THE REAL-WORLD-SEMANTICS INTERPRETABILITY OF LINGUISTIC RULE BASES AND THE APPROXIMATE REASONING METHOD OF FUZZY SYSTEMS

The real-world-semantics interpretability concept of fuzzy systems introduced in [1] is new for the both methodology and application and is necessary to meet the demand of establishing a mathematical basis to construct computational semantics of linguistic words so that a method developed based on handling the computational semantics of linguistic terms to simulate a human method immediately handling words can produce outputs similar to the one produced by the human method. As the real world of each application problem having its own structure which is described by certain linguistic expressions, this requirement can be ensured by imposing constraints on the interpretation assigning computational objects in the appropriate computational structure to the words so that the relationships between the computational semantics in the computational structure is the image of relationships between the real-world objects described by the word-expressions. This study will discuss more clearly the concept of real-world-semantics interpretability and point out that such requirement is a challenge to the study of the interpretability of fuzzy systems, especially for approaches within the fuzzy set framework. A methodological challenge is that it requires both the computational expression representing a given linguistic fuzzy rule base and an approximate reasoning method working on this computation expression must also preserve the real-world semantics of the application problem. Fortunately, the hedge algebra (HA) based approach demonstrates the expectation that the graphical representation of the rule of fuzzy systems and the interpolation reasoning method on them are able to preserve the real-world semantics of the real-world counterpart of the given application problem

Evolutionary Learning of Fuzzy Rules for Regression

The objective of this PhD Thesis is to design Genetic Fuzzy Systems (GFS) that learn Fuzzy Rule Based Systems to solve regression problems in a general manner. Particularly, the aim is to obtain models with low complexity while maintaining high precision without using expert-knowledge about the problem to be solved. This means that the GFSs have to work with raw data, that is, without any preprocessing that help the learning process to solve a particular problem. This is of particular interest, when no knowledge about the input data is available or for a first approximation to the problem. Moreover, within this objective, GFSs have to cope with large scale problems, thus the algorithms have to scale with the data

A cloned linguistic decision tree controller for real-time path planning in hostile environments

AbstractThe idea of a Cloned Controller to approximate optimised control algorithms in a real-time environment is introduced. A Cloned Controller is demonstrated using Linguistic Decision Trees (LDTs) to clone a Model Predictive Controller (MPC) based on Mixed Integer Linear Programming (MILP) for Unmanned Aerial Vehicle (UAV) path planning through a hostile environment. Modifications to the LDT algorithm are proposed to account for attributes with circular domains, such as bearings, and discontinuous output functions. The cloned controller is shown to produce near optimal paths whilst significantly reducing the decision period. Further investigation shows that the cloned controller generalises to the multi-obstacle case although this can lead to situations far outside of the training dataset and consequently result in decisions with a high level of uncertainty. A modification to the algorithm to improve the performance in regions of high uncertainty is proposed and shown to further enhance generalisation. The resulting controller combines the high performance of MPC–MILP with the rapid response of an LDT while providing a degree of transparency/interpretability of the decision making

Optimization of fuzzy rule sets using a bacterial evolutionary algorithm

In this paper we present a novel approach where we rst create a large set of (possibly) redundant rules using inductive rule learning and where we use a bacterial evolutionary algorithm to identify the best subset of rules in a subsequent step. This enables us to nd an optimal rule set with respect to a freely de nable global goal function, which gives us the possibility to integrate interpretability related quality criteria explicitly in the goal function and to consider the interplay of the overlapping fuzzy rulesPeer Reviewe

An overview of recent distributed algorithms for learning fuzzy models in Big Data classification

AbstractNowadays, a huge amount of data are generated, often in very short time intervals and in various formats, by a number of different heterogeneous sources such as social networks and media, mobile devices, internet transactions, networked devices and sensors. These data, identified as Big Data in the literature, are characterized by the popular Vs features, such as Value, Veracity, Variety, Velocity and Volume. In particular, Value focuses on the useful knowledge that may be mined from data. Thus, in the last years, a number of data mining and machine learning algorithms have been proposed to extract knowledge from Big Data. These algorithms have been generally implemented by using ad-hoc programming paradigms, such as MapReduce, on specific distributed computing frameworks, such as Apache Hadoop and Apache Spark. In the context of Big Data, fuzzy models are currently playing a significant role, thanks to their capability of handling vague and imprecise data and their innate characteristic to be interpretable. In this work, we give an overview of the most recent distributed learning algorithms for generating fuzzy classification models for Big Data. In particular, we first show some design and implementation details of these learning algorithms. Thereafter, we compare them in terms of accuracy and interpretability. Finally, we argue about their scalability

Evolutionary Fuzzy Systems for Explainable Artificial Intelligence: Why, When, What for, and Where to?

