, it is combined with the least-squares method for measurement conversion. Moreover, the kernel width is set adaptively. Simulations show that the proposed algorithm can track a target more accurately than the interactive multi-model extended Kalman filter (IMMEKF), the interactive multi-model unscented Kalman filter (IMMUKF), or the maximum correntropy Kalman filter (MCKF).

Application of many-objective particle swarm algorithm based on fitness allocation in WSN coverage optimisation

In order to improve the situation that the Wireless Sensor Network (WSN) nodes in the random deployment are not uniform and improve the network coverage performance, many-objective Particle Swarm Algorithm based on Fitness Allocation (FAMPSO) is proposed. The algorithm combines the fuzzy information theory to associate the Ideal Solution (IS) with the Pareto Solution (PS) and proposes a new fitness allocation method, which increases the pressure of population selection and enhances the convergence of the algorithm. The FAMPSO algorithm is compared with three other representative multi-objective evolution algorithms on the DTLZ series test function set. At the same time, the FAMPSO algorithm was applied to the coverage optimisation of WSN, and the simulation analysis was carried out. The simulation results show that the FAMPSO algorithm has a significant performance advantage in terms of convergence, diversity and robustness. FAMPSO algorithm improves the coverage performance of WSN.

(1709-3928) MULTIPLE ATTRIBUTE GROUP DECISION MAKING WITH LINGUISTIC VARIABLES AND COMPLETE UNKNOWN WEIGHT INFORMATION

Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are a very useful means to depict the linguistic information in the process of decision making. In this article, we investigate the group decision making problems in which all the linguistic information provided by the decision makers is expressed as interval type-2 fuzzy decision matrices where each of the elements is characterized by interval type-2 fuzzy set, and the information about attribute weights is completely unknown.We first introduce the average centroid matrix of the interval type-2 fuzzy decision matrix, and then utilize the interval type-2 fuzzy averaging operator to aggregate all individual interval type-2 fuzzy decision matrices into a collective interval type-2 fuzzy decision matrix. Based on the average centroid matrix of the collective interval type-2 fuzzy decision matrix and information theory, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the interval type-2 fuzzy averaging operator, we utilize the average centroid measure to give an approach to ranking the given alternatives and then selecting the most desirable one(s). Finally, we give an illustrative example.

COMBINING FUZZY LOGIC AND INFORMATION THEORY FOR PRODUCING A LANDSLIDE SUSCEPTIBILITY MODEL

The main objective of the present study was to develop a landslide susceptibility model by combining Fuzzy logic and Information Theory in order to estimate the spatial probability of landslide manifestation, in the mountains of central Tzoumerka, Greece. Specifically, Fuzzy logic was enabled for weighting the landslide related variables based on expert knowledge and in respect to landslide susceptibility, while the Shannon’s entropy index, an index from Information Theory, was calculated to weight the significance of each landslide related variable based on the available data. The final landslide susceptibility map was produced by applying the weighted sum method. Engineering lithological units, slope angle, slope aspect, distance from tectonic features, distance from river network and distance from road network were among the six landslide related variables that were included in the landslide database used in the training phase. The landslide inventory map was constructed by interpreting aerial photographs, satellite images and field surveys and was separated into two datasets, one for training and one for validating the model. The outcomes of the validation process illustrated that the developed methodology efficiently provided the most susceptible areas and was in good agreement with the actual landslide locations. The area under the curve was estimated to be for the training and validating datasets 0.7575 and 0.7828 respectively. The produced landslide susceptibility map could be regarded from local and national authorities as a valuable mean to evaluate strategies or to prevent and mitigate the impact of landslides. Keywords: slope stability, fuzzy weighting, Shannon’s entropy index, Tzoumerka, Greece.

Fuzzy Adaptive Repetitive Control for Periodic Disturbance with Its Application to High Performance Permanent Magnet Synchronous Motor Speed Servo Systems

For reducing the steady state speed ripple, especially in high performance speed servo system applications, the steady state precision is more and more important for real servo systems. This paper investigates the steady state speed ripple periodic disturbance problem for a permanent magnet synchronous motor (PMSM) servo system; a fuzzy adaptive repetitive controller is designed in the speed loop based on repetitive control and fuzzy information theory for reducing periodic disturbance. Firstly, the various sources of the PMSM speed ripple problem are described and analyzed. Then, the mathematical model of PMSM is given. Subsequently, a fuzzy adaptive repetitive controller based on repetitive control and fuzzy logic control is designed for the PMSM speed servo system. In addition, the system stability analysis is also deduced. Finally, the simulation and experiment implementation are respectively based on the MATLAB/Simulink and TMS320F2808 of Texas instrument company, DSP (digital signal processor) hardware platform. Comparing to the proportional integral (PI) controller, simulation and experimental results show that the proposed fuzzy adaptive repetitive controller has better periodic disturbance rejection ability and higher steady state precision.

