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Fuzzy Logic: Instructional Materials


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Fuzzy Logic isn't often mentioned in the same room as Artificial Intelligence (AI). Pardon the pun, but most people find the idea of fuzzy logic to be fuzzy. However fuzzy logic has been working behind the scenes and bringing forth amazing technological advances for more than two decades. Fuzzy logic is a rule-based system that can rely on the practical experience of a data scientist or an expert. Fuzzy logic is a form of artificial intelligence, thus it is considered a subset of AI. Since it is performing a form of decision making, it can be included as a member of the AI family which includes Machine Learning and Deep Learning.


An Adaptive Neuro-Fuzzy System with Integrated Feature Selection and Rule Extraction for High-Dimensional Classification Problems

arXiv.org Artificial Intelligence

A major limitation of fuzzy or neuro-fuzzy systems is their failure to deal with high-dimensional datasets. This happens primarily due to the use of T-norm, particularly, product or minimum (or a softer version of it). Thus, there are hardly any work dealing with datasets with dimensions more than hundred or so. Here, we propose a neuro-fuzzy framework that can handle datasets with dimensions even more than 7000! In this context, we propose an adaptive softmin (Ada-softmin) which effectively overcomes the drawbacks of ``numeric underflow" and ``fake minimum" that arise for existing fuzzy systems while dealing with high-dimensional problems. We call it an Adaptive Takagi-Sugeno-Kang (AdaTSK) fuzzy system. We then equip the AdaTSK system to perform feature selection and rule extraction in an integrated manner. In this context, a novel gate function is introduced and embedded only in the consequent parts, which can determine the useful features and rules, in two successive phases of learning. Unlike conventional fuzzy rule bases, we design an enhanced fuzzy rule base (En-FRB), which maintains adequate rules but does not grow the number of rules exponentially with dimension that typically happens for fuzzy neural networks. The integrated Feature Selection and Rule Extraction AdaTSK (FSRE-AdaTSK) system consists of three sequential phases: (i) feature selection, (ii) rule extraction, and (iii) fine tuning. The effectiveness of the FSRE-AdaTSK is demonstrated on 19 datasets of which five are in more than 2000 dimension including two with dimension greater than 7000. This may be the first time fuzzy systems are realized for classification involving more than 7000 input features.


GBRS: An Unified Model of Pawlak Rough Set and Neighborhood Rough Set

arXiv.org Artificial Intelligence

Pawlak rough set and neighborhood rough set are the two most common rough set theoretical models. Pawlawk can use equivalence classes to represent knowledge, but it cannot process continuous data; neighborhood rough sets can process continuous data, but it loses the ability of using equivalence classes to represent knowledge. To this end, this paper presents a granular-ball rough set based on the granlar-ball computing. The granular-ball rough set can simultaneously represent Pawlak rough sets, and the neighborhood rough set, so as to realize the unified representation of the two. This makes the granular-ball rough set not only can deal with continuous data, but also can use equivalence classes for knowledge representation. In addition, we propose an implementation algorithms of granular-ball rough sets. The experimental resuts on benchmark datasets demonstrate that, due to the combination of the robustness and adaptability of the granular-ball computing, the learning accuracy of the granular-ball rough set has been greatly improved compared with the Pawlak rough set and the traditional neighborhood rough set. The granular-ball rough set also outperforms nine popular or the state-of-the-art feature selection methods.


Time Series Forecasting Using Fuzzy Cognitive Maps: A Survey

arXiv.org Artificial Intelligence

Increasing complexity comes from some factors including uncertainty, ambiguity, inconsistency, multiple dimensionalities, increasing the number of effective factors and relation between them. Some of these features are common among most real-world problems which are considered complex and dynamic problems. In other words, since the data and relations in real world applications are usually highly complex and inaccurate, modeling real complex systems based on observed data is a challenging task especially for large scale, inaccurate and non stationary datasets. Therefore, to cover and address these difficulties, the existence of a computational system with the capability of extracting knowledge from the complex system with the ability to simulate its behavior is essential. In other words, it is needed to find a robust approach and solution to handle real complex problems in an easy and meaningful way [1]. Hard computing methods depend on quantitative values with expensive solutions and lack of ability to represent the problem in real life due to some uncertainties. In contrast, soft computing approaches act as alternative tools to deal with the reasoning of complex problems [2]. Using soft computing methods such as fuzzy logic, neural network, genetic algorithms or a combination of these allows achieving robustness, tractable and more practical solutions. Generally, two types of methods are used for analyzing and modeling dynamic systems including quantitative and qualitative approaches.