Evolutionary fuzzy systems are one of the greatest advances within the area of computational intelligence. They consist of evolutionary algorithms applied to the design of fuzzy systems. Thanks to this hybridization, superb abilities are provided to fuzzy modeling in many different data science scenarios. This contribution is intended to comprise a position paper developing a comprehensive analysis of the evolutionary fuzzy systems research field. To this end, the "4 W" questions are posed and addressed with the aim of understanding the current context of this topic and its significance. Specifically, it will be pointed out why evolutionary fuzzy systems are important from an explainable point of view, when they began, what they are used for, and where the attention of researchers should be directed to in the near future in this area. They must play an important role for the emerging area of eXplainable Artificial Intelligence (XAI) learning from data

Literature Review of the Recent Trends and Applications in various Fuzzy Rule based systems

Fuzzy rule based systems (FRBSs) is a rule-based system which uses linguistic fuzzy variables as antecedents and consequent to represent human understandable knowledge. They have been applied to various applications and areas throughout the soft computing literature. However, FRBSs suffers from many drawbacks such as uncertainty representation, high number of rules, interpretability loss, high computational time for learning etc. To overcome these issues with FRBSs, there exists many extensions of FRBSs. This paper presents an overview and literature review of recent trends on various types and prominent areas of fuzzy systems (FRBSs) namely genetic fuzzy system (GFS), hierarchical fuzzy system (HFS), neuro fuzzy system (NFS), evolving fuzzy system (eFS), FRBSs for big data, FRBSs for imbalanced data, interpretability in FRBSs and FRBSs which use cluster centroids as fuzzy rules. The review is for years 2010-2021. This paper also highlights important contributions, publication statistics and current trends in the field. The paper also addresses several open research areas which need further attention from the FRBSs research community.Comment: 49 pages, Accepted for publication in ijf

A HEDGE ALGEBRAS BASED CLASSIFICATION REASONING METHOD WITH MULTI-GRANULARITY FUZZY PARTITIONING

During last years, lots of the fuzzy rule based classifier (FRBC) design methods have been proposed to improve the classification accuracy and the interpretability of the proposed classification models. Most of them are based on the fuzzy set theory approach in such a way that the fuzzy classification rules are generated from the grid partitions combined with the pre-designed fuzzy partitions using fuzzy sets. Some mechanisms are studied to automatically generate fuzzy partitions from data such as discretization, granular computing, etc. Even those, linguistic terms are intuitively assigned to fuzzy sets because there is no formalisms to link inherent semantics of linguistic terms to fuzzy sets. In view of that trend, genetic design methods of linguistic terms along with their (triangular and trapezoidal) fuzzy sets based semantics for FRBCs, using hedge algebras as the mathematical formalism, have been proposed. Those hedge algebras-based design methods utilize semantically quantifying mapping values of linguistic terms to generate their fuzzy sets based semantics so as to make use of fuzzy sets based-classification reasoning methods proposed in design methods based on fuzzy set theoretic approach for data classification. If there exists a classification reasoning method which bases merely on semantic parameters of hedge algebras, fuzzy sets-based semantics of the linguistic terms in fuzzy classification rule bases can be replaced by semantics - based hedge algebras. This paper presents a FRBC design method based on hedge algebras approach by introducing a hedge algebra- based classification reasoning method with multi-granularity fuzzy partitioning for data classification so that the semantic of linguistic terms in rule bases can be hedge algebras-based semantics. Experimental results over 17 real world datasets are compared to existing methods based on hedge algebras and the state-of-the-art fuzzy sets theoretic-based approaches, showing that the proposed FRBC in this paper is an effective classifier and produces good results