Decision Making Approach using Weighted Coefficient of Correlation along with Generalized Parametric Fuzzy Entropy Measure

Decision making involves various attributes along with several decision takers. Recently it has become more complex. This gives raise to uncertainty and associated with the information provided. So it may be appropriate to suggest that uncertainty demonstrates itself in numerous forms and of different types. Uncertainties may arise due to human behaviour, fluctuations of information, unknown facts. Fuzzy set theory is tool to deal with uncertainty in a better way. Both Fuzzy set theory and information theory are involved in dealing with various real-world problems such as segmentation of images, medical diagnosis, managerial decision making etc. Several methods and concepts dealing with imprecision and uncertainty have been proposed by many researchers. In the present communication, the authors have proposed a parametric generalization of entropy introduced by De Luca and Termini along with its basic properties. Further, a new measure of weighted coefficient of correlation is developed and applied to solve decision making problems involving uncertainty.

Two New Parametric Generalized R?Norm Fuzzy Information Measures

The paper introduces two new parametric generalizations of one of existing R  norm fuzzy information measures with the proof of their validity. In addition, particular cases and important properties of the proposed measures are discussed. A numerical example is given to establish the similarity between the proposed R  norm fuzzy information measures with one of the existing R  norm fuzzy information measures. Further, a comparison among them is shown with the help of a table and graph. General Terms Fuzzy Set Theory, Fuzzy Information Theory.

Analysis of algal bloom risk with uncertainties in lakes by integrating self-organizing map and fuzzy information theory

Algal blooms are a serious problem in waters, which damage aquatic ecosystems and threaten drinking water safety. However, the outbreak mechanism of algal blooms is very complex with great uncertainty, especially for large water bodies where environmental conditions have obvious variation in both space and time. This study developed an innovative method which integrated a self-organizing map (SOM) and fuzzy information diffusion theory to comprehensively analyze algal bloom risks with uncertainties. The Lake Taihu was taken as study case and the long-term (2004–2010) on-site monitoring data were used. The results showed that algal blooms in Taihu Lake were classified into four categories and exhibited obvious spatial–temporal patterns. The lake was mainly characterized by moderate bloom but had high uncertainty, whereas severe blooms with low uncertainty were observed in the northwest part of the lake. The study gives insight on the spatial–temporal dynamics of algal blooms, and should help government and decision-makers outline policies and practices on bloom monitoring and prevention. The developed method provides a promising approach to estimate algal bloom risks under uncertainties.

Ego-motion-compensated object recognition using type-2 fuzzy set for a moving robot

This paper presents an efficient stereovision-based motion compensation method for moving robots. The vision system of a moving robot enables it to detect and localize known objects in the images obtained from the camera mounted in its head. However, ego-motion causes some errors that need to be eliminated. We therefore propose an ego-motion compensation method that eliminates the errors in environment recognition caused by the ego-motion of a moving robot, in addition to efficiently improving recognition accuracy. The proposed method uses the disparity map obtained from three-dimensional (3D) vision and can be divided into three modules: segmentation, feature extraction, and estimation. In the segmentation module, we propose the use of extended type-2 fuzzy information theory (ET2FIT) to extract the objects. The results of using ET2FIT are then compared and analyzed to those obtained using type-2 fuzzy set and normal type-1 fuzzy set. The conventional fuzzy information theory [11] can only be applied to the binary image case. Therefore, we need to modify the existing method.In the feature extraction module, features are extracted using wavelet level-set transform, and least-square ellipse approximation is used in the estimation module to calculate the displacement for the rotation and translation between image sequences. The results of experiments indicate that our proposed method is highly effective when applied to moving robots, especially humanoid robots walking and operating in the real world.

Logo recognition based on membership degree and closeness degree of fuzzy sets

Fuzzy information theory which is based on fuzzy theory is a departure from information science. Higher performance could be obtained in pattern recognition with fuzzy sets theory. People combine fuzzy sets theory with pattern recognition and established fuzzy pattern recognition. This paper presents our work in the field of logo recognition by using fuzzy sets theory. Aim at the application requirement of logo recognition in image intelligent processing, a logo recognition algorithm based on membership degree and closeness degree of fuzzy sets is proposed. By fuzzy mapping, the logo's gridding feature is transformed to the membership degree of fuzzy sets; then using closeness degree and closest principle of fuzzy sets to accomplish logo recognition. The algorithm significantly enhances the adaptability and anti-interference to poor quality images and effectively improves the flexible processing capability of logo recognition system. Experimental results show that the recognition rate of this logo recognition algorithm can reach as high as 94.5%.

On Fuzzy Information Theory

Information theory is generally considered to have been founded in 1948 by Claude Shannon. In this paper we introduce the concept of fuzzy information theory using the notion of fuzzy sets. We study it and give some example of it.