An artificial immune systems based predictive modelling approach for the multi-objective elicitation of Mamdani fuzzy rules: a special application to modelling alloys

In this paper, a systematic multi-objective Mamdani fuzzy modeling approach is proposed, which can be viewed as an extended version of the previously proposed Singleton fuzzy modeling paradigm. A set of new back-error propagation (BEP) updating formulas are derived so that they can replace the old set developed in the singleton version. With the substitution, the extension to the multi-objective Mamdani Fuzzy Rule-Based Systems (FRBS) is almost endemic. Due to the carefully chosen output membership functions, the inference and the defuzzification methods, a closed form integral can be deducted for the defuzzification method, which ensures the efficiency of the developed Mamdani FRBS. Some important factors, such as the variable length coding scheme and the rule alignment, are also discussed. Experimental results for a real data set from the steel industry suggest that the proposed approach is capable of eliciting not only accurate but also transparent FRBS with good generalization ability

A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels

In this paper, a systematic data-driven fuzzy modelling methodology is proposed, which allows to construct Mamdani fuzzy models considering both accuracy (precision) and transparency (interpretability) of fuzzy systems. The new methodology employs a fast hierarchical clustering algorithm to generate an initial fuzzy model efficiently; a training data selection mechanism is developed to identify appropriate and efficient data as learning samples; a high-performance Particle Swarm Optimisation (PSO) based multi-objective optimisation mechanism is developed to further improve the fuzzy model in terms of both the structure and the parameters; and a new tolerance analysis method is proposed to derive the confidence bands relating to the final elicited models. This proposed modelling approach is evaluated using two benchmark problems and is shown to outperform other modelling approaches. Furthermore, the proposed approach is successfully applied to complex high-dimensional modelling problems for manufacturing of alloy steels, using ‘real’ industrial data. These problems concern the prediction of the mechanical properties of alloy steels by correlating them with the heat treatment process conditions as well as the weight percentages of the chemical compositions

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

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

On-line multiobjective automatic control system generation by evolutionary algorithms

Evolutionary algorithms are applied to the on- line generation of servo-motor control systems. In this paper, the evolving population of controllers is evaluated at run-time via hardware in the loop, rather than on a simulated model. Disturbances are also introduced at run-time in order to pro- duce robust performance. Multiobjective optimisation of both PI and Fuzzy Logic controllers is considered. Finally an on-line implementation of Genetic Programming is presented based around the Simulink standard blockset. The on-line designed controllers are shown to be robust to both system noise and ex- ternal disturbances while still demonstrating excellent steady- state and dvnamic characteristics

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 Artificial Immune Systems based Predictive Modelling Approach for the Multi-Objective Elicitation of Mamdani Fuzzy Rules A Special Application to Modelling Alloys

Abstract-In this paper, a systematic multi-objective Mamdani fuzzy modeling approach is proposed, which can be viewed as an extended version of the previously proposed Singleton fuzzy modeling paradigm. A set of new back-error propagation (BEP) updating formulas are derived so that they can replace the old set developed in the singleton version. With the substitution, the extension to the multi-objective Mamdani Fuzzy Rule-Based Systems (FRBS) is almost endemic. Due to the carefully chosen output membership functions, the inference and the defuzzification methods, a closed form integral can be deducted for the defuzzification method, which ensures the efficiency of the developed Mamdani FRBS. Some important factors, such as the variable length coding scheme and the rule alignment, are also discussed. Experimental results for a real data set from the steel industry suggest that the proposed approach is capable of eliciting not only accurate but also transparent FRBS with good generalization ability

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

Introducing a novel multi-objective optimization model for volunteer assignment in the post-disaster phase: Combining fuzzy inference systems with NSGA-II and NRGA

Each year, disasters (natural or man-made) cause a lot of damage and take many people’s lives. In this situation, many volunteers come to help. While the proper management of volunteers is very effective in controlling the crisis, the lack of proper management of volunteers can create another crisis. Therefore, we introduce a model to deal with the volunteer assignment problem by considering two qualitative objective functions: The first one is minimizing the mean importance of Emergency Department (ED) centers’ unmet needs by volunteers, and the second one is minimizing the mean degree of unsatisfied preferences of selected volunteers. To evaluate the introduced qualitative indexes, two Fuzzy Inference Systems (FISs) are used to encapsulate decision makers’ knowledge as well as the human reasoning process. FISs are embedded in two evolutionary algorithms for solving the proposed model: Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Non-Dominated Ranked Genetic Algorithm (NRGA). Also, 30 small-size problems, as well as 30 large-size problems, are randomly generated and solved by both metaheuristic algorithms. Using the obtained data, the performance of NSGA-II and NRGA is measured and compared based on four criteria: CPU Time, Number of Non-dominated Solutions (NNS), Mean Ideal Distance (MID), and Spacing Metric (SM). Statistical tests show that both algorithms have the same performance in small-size problems. However, in large-size problems, NSGA-II is faster, and NRGA produces more optimal solutions. The proposed model is flexible enough to adapt to different scenarios just by updating linguistic rules in FISs. Also, since employed algorithms produce a set of optimal solutions, decision-makers can easily choose the most appropriate solution among the Pareto front based on the circumstancesH2020-EU.1.3. – EXCELLEN

Global plant characterisation and distribution with evolution and climate

Since Arrhenius published seminal work in 1921, research interest in the description of plant traits and grouped characteristics of plant species has grown, underpinning diversity in trophic levels. Geographic exploration and diversity studies prior to and after 1921 culminated in biological, chemical and computer-simulated approaches describing rudiments of growth patterns within dynamic conditions of Earth. This thesis has two parts:- classical theory and multidisciplinary fusion to give mathematical strength to characterising plant species in space and time.Individual plant species occurrences are used to obtain a Species-Area Relationship. The use of both Boolean and logic-based mathematics is then integrated to describe classical methods and propose fuzzy logic control to predict species ordination. Having demonstrated a lack of significance between species and area for data modelled in this thesis a logic based approach is taken. Mamdani and T-S-K fuzzy system stability is verified by application to individual plant occurrences, validated by a multiple interfaced data portal. Quantitative mathematical models are differentiated with a genetic programming approach, enabling visualisation of multi-objective dispersal of plant strategies, plant metabolism and life-forms within the water-energy dynamic of a fixed time-scale scenario. The distributions of plant characteristics are functionally enriched through the use of Gaussian process models. A generic framework of a Geographic Information System is used to visualise distributions and it is noted that such systems can be used to assist in design and implementation of policies. The study has made use of field based data and the application of mathematic methods is shown to be appropriate and generative in the description of characteristics of plant species, with the aim of application of plant strategies, