Automatic synthesis of fuzzy systems: An evolutionary overview with a genetic programming perspective

Studies in Evolutionary Fuzzy Systems (EFSs) began in the 90s and have experienced a fast development since then, with applications to areas such as pattern recognition, curve‐fitting and regression, forecasting and control. An EFS results from the combination of a Fuzzy Inference System (FIS) with an Evolutionary Algorithm (EA). This relationship can be established for multiple purposes: fine‐tuning of FIS's parameters, selection of fuzzy rules, learning a rule base or membership functions from scratch, and so forth. Each facet of this relationship creates a strand in the literature, as membership function fine‐tuning, fuzzy rule‐based learning, and so forth and the purpose here is to outline some of what has been done in each aspect. Special focus is given to Genetic Programming‐based EFSs by providing a taxonomy of the main architectures available, as well as by pointing out the gaps that still prevail in the literature. The concluding remarks address some further topics of current research and trends, such as interpretability analysis, multiobjective optimization, and synthesis of a FIS through Evolving methods

Improving Transparency in Approximate Fuzzy Modeling Using Multi-objective Immune-Inspired Optimisation

In this paper, an immune inspired multi-objective fuzzy modeling (IMOFM) mechanism is proposed specifically for high-dimensional regression problems. For such problems, prediction accuracy is often the paramount requirement. With such a requirement in mind, however, one should also put considerable efforts in eliciting models which are as transparent as possible, a ‘tricky’ exercise in itself. The proposed mechanism adopts a multi-stage modeling procedure and a variable length coding scheme to account for the enlarged search space due to simultaneous optimisation of the rule-base structure and its associated parameters. We claim here that IMOFM can account for both Singleton and Mamdani Fuzzy Rule-Based Systems (FRBS) due to the carefully chosen output membership functions, the inference scheme and the defuzzification method. The proposed modeling approach has been compared to other representatives using a benchmark problem, and was further applied to a high-dimensional problem, taken from the steel industry, which concerns the prediction of mechanical properties of hot rolled steels. Results confirm that IMOFM is capable of eliciting not only accurate but also transparent FRBSs from quantitative data

Multiobjective programming for type-2 hierarchical fuzzy inference trees

This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An HFIT produces an optimum tree-like structure. Specifically, a natural hierarchical structure that accommodates simplicity by combining several low-dimensional fuzzy inference systems (FISs). Such a natural hierarchical structure provides a high degree of approximation accuracy. The construction of HFIT takes place in two phases. Firstly, a nondominated sorting based multiobjective genetic programming (MOGP) is applied to obtain a simple tree structure (low model’s complexity) with a high accuracy. Secondly, the differential evolution algorithm is applied to optimize the obtained tree’s parameters. In the obtained tree, each node has a different input’s combination, where the evolutionary process governs the input’s combination. Hence, HFIT nodes are heterogeneous in nature, which leads to a high diversity among the rules generated by the HFIT. Additionally, the HFIT provides an automatic feature selection because it uses MOGP for the tree’s structural optimization that accept inputs only relevant to the knowledge contained in data. The HFIT was studied in the context of both type-1 and type-2 FISs, and its performance was evaluated through six application problems. Moreover, the proposed multiobjective HFIT was compared both theoretically and empirically with recently proposed FISs methods from the literature, such as McIT2FIS, TSCIT2FNN, SIT2FNN, RIT2FNS-WB, eT2FIS, MRIT2NFS, IT2FNN-SVR, etc. From the obtained results, it was found that the HFIT provided less complex and highly accurate models compared to the models produced by most of the other methods. Hence, the proposed HFIT is an efficient and competitive alternative to the other FISs for function approximation and feature selectio

An experimental study of a fuzzy adaptive emperor penguin optimizer for global optimization problem

