"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 paper, we propose an intelligence approach based on fuzzy logic to modeling human intelligence in washing clothes. At first, an intelligent feedback loop is designed for perception-based sensing of dirt inspired by human color understanding. Then, when color stains leak out of some colored clothes the human probabilistic decision making is computationally modeled to detect this stain leakage and thus the problem of recognizing dirt from stain can be considered in the washing process. Finally, we discuss the fuzzy control of washing clothes and design and simulate a smart controller based on the fuzzy intelligence feedback loop.
FRI methods are less popular in the practical application domain. One possible reason is the missing common framework. There are many FRI methods developed independently, having different interpolation concepts and features. One trial for setting up a common FRI framework was the MATLAB FRI Toolbox, developed by Johany\'ak et. al. in 2006. The goals of this paper are divided as follows: firstly, to present a brief introduction of the FRI methods. Secondly, to introduce a brief description of the refreshed and extended version of the original FRI Toolbox. And thirdly, to use different unified numerical benchmark examples to evaluate and analyze the Fuzzy Rule Interpolation Techniques (FRI) (KH, KH Stabilized, MACI, IMUL, CRF, VKK, GM, FRIPOC, LESFRI, and SCALEMOVE), that will be classified and compared based on different features by following the abnormality and linearity conditions .
Supplier selection problem has gained extensive attention in the prior studies. However, research based on Fuzzy Multi-Attribute Decision Making (F-MADM) approach in ranking resilient suppliers in logistic 4.0 is still in its infancy. Traditional MADM approach fails to address the resilient supplier selection problem in logistic 4.0 primarily because of the large amount of data concerning some attributes that are quantitative, yet difficult to process while making decisions. Besides, some qualitative attributes prevalent in logistic 4.0 entail imprecise perceptual or judgmental decision relevant information, and are substantially different than those considered in traditional suppler selection problems. This study, for the first time, develops a Decision Support System (DSS) that will help the decision maker to incorporate and process such imprecise heterogeneous data in a unified framework to rank a set of resilient suppliers in the logistic 4.0 environment. The proposed framework induces a triangular fuzzy number from large-scale temporal data using probability-possibility consistency principle. Large number of non-temporal data presented graphically are computed by extracting granular information that are imprecise in nature. Fuzzy linguistic variables are used to map the qualitative attributes. Finally, fuzzy based TOPSIS method is adopted to generate the ranking score of alternative suppliers. These ranking scores are used as input in a Multi-Choice Goal Programming (MCGP) model to determine optimal order allocation for respective suppliers. Finally, a sensitivity analysis assesses how the Cost versus Resilience Index (SCRI) changes when differential priorities are set for respective cost and resilience attributes.
Artificial intelligence (AI) is dominated by pattern recognition techniques. Recently, major advances have been made in the fields of image recognition, machine translation, audio processing and several others thanks to the development and refinement of deep learning. But deep learning is not the cure for every problem. In fact, it can be a disease in its own right. No biological system, even over generations of evolution, requires the same scale of training data for simple tasks that state-of-the-art machine learning algorithms require.
Takagi-Sugeno-Kang (TSK) fuzzy systems are very useful machine learning models for regression problems. However, to our knowledge, there has not existed an efficient and effective training algorithm that enables them to deal with big data. Inspired by the connections between TSK fuzzy systems and neural networks, we extend three powerful neural network optimization techniques, i.e., mini-batch gradient descent, regularization, and AdaBound, to TSK fuzzy systems, and also propose a novel DropRule technique specifically for training TSK fuzzy systems. Our final algorithm, mini-batch gradient descent with regularization, DropRule and AdaBound (MBGD-RDA), can achieve fast convergence in training TSK fuzzy systems, and also superior generalization performance in testing. It can be used for training TSK fuzzy systems on datasets of any size; however, it is particularly useful for big datasets, on which currently no other efficient training algorithms exist.
