Heuristic design of fuzzy inference systems: a review of three decades of research

This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multi-objective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi–Sugeno–Kang-type fuzzy systems. Whereas, the NFS combines the FIS with neural network learning systems to improve the approximation ability. An HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. An EFS solves the data streaming issues by evolving the system incrementally, and an MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. This paper offers a synthesis of these dimensions and explores their potentials, challenges, and opportunities in FIS research. This review also examines the complex relations among these dimensions and the possibilities of combining one or more computational frameworks adding another dimension: deep fuzzy systems

Type-2 Fuzzy Hybrid Controller Network for Robotic Systems

Dynamic control, including robotic control, faces both the theoretical challenge of obtaining accurate system models and the practical difficulty of defining uncertain system bounds. To facilitate such challenges, this paper proposes a control system consisting of a novel type of fuzzy neural network and a robust compensator controller. The new fuzzy neural network is implemented by integrating a number of key components embedded in a Type-2 fuzzy cerebellar model articulation controller (CMAC) and a brain emotional learning controller (BELC) network, thereby mimicking an ideal sliding mode controller. The system inputs are fed into the neural network through a Type-2 fuzzy inference system (T2FIS), with the results subsequently piped into sensory and emotional channels which jointly produce the final outputs of the network. That is, the proposed network estimates the nonlinear equations representing the ideal sliding mode controllers using a powerful compensator controller with the support of T2FIS and BELC, guaranteeing robust tracking of the dynamics of the controlled systems. The adaptive dynamic tuning laws of the network are developed by exploiting the popular brain emotional learning rule and the Lyapunov function. The proposed system was applied to a robot manipulator and a mobile robot, demonstrating its efficacy and potential; and a comparative study with alternatives indicates a significant improvement by the proposed system in performing the intelligent dynamic control

Bypassing the Natural Visual-Motor Pathway to Execute Complex Movement Related Tasks Using Interval Type-2 Fuzzy Sets

In visual-motor coordination, the human brain processes visual stimuli representative of complex motion-related tasks at the occipital lobe to generate the necessary neuronal signals for the parietal and pre-frontal lobes, which in turn generates movement related plans to excite the motor cortex to execute the actual tasks. The paper introduces a novel approach to provide rehabilitative support to patients suffering from neurological damage in their pre-frontal, parietal and/or motor cortex regions. An attempt to bypass the natural visual-motor pathway is undertaken using interval type-2 fuzzy sets to generate the approximate EEG response of the damaged pre-frontal/parietal/motor cortex from the occipital EEG signals. The approximate EEG response is used to trigger a pre-trained joint coordinate generator to obtain desired joint coordinates of the link end-points of a robot imitating the human subject. The robot arm is here employed as a rehabilitative aid in order to move each link end-points to the desired locations in the reference coordinate system by appropriately activating its links using the well-known inverse kinematics approach. The mean-square positional errors obtained for each link end-points is found within acceptable limits for all experimental subjects including subjects with partial parietal damage, indicating a possible impact of the proposed approach in rehabilitative robotics. Subjective variation in EEG features over different sessions of experimental trials is modelled here using interval type-2 fuzzy sets for its inherent power to handle uncertainty. Experiments undertaken confirm that interval type-2 fuzzy realization outperforms its classical type-1 counterpart and back-propagation neural approaches in all experimental cases, considering link positional error as a metric. The proposed research offers a new opening for the development of possible rehabilitative aids for people with partial impairment in visual-motor coordination

Many-Objective Genetic Type-2 Fuzzy Logic Based Workforce Optimisation Strategies for Large Scale Organisational Design

Workforce optimisation aims to maximise the productivity of a workforce and is a crucial practice for large organisations. The more effective these workforce optimisation strategies are, the better placed the organisation is to meet their objectives. Usually, the focus of workforce optimisation is scheduling, routing and planning. These strategies are particularly relevant to organisations with large mobile workforces, such as utility companies. There has been much research focused on these areas. One aspect of workforce optimisation that gets overlooked is organisational design. Organisational design aims to maximise the potential utilisation of all resources while minimising costs. If done correctly, other systems (scheduling, routing and planning) will be more effective. This thesis looks at organisational design, from geographical structures and team structures to skilling and resource management. A many-objective optimisation system to tackle large-scale optimisation problems will be presented. The system will employ interval type-2 fuzzy logic to handle the uncertainties with the real-world data, such as travel times and task completion times. The proposed system was developed with data from British Telecom (BT) and was deployed within the organisation. The techniques presented at the end of this thesis led to a very significant improvement over the standard NSGA-II algorithm by 31.07% with a P-Value of 1.86-10. The system has delivered an increase in productivity in BT of 0.5%, saving an estimated £1million a year, cut fuel consumption by 2.9%, resulting in an additional saving of over £200k a year. Due to less fuel consumption Carbon Dioxide (CO2) emissions have been reduced by 2,500 metric tonnes. Furthermore, a report by the United Kingdom’s (UK’s) Department of Transport found that for every billion vehicle miles travelled, there were 15,409 serious injuries or deaths. The system saved an estimated 7.7 million miles, equating to preventing more than 115 serious casualties and fatalities

