"Fuzzy Logic is basically a multivalued logic that allows intermediate values to be defined between conventional evaluations like yes/no, true/false, black/white, etc. Notions like rather warm or pretty cold can be formulated mathematically and processed by computers."
– Peter Bauer, Stephan Nouak, and Roman Winkler. A Brief Course in Fuzzy Logic and Fuzzy Control. Available from ESRU [Energy Systems Research Unit], Department of Mechanical Engineering, University of Strathclyde. 1996.
In this exploratory article, we draw attention to the common formal ground among various estimators such as the belief functions of evidence theory and their relatives, approximation quality of rough set theory, and contextual probability. The unifying concept will be a general filter function composed of a basic probability and a weighting which varies according to the problem at hand. To compare the various filter functions we conclude with a simulation study with an example from the area of item response theory.
Cluster analysis is widely used in the areas of machine learning and data mining. Fuzzy clustering is a particular method that considers that a data point can belong to more than one cluster. Fuzzy clustering helps obtain flexible clusters, as needed in such applications as text categorization. The performance of a clustering algorithm critically depends on the number of clusters, and estimating the optimal number of clusters is a challenging task. Quality indices help estimate the optimal number of clusters. However, there is no quality index that can obtain an accurate number of clusters for different datasets. Thence, in this paper, we propose a new cluster quality index associated with a visual, graph-based solution that helps choose the optimal number of clusters in fuzzy partitions. Moreover, we validate our theoretical results through extensive comparison experiments against state-of-the-art quality indices on a variety of numerical real-world and artificial datasets.
Resilient supplier selection problem is a key decision problem for an organization to gain competitive advantage. In the presence of multiple conflicting evaluation criteria, contradicting decision makers, and imprecise information sources, this problem becomes even more difficult to solve with the classical optimization approaches. Multi-Criteria Decision Analysis (MCDA) is a viable alternative approach for handling the imprecise information associated with the evaluation proffered by the decision makers. In this work, we present a comprehensive algorithm for ranking a set of suppliers based on aggregated information obtained from crisp numerical assessments and reliability adjusted linguistic appraisals from a group of decision makers. We adapted two popular tools - Single Valued Neutrosophic Sets (SVNS) and Interval-valued fuzzy sets (IVFS) and extended them to incorporate both crisp and linguistic evaluations from the decision makers to obtain aggregated SVNS and IVFS. This information is then used to rank the suppliers by using TOPSIS method. We present a case study to illustrate the mechanism of the proposed algorithm and show sensitivity of the supplier ranking with respect to the priorities of evaluation criteria.
In this study, we present a hierarchical fuzzy system by evaluating the risk state for a Driver Assistance System in order to contribute in reducing the road accident's number. A key component of this system is its ability to continually detect and test the inside and outside risks in real time: The outside car risks by detecting various road moving objects; this proposed system stands on computer vision approaches. The inside risks by presenting an automatic system for drowsy driving identification or detection by evaluating EEG signals of the driver; this developed system is based on computer vision techniques and biometrics factors (electroencephalogram EEG). This proposed system is then composed of three main modules. The first module is responsible for identifying the driver drowsiness state through his eye movements (physical drowsiness). The second one is responsible for detecting and analysing his physiological signals to also identify his drowsiness state (moral drowsiness). The third module is responsible to evaluate the road driving risks by detecting of the road different moving objects in a real time. The final decision will be obtained by merging of the three detection systems through the use of fuzzy decision rules. Finally, the proposed approach has been improved on ten samples from a proposed dataset.
Mao H. (2017, Representing attribute reduction and concepts in concept lattice using graphs. Soft Computing 21(24):7293--7311) claims to make contributions to the study of reduction of attributes in concept lattices by using graph theory. We show that her results are either trivial or already well-known and all three algorithms proposed in the paper are incorrect.
We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempster's multivalued mappings and lower and upper probabilities and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set if those sets are related by a partial monotone S-approximation space.
Mathematics has played a substantial role to revolutionize the medical science. Intelligent systems based on mathematical theories have proved to be efficient in diagnosing various diseases. In this paper, we used an expert system based on soft set theory and fuzzy set theory named as a soft expert system to diagnose tropical disease dengue. The objective to use soft expert system is to predict the risk level of a patient having dengue fever by using input variables like age, TLC, SGOT, platelets count and blood pressure. The proposed method explicitly demonstrates the exact percentage of the risk level of dengue fever automatically circumventing for all possible (medical) imprecisions.
The system's ability to adapt and self-organize are two key factors when it comes to how well the system can survive the changes to the environment and the plant they work within. Intelligent control improves these two factors in controllers. Considering the increasing complexity of dynamic systems along with their need for feedback controls, using more complicated controls has become necessary and intelligent control can be a suitable response to this necessity. This paper briefly describes the structure of intelligent control and provides a review on fuzzy logic and neural networks which are some of the base methods for intelligent control. The different aspects of these two methods are then compared together and an example of a combined method is presented.
Autonomously training interpretable control strategies, called policies, using pre-existing plant trajectory data is of great interest in industrial applications. Fuzzy controllers have been used in industry for decades as interpretable and efficient system controllers. In this study, we introduce a fuzzy genetic programming (GP) approach called fuzzy GP reinforcement learning (FGPRL) that can select the relevant state features, determine the size of the required fuzzy rule set, and automatically adjust all the controller parameters simultaneously. Each GP individual's fitness is computed using model-based batch reinforcement learning (RL), which first trains a model using available system samples and subsequently performs Monte Carlo rollouts to predict each policy candidate's performance. We compare FGPRL to an extended version of a related method called fuzzy particle swarm reinforcement learning (FPSRL), which uses swarm intelligence to tune the fuzzy policy parameters. Experiments using an industrial benchmark show that FGPRL is able to autonomously learn interpretable fuzzy policies with high control performance.
Rehabilitation robotics combined with video game technology provides a means of assisting in the rehabilitation of patients with neuromuscular disorders by performing various facilitation movements. The current work presents ReHabGame, a serious game using a fusion of implemented technologies that can be easily used by patients and therapists to assess and enhance sensorimotor performance and also increase the activities in the daily lives of patients. The game allows a player to control avatar movements through a Kinect Xbox, Myo armband and rudder foot pedal, and involves a series of reach-grasp-collect tasks whose difficulty levels are learnt by a fuzzy interface. The orientation, angular velocity, head and spine tilts and other data generated by the player are monitored and saved, whilst the task completion is calculated by solving an inverse kinematics algorithm which orientates the upper limb joints of the avatar. The different values in upper body quantities of movement provide fuzzy input from which crisp output is determined and used to generate an appropriate subsequent rehabilitation game level. The system can thus provide personalised, autonomously-learnt rehabilitation programmes for patients with neuromuscular disorders with superior predictions to guide the development of improved clinical protocols compared to traditional theraputic activities.