A Mixed Binary-Real NSGA II Algorithm Ensuring Both Accuracy and Interpretability of a Neuro-Fuzzy Controller

In this work, a Neuro-Fuzzy Controller network, called NFC that implements a Mamdani fuzzy inference system is proposed. This network includes neurons able to perform fundamental fuzzy operations. Connections between neurons are weighted through binary and real weights. Then a mixed binary-real Non dominated Sorting Genetic Algorithm II (NSGA II) is used to perform both accuracy and interpretability of the NFC by minimizing two objective functions; one objective relates to the number of rules, for compactness, while the second is the mean square error, for accuracy. In order to preserve interpretability of fuzzy rules during the optimization process, some constraints are imposed. The  approach  is  tested  on  two  control examples:  a single  input  single  output (SISO) system  and  a  multivariable (MIMO) system

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

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

Fuzzy control in manufacturing systems

XIV+119hlm.;24c

Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling

This paper aims at providing an in-depth overview of designing interpretable fuzzy inference models from data within a unified framework. The objective of complex system modelling is to develop reliable and understandable models for human being to get insights into complex real-world systems whose first-principle models are unknown. Because system behaviour can be described naturally as a series of linguistic rules, data-driven fuzzy modelling becomes an attractive and widely used paradigm for this purpose. However, fuzzy models constructed from data by adaptive learning algorithms usually suffer from the loss of model interpretability. Model accuracy and interpretability are two conflicting objectives, so interpretation preservation during adaptation in data-driven fuzzy system modelling is a challenging task, which has received much attention in fuzzy system modelling community. In order to clearly discriminate the different roles of fuzzy sets, input variables, and other components in achieving an interpretable fuzzy model, a taxonomy of fuzzy model interpretability is first proposed in terms of low-level interpretability and high-level interpretability in this paper. The low-level interpretability of fuzzy models refers to fuzzy model interpretability achieved by optimizing the membership functions in terms of semantic criteria on fuzzy set level, while the high-level interpretability refers to fuzzy model interpretability obtained by dealing with the coverage, completeness, and consistency of the rules in terms of the criteria on fuzzy rule level. Some criteria for low-level interpretability and high-level interpretability are identified, respectively. Different data-driven fuzzy modelling techniques in the literature focusing on the interpretability issues are reviewed and discussed from the perspective of low-level interpretability and high-level interpretability. Furthermore, some open problems about interpretable fuzzy models are identified and some potential new research directions on fuzzy model interpretability are also suggested. Crown Copyright © 2008

Data Analytic Approach to Support the Activation of Special Signal Timing Plans in Response to Congestion

Improving arterial network performance has become a major challenge that is significantly influenced by signal timing control. In recent years, transportation agencies have begun focusing on Active Arterial Management Program (AAM) strategies to manage the performance of arterial streets under the flagship of Transportation Systems Management & Operations (TSM&O) initiatives. The activation of special traffic signal plans during non-recurrent events is an essential component of AAM and can provide significant benefits in managing congestion. Events such as surges in demands or lane blockages can create queue spillbacks, even during off-peak periods resulting in delays and spillbacks to upstream intersections. To address this issue, some transportation agencies have started implementing processes to change the signal timing in real time based on traffic signal engineer/expert observations of incident and traffic conditions at the intersections upstream and downstream of congested locations. This dissertation develops methods to automate and enhance such decisions made at traffic management centers. First, a method is developed to learn from experts’ decisions by utilizing a combination of Recursive Partitioning and Regression Decision Tree (RPART) and Fuzzy Rule-Based System (FRBS) to deal with the vagueness and uncertainty of human decisions. This study demonstrates the effectiveness of this method in selecting plans to reduce congestion during non-recurrent events. However, the method can only recommend the changes in green time to the movement affected by the incident and does not give an optimized solution that considers all movements. Thus, there was a need to extend the method to decide how the reduction of green times should be distributed to other movements at the intersection. Considering the above, this dissertation further develops a method to derive optimized signal timing plans during non-recurrent congestion that considers the operations of the critical direction impacted by the incident, the overall corridor, as well as the critical intersection movement performance. The prerequisite of optimizing the signal plans is the accurate measurements of traffic flow conditions and turning movement counts. It is also important to calibrate any utilized simulation and optimization models to replicate the field traffic states according to field traffic conditions and local driver behaviors. This study evaluates the identified special signal-timing plan based on both the optimization and the DT and FRBS approaches. Although the DT and FRBS model outputs are able to reduce the existing queue and improve all other performance measures, the evaluation results show that the special signal timing plan obtained from the optimization method produced better performance compared to the DT and FRBS approaches for all of the evaluated non-recurrent conditions. However, there are opportunities to combine both approaches for the best selection of signal plans

A new fuzzy set merging technique using inclusion-based fuzzy clustering

This paper proposes a new method of merging parameterized fuzzy sets based on clustering in the parameters space, taking into account the degree of inclusion of each fuzzy set in the cluster prototypes. The merger method is applied to fuzzy rule base simplification by automatically replacing the fuzzy sets corresponding to a given cluster with that pertaining to cluster prototype. The feasibility and the performance of the proposed method are studied using an application in mobile robot navigation. The results indicate that the proposed merging and rule base simplification approach leads to good navigation performance in the application considered and to fuzzy models that are interpretable by experts. In this paper, we concentrate mainly on fuzzy systems with Gaussian membership functions, but the general approach can also be applied to other parameterized fuzzy sets

A Fuzzy Logic Approach to Prove Bullwhip Effect in Supply Chains

The bullwhip effect in nowadays Supply Chains has become a major source of problems and has attracted supply chain scientists attentions. This paper explores the concept of bullwhip effect in supply chains throughout a completely new approach. Assuming all demands are fuzzy in supply chain, fuzzy If-Then rules are used to show the bullwhip effect. Application of fuzzy logic is due to the fuzzy nature of supply chain problems. The new approach can be the source of inspiration for new solutions to the bullwhip effect in supply chains base on fuzzy logic and fuzzy If-Then rules. Fuzzy time series are widely used in this paper. First for data generation, we apply a modified version of Hwang fuzzy time series with a neural network for defuzzification and finally to show the bullwhip effect, we use Lee fuzzy time series which is based on Fuzzy If-Then rules, Genetic Algorithm and Simulated Annealing

Fuzzy Controllers

Trying to meet the requirements in the field, present book treats different fuzzy control architectures both in terms of the theoretical design and in terms of comparative validation studies in various applications, numerically simulated or experimentally developed. Through the subject matter and through the inter and multidisciplinary content, this book is addressed mainly to the researchers, doctoral students and students interested in developing new applications of intelligent control, but also to the people who want to become familiar with the control concepts based on fuzzy techniques. Bibliographic resources used to perform the work includes books and articles of present interest in the field, published in prestigious journals and publishing houses, and websites dedicated to various applications of fuzzy control. Its structure and the presented studies include the book in the category of those who make a direct connection between theoretical developments and practical applications, thereby constituting a real support for the specialists in artificial intelligence, modelling and control fields