Aspiration Based Decision Analysis and Support Part I: Theoretical and Methodological Backgrounds

In the interdisciplinary and intercultural systems analysis that constitutes the main theme of research in IIASA, a basic question is how to analyze and support decisions with help of mathematical models and logical procedures. This question -- particularly in its multi-criteria and multi-cultural dimensions -- has been investigated in System and Decision Sciences Program (SDS) since the beginning of IIASA. Researchers working both at IIASA and in a large international network of cooperating institutions contributed to a deeper understanding of this question. Around 1980, the concept of reference point multiobjective optimization was developed in SDS. This concept determined an international trend of research pursued in many countries cooperating with IIASA as well as in many research programs at IIASA -- such as energy, agricultural, environmental research. SDS organized since this time numerous international workshops, summer schools, seminar days and cooperative research agreements in the field of decision analysis and support. By this international and interdisciplinary cooperation, the concept of reference point multiobjective optimization has matured and was generalized into a framework of aspiration based decision analysis and support that can be understood as a synthesis of several known, antithetical approaches to this subject -- such as utility maximization approach, or satisficing approach, or goal -- program -- oriented planning approach. Jointly, the name of quasisatisficing approach can be also used, since the concept of aspirations comes from the satisficing approach. Both authors of the Working Paper contributed actively to this research: Andrzej Wierzbicki originated the concept of reference point multiobjective optimization and quasisatisficing approach, while Andrzej Lewandowski, working from the beginning in the numerous applications and extensions of this concept, has had the main contribution to its generalization into the framework of aspiration based decision analysis and support systems. This paper constitutes a draft of the first part of a book being prepared by these two authors. Part I, devoted to theoretical foundations and methodological background, written mostly by Andrzej Wierzbicki, will be followed by Part II, devoted to computer implementations and applications of decision support systems based on mathematical programming models, written mostly by Andrzej Lewandowski. Part III, devoted to decision support systems for the case of subjective evaluations of discrete decision alternatives, will be written by both authors

A single-objective and a multi-objective genetic algorithm to generate accurate and interpretable fuzzy rule based classifiers for the analysis of complex financial data

Nowadays, organizations deal with rapidly increasing amount of data that is stored in their databases. It has therefore become of crucial importance for them to identify the necessary patterns in these large databases to turn row data into valuable and actionable information. By exploring these important datasets, the organizations gain competitive advantage against other competitors, based on the assumption that the added value of Knowledge Management Systems strength is first and foremost to facilitate the decision making process. Especially if we consider the importance of knowledge in the 21st century, data mining can be seen as a very effective tool to explore the essential data that foster competitive gain in a changing environment. The overall aim of this study is to design the rule base component of a fuzzy rule-based system (FRBS) through the use of genetic algorithms. The main objective is to generate accurate and interpretable models of the data trying to overcome the existing tradeoff between accuracy and interpretability. We propose two different approaches: an accuracy-driven single-objective genetic algorithm, and a three-objective genetic algorithm that produce a Pareto front approximation, composed of classifiers with different tradeoffs between accuracy and complexity. The proposed approaches have been compared with two other systems, namely a rule selection single-objective algorithm, and a three-objective algorithm. The latter has been developed by the University of Pisa and is able to generate the rule base, while simultaneously learning the definition points of the membership functions, by taking into account both the accuracy and the interpretability of the final model

Multiobjective Optimization and Comparison of Nonsingleton Type-1 and Singleton Interval Type-2 Fuzzy Logic Systems

Singleton interval type-2 fuzzy logic systems (FLSs) have been widely applied in several real-world applications, where it was shown that the singleton interval type-2 FLSs outperform their singleton type-1 counterparts in applications with high uncertainty levels. However, one of the main criticisms of singleton interval type-2 FLSs is the fact that they outperform singleton type-1 FLSs solely based on their use of extra degrees of freedom (extra parameters) and that type-1 FLSs with a sufficiently large number of parameters may provide the same performance as interval type-2 FLSs. In addition, most works on type-2 FLSs only compare their results with singleton type-1 FLSs but fail to consider nonsingleton type-1 systems. In this paper, we aim to directly address and investigate this criticism. In order to do so, we will perform a comparative study between optimized singleton type-1, nonsingleton type-1, and singleton interval type-2 FLSs under the presence of noise. We will also present a multiobjective evolutionary algorithm (MOEA) for the optimization of singleton type-1, nonsingleton type-1, and singleton interval type-2 fuzzy systems for function approximation problems. The MOEA will aim to satisfy two objectives to maximize the accuracy of the FLS and minimize the number of rules in the FLS, thus improving its interpretability. Furthermore, we will present a methodology to obtain ``optimal'' consequents for the FLSs. Hence, this paper has two main contributions: First, it provides a common methodology to learn the three types of FLSs (i.e., singleton type-1, nonsingleton type-1, and singleton interval type-2 FLSs) from data samples. The second contribution is the creation of a common framework for the comparison of type-1 and type-2 FLSs that allows us to address the aforementioned criticism. We provide details of a series of experiments and include statistical analysis showing that the type-2 FLS is able to handle higher levels of noise than its nonsingleton and singleton type-1 counterparts

A type-2 fuzzy logic based goal-driven simulation for optimising field service delivery

This thesis develops an intelligent system capable of incorporating the conditions that drive operational activity while implementing the means to handle unexpected factors to protect business sustainability. This solution aims to optimise field service operations in the utility-based industry, especially within one of the world's leading communications services companies, namely BT (British Telecom), which operates in highly regulated and competitive markets. Notably, the telecommunication sector is an essential driver of economic activity. Consequently, intelligent solutions must incorporate the ability to explain their underlying algorithms that power their final decisions to humans. In this regard, this thesis studies the following research gaps: the lack of integrated solutions that go beyond isolated monolithic architectures, the lack of agile end-to-end frameworks for handling uncertainty while business targets are defined, current solutions that address target-oriented problems do not incorporate explainable methodologies; as a result, limited explainability features result in inapplicability for highly regulated industries, and most tools do not support scalability for real-world scenarios. Hence, the need for an integrated, intelligent solution to address these target-oriented simulation problems. This thesis aims to reduce the gaps mentioned above by exploiting fuzzy logic capabilities such as mimicking human thinking and handling uncertainty. Moreover, this thesis also finds support in the Explainable AI field, particularly in the strategies and characteristics to deploy more transparent intelligent solutions that humans can understand. Hence, these foundations support the thesis to unlock explainability, transparency and interpretability. This thesis develops a series of techniques with the following features: the formalisation of an end-to-end framework that dynamically learns form data, the implementation of a novel fuzzy membership correlation analysis approach to enhance performance, the development of a novel fuzzy logic-based method to evaluate the relevancy of inputs, the modelling of a robust optimisation method for operational sustainability in the telecommunications sector, the design of an agile modelling approach for scalability and consistency, the formalisation of a novel fuzzy-logic system for goal-driven simulation for achieving specific business targets before being implemented in real-life conditions, and a novel simulation environment that incorporates visual tools to enhance interpretability while moving from conventional simulation to a target-oriented model. The proposed tool was developed based on data from BT, reflecting their real-world operational conditions. The data was protected and anonymised in compliance with BT’s sharing of information regulations. The techniques presented in the development of this thesis yield significant improvements aligned to institutional targets. Precisely, as detailed in Section 9.5, the proposed system can model a reduction between 3.78% and 5.36% of footprint carbon emission due to travel times for jobs completion on customer premises for specific geographical areas. The proposed framework allows generating simulation scenarios 13 times faster than conventional approaches. As described in Section 9.6, these improvements contribute to increased productivity and customer satisfaction metrics regarding keeping appointment times, completing orders in the promised timeframe or fixing faults when agreed by an estimated 2.6%. The proposed tool allows to evaluate decisions before acting; as detailed in Section 9.7, this contributes to the ‘promoters’ minus ‘detractors’ across business units measure by an estimated 1%