Introducing Randomized High Order Fuzzy Cognitive Maps as Reservoir Computing Models: A Case Study in Solar Energy and Load Forecasting

arXiv.org Artificial Intelligence

Fuzzy Cognitive Maps (FCMs) have emerged as an interpretable signed weighted digraph method consisting of nodes (concepts) and weights which represent the dependencies among the concepts. Although FCMs have attained considerable achievements in various time series prediction applications, designing an FCM model with time-efficient training method is still an open challenge. Thus, this paper introduces a novel univariate time series forecasting technique, which is composed of a group of randomized high order FCM models labeled R-HFCM. The novelty of the proposed R-HFCM model is relevant to merging the concepts of FCM and Echo State Network (ESN) as an efficient and particular family of Reservoir Computing (RC) models, where the least squares algorithm is applied to train the model. From another perspective, the structure of R-HFCM consists of the input layer, reservoir layer, and output layer in which only the output layer is trainable while the weights of each sub-reservoir components are selected randomly and keep constant during the training process. As case studies, this model considers solar energy forecasting with public data for Brazilian solar stations as well as Malaysia dataset, which includes hourly electric load and temperature data of the power supply company of the city of Johor in Malaysia. The experiment also includes the effect of the map size, activation function, the presence of bias and the size of the reservoir on the accuracy of R-HFCM method. The obtained results confirm the outperformance of the proposed R-HFCM model in comparison to the other methods. This study provides evidence that FCM can be a new way to implement a reservoir of dynamics in time series modelling.


Forecasting: theory and practice

arXiv.org Machine Learning

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.


Fuzzy Win-Win: A Novel Approach to Quantify Win-Win Using Fuzzy Logic

arXiv.org Artificial Intelligence

The classic win-win has a key flaw in that it cannot offer the parties the right amounts of winning because each party believes they are winners. In reality, one party may win more than the other. This strategy is not limited to a single product or negotiation; it may be applied to a variety of situations in life. We present a novel way to measure the win-win situation in this paper. The proposed method employs Fuzzy logic to create a mathematical model that aids negotiators in quantifying their winning percentages. The model is put to the test on real-life negotiations scenarios such as the Iranian uranium enrichment negotiations, the Iraqi-Jordanian oil deal, and the iron ore negotiation (2005-2009). The presented model has shown to be a useful tool in practice and can be easily generalized to be utilized in other domains as well.


First-Order Regret in Reinforcement Learning with Linear Function Approximation: A Robust Estimation Approach

arXiv.org Machine Learning

Obtaining first-order regret bounds -- regret bounds scaling not as the worst-case but with some measure of the performance of the optimal policy on a given instance -- is a core question in sequential decision-making. While such bounds exist in many settings, they have proven elusive in reinforcement learning with large state spaces. In this work we address this gap, and show that it is possible to obtain regret scaling as $\mathcal{O}(\sqrt{V_1^\star K})$ in reinforcement learning with large state spaces, namely the linear MDP setting. Here $V_1^\star$ is the value of the optimal policy and $K$ is the number of episodes. We demonstrate that existing techniques based on least squares estimation are insufficient to obtain this result, and instead develop a novel robust self-normalized concentration bound based on the robust Catoni mean estimator, which may be of independent interest.


Learning Stochastic Shortest Path with Linear Function Approximation

arXiv.org Machine Learning

The Stochastic Shortest Path (SSP) model refers to a type of reinforcement learning (RL) problems where an agent repeatedly interacts with a stochastic environment and aims to reach some specific goal state while minimizing the cumulative cost. Compared with other popular RL settings such as episodic and infinite-horizon Markov Decision Processes (MDPs), the horizon length in SSP is random, varies across different policies, and can potentially be infinite because the interaction only stops when arriving at the goal state. Therefore, the SSP model includes both episodic and infinitehorizon MDPs as special cases, and is comparably more general and of broader applicability. In particular, many goal-oriented real-world problems fit better into the SSP model, such as navigation and GO game (Andrychowicz et al., 2017; Nasiriany et al., 2019). In recent years, there emerges a line of works on developing efficient algorithms and the corresponding analyses for learning SSP. Most of them consider the episodic setting, where the interaction between the agent and the environment proceeds in K episodes (Cohen et al., 2020; Tarbouriech et al., 2020a). For tabular SSP models where the sizes of the action and state space are finite, Cohen et al. (2021) developed a finite-horizon reduction algorithm that achieves the minimax


Learner to learner fuzzy profiles similarity using a hybrid interaction analysis grid

arXiv.org Artificial Intelligence

The analysis of remote discussions is not yet at the same level as the face-to-face ones. The present paper aspires two-fold. On the one hand, it attempts to establish a suitable environment of interaction and collaboration among learners by using the speech acts via a semi structured synchronous communication tool. On the other, it aims to define behavioral profiles and interpersonal skills hybrid grid by matching the BALES' IPA and PLETY's analysis system. By applying the fuzzy logic, we formalize human reasoning and, thus, giving very appreciable flexibility to the reasoning that use it, which makes it possible to take into account imprecisions and uncertainties. In addition, the educational data mining techniques are used to optimize the mapping of behaviors to learner's profile, with similarity-based clustering, using Eros and PCA measures. In order to show the validity of our system, we performed an experiment on real-world data. The results show, among others: (1) the usefulness of fuzzy logic to properly translate the profile text descriptions into a mathematical format, (2) an irregularity in the behavior of the learners, (3) the correlation between the profiles, (4) the superiority of Eros method to the PCA factor in precision.