Emperor Penguin Optimizer (EPO) is a recently developed population-based meta-heuristic algorithm that simulates the huddling behavior of emperor penguins. Mixed results have been observed on the performance of EPO in solving general optimization problems. Within the EPO, two parameters need to be tuned (namely f and l ) to ensure a good balance between exploration (i.e., roaming unknown locations) and exploitation (i.e., manipulating the current known best). Since the search contour varies depending on the optimization problem, the tuning of f and l is problem-dependent, and there is no one-size-fits-all approach. To alleviate these problems, an adaptive mechanism can be introduced in EPO. This paper proposes a fuzzy adaptive variant of EPO, namely Fuzzy Adaptive Emperor Penguin Optimizer (FAEPO), to solve this problem. As the name suggests, FAEPO can adaptively tune the parameters f and l throughout the search based on three measures (i.e., quality, success rate, and diversity of the current search) via fuzzy decisions. A test suite of twelve optimization benchmark test functions and three global optimization problems (Team Formation Optimization - TFO, Low Autocorrelation Binary Sequence - LABS, and Modified Condition/Decision Coverage - MC/DC test case generation) were solved using the proposed algorithm. The respective solution results of the benchmark meta-heuristic algorithms were compared. The experimental results demonstrate that FAEPO significantly improved the performance of its predecessor (EPO) and gives superior performance against the competing meta-heuristic algorithms, including an improved variant of EPO (IEPO)

Multiple instance fuzzy inference.

A novel fuzzy learning framework that employs fuzzy inference to solve the problem of multiple instance learning (MIL) is presented. The framework introduces a new class of fuzzy inference systems called Multiple Instance Fuzzy Inference Systems (MI-FIS). Fuzzy inference is a powerful modeling framework that can handle computing with knowledge uncertainty and measurement imprecision effectively. Fuzzy Inference performs a non-linear mapping from an input space to an output space by deriving conclusions from a set of fuzzy if-then rules and known facts. Rules can be identified from expert knowledge, or learned from data. In multiple instance problems, the training data is ambiguously labeled. Instances are grouped into bags, labels of bags are known but not those of individual instances. MIL deals with learning a classifier at the bag level. Over the years, many solutions to this problem have been proposed. However, no MIL formulation employing fuzzy inference exists in the literature. In this dissertation, we introduce multiple instance fuzzy logic that enables fuzzy reasoning with bags of instances. Accordingly, different multiple instance fuzzy inference styles are proposed. The Multiple Instance Mamdani style fuzzy inference (MI-Mamdani) extends the standard Mamdani style inference to compute with multiple instances. The Multiple Instance Sugeno style fuzzy inference (MI-Sugeno) is an extension of the standard Sugeno style inference to handle reasoning with multiple instances. In addition to the MI-FIS inference styles, one of the main contributions of this work is an adaptive neuro-fuzzy architecture designed to handle bags of instances as input and capable of learning from ambiguously labeled data. The proposed architecture, called Multiple Instance-ANFIS (MI-ANFIS), extends the standard Adaptive Neuro Fuzzy Inference System (ANFIS). We also propose different methods to identify and learn fuzzy if-then rules in the context of MIL. In particular, a novel learning algorithm for MI-ANFIS is derived. The learning is achieved by using the backpropagation algorithm to identify the premise parameters and consequent parameters of the network. The proposed framework is tested and validated using synthetic and benchmark datasets suitable for MIL problems. Additionally, we apply the proposed Multiple Instance Inference to the problem of region-based image categorization as well as to fuse the output of multiple discrimination algorithms for the purpose of landmine detection using Ground Penetrating Radar

Context dependent fuzzy modelling and its applications

Fuzzy rule-based systems (FRBS) use the principle of fuzzy sets and fuzzy logic to describe vague and imprecise statements and provide a facility to express the behaviours of the system with a human-understandable language. Fuzzy information, once defined by a fuzzy system, is fixed regardless of the circumstances and therefore makes it very difficult to capture the effect of context on the meaning of the fuzzy terms. While efforts have been made to integrate contextual information into the representation of fuzzy sets, it remains the case that often the context model is very restrictive and/or problem specific. The work reported in this thesis is our attempt to create a practical frame work to integrate contextual information into the representation of fuzzy sets so as to improve the interpretability as well as the accuracy of the fuzzy system. Throughout this thesis, we have looked at the capability of the proposed context dependent fuzzy sets as a stand alone as well as in combination with other methods in various application scenarios ranging from time series forecasting to complicated car racing control systems. In all of the applications, the highly competitive performance nature of our approach has proven its effectiveness and efficiency compared with existing techniques in the literature

Access Network Selection in Heterogeneous Networks

The future Heterogeneous Wireless Network (HWN) is composed of multiple Radio Access Technologies (RATs), therefore new Radio Resource Management (RRM) schemes and mechanisms are necessary to benefit from the individual characteristics of each RAT and to exploit the gain resulting from jointly considering the whole set of the available radio resources in each RAT. These new RRM schemes have to support mobile users who can access more than one RAT alternatively or simultaneously using a multi-mode terminal. An important RRM consideration for overall HWN stability, resource utilization, user satisfaction, and Quality of Service (QoS) provisioning is the selection of the most optimal and promising Access Network (AN) for a new service request. The RRM mechanism that is responsible for selecting the most optimal and promising AN for a new service request in the HWN is called the initial Access Network Selection (ANS). This thesis explores the issue of ANS in the HWN. Several ANS solutions that attempt to increase the user satisfaction, the operator benefits, and the QoS are designed, implemented, and evaluated. The thesis first presents a comprehensive foundation for the initial ANS in the H\VN. Then, the thesis analyses and develops a generic framework for solving the ANS problem and any other similar optimized selection problem. The advantages and strengths of the developed framework are discussed. Combined Fuzzy Logic (FL), Multiple Criteria Decision Making (MCDM) and Genetic Algorithms (GA) are used to give the developed framework the required scalability, flexibility, and simplicity. The developed framework is used to present and design several novel ANS algorithms that consider the user, the operator, and the QoS view points. Different numbers of RATs, MCDM tools, and FL inference system types are used in each algorithm. A suitable simulation models over the HWN with a new set of performance evolution metrics for the ANS solution are designed and implemented. The simulation results show that the new algorithms have better and more robust performance over the random, the service type, and the terminal speed based selection algorithms that are used as reference algorithms. Our novel algorithms outperform the reference algorithms in- terms of the percentage of the satisfied users who are assigned to the network of their preferences and the percentage of the users who are assigned to networks with stronger signal strength. The new algorithms maximize the operator benefits by saving the high cost network resources and utilizing the usage of the low cost network resources. Usually better results are achieved by assigning the weights using the GA optional component in the implemented algorithms

Learning lost temporal fuzzy association rules

Fuzzy association rule mining discovers patterns in transactions, such as shopping baskets in a supermarket, or Web page accesses by a visitor to a Web site. Temporal patterns can be present in fuzzy association rules because the underlying process generating the data can be dynamic. However, existing solutions may not discover all interesting patterns because of a previously unrecognised problem that is revealed in this thesis. The contextual meaning of fuzzy association rules changes because of the dynamic feature of data. The static fuzzy representation and traditional search method are inadequate. The Genetic Iterative Temporal Fuzzy Association Rule Mining (GITFARM) framework solves the problem by utilising flexible fuzzy representations from a fuzzy rule-based system (FRBS). The combination of temporal, fuzzy and itemset space was simultaneously searched with a genetic algorithm (GA) to overcome the problem. The framework transforms the dataset to a graph for efficiently searching the dataset. A choice of model in fuzzy representation provides a trade-off in usage between an approximate and descriptive model. A method for verifying the solution to the hypothesised problem was presented. The proposed GA-based solution was compared with a traditional approach that uses an exhaustive search method. It was shown how the GA-based solution discovered rules that the traditional approach did not. This shows that simultaneously searching for rules and membership functions with a GA is a suitable solution for mining temporal fuzzy association rules. So, in practice, more knowledge can be discovered for making well-informed decisions that would otherwise be lost with a traditional approach.EPSRC DT