Fuzzy systems have achieved great success in numerous applications. However, there are still many challenges in designing an optimal fuzzy system, e.g., how to efficiently train its parameters, how to improve its performance without adding too many parameters, how to balance the trade-off between cooperations and competitions among the rules, how to overcome the curse of dimensionality, etc. Literature has shown that by making appropriate connections between fuzzy systems and other machine learning approaches, good practices from other domains may be used to improve the fuzzy systems, and vice versa. This paper gives an overview on the functional equivalence between Takagi-Sugeno-Kang fuzzy systems and four classic machine learning approaches -- neural networks, mixture of experts, classification and regression trees, and stacking ensemble regression -- for regression problems. We also point out some promising new research directions, inspired by the functional equivalence, that could lead to solutions to the aforementioned problems. To our knowledge, this is so far the most comprehensive overview on the connections between fuzzy systems and other popular machine learning approaches, and hopefully will stimulate more hybridization between different machine learning algorithms.
The Era of Big Data has forced researchers to explore new distributed solutions for building fuzzy classifiers, which often introduce approximation errors or make strong assumptions to reduce computational and memory requirements. As a result, Big Data classifiers might be expected to be inferior to those designed for standard classification tasks (Small Data) in terms of accuracy and model complexity. To our knowledge, however, there is no empirical evidence to confirm such a conjecture yet. Here, we investigate the extent to which state-of-the-art fuzzy classifiers for Big Data sacrifice performance in favor of scalability. To this end, we carry out an empirical study that compares these classifiers with some of the best performing algorithms for Small Data. Assuming the latter were generally designed for maximizing performance without considering scalability issues, the results of this study provide some intuition around the tradeoff between performance and scalability achieved by current Big Data solutions. Our findings show that, although slightly inferior, Big Data classifiers are gradually catching up with state-of-the-art classifiers for Small data, suggesting that a unified learning algorithm for Big and Small Data might be possible.
This paper shows that the fuzzy temporal logic can model figures of thought to describe decision-making behaviors. In order to exemplify, some economic behaviors observed experimentally were modeled from problems of choice containing time, uncertainty and fuzziness. Related to time preference, it is noted that the subadditive discounting is mandatory in positive rewards situations and, consequently, results in the magnitude effect and time effect, where the last has a stronger discounting for earlier delay periods (as in, one hour, one day), but a weaker discounting for longer delay periods (for instance, six months, one year, ten years). In addition, it is possible to explain the preference reversal (change of preference when two rewards proposed on different dates are shifted in the time). Related to the Prospect Theory, it is shown that the risk seeking and the risk aversion are magnitude dependents, where the risk seeking may disappear when the values to be lost are very high.
Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited. One exception is Rowland et al. (2018)'s analysis of the C51 algorithm in terms of the Cram\'er distance, but their results only apply to the tabular setting and ignore C51's use of a softmax to produce normalized distributions. In this paper we adapt the Cram\'er distance to deal with arbitrary vectors. From it we derive a new distributional algorithm which is fully Cram\'er-based and can be combined to linear function approximation, with formal guarantees in the context of policy evaluation. In allowing the model's prediction to be any real vector, we lose the probabilistic interpretation behind the method, but otherwise maintain the appealing properties of distributional approaches. To the best of our knowledge, ours is the first proof of convergence of a distributional algorithm combined with function approximation. Perhaps surprisingly, our results provide evidence that Cram\'er-based distributional methods may perform worse than directly approximating the value function.
This paper introduces Bounded Fuzzy Possibilistic Method (BFPM) by addressing several issues that previous clustering/classification methods have not considered. In fuzzy clustering, object's membership values should sum to 1. Hence, any object may obtain full membership in at most one cluster. Possibilistic clustering methods remove this restriction. However, BFPM differs from previous fuzzy and possibilistic clustering approaches by allowing the membership function to take larger values with respect to all clusters. Furthermore, in BFPM, a data object can have full membership in multiple clusters or even in all clusters. BFPM relaxes the boundary conditions (restrictions) in membership assignment. The proposed methodology satisfies the necessity of obtaining full memberships and overcomes the issues with conventional methods on dealing with overlapping. Analysing the objects' movements from their own cluster to another (mutation) is also proposed in this paper. BFPM has been applied in different domains in geometry, set theory, anomaly detection, risk management, diagnosis diseases, and other disciplines. Validity and comparison indexes have been also used to evaluate the accuracy of BFPM. BFPM has been evaluated in terms of accuracy, fuzzification constant (different norms), objects' movement analysis, and covering diversity. The promising results prove the importance of considering the proposed methodology in learning methods to track the behaviour of data objects, in addition to obtain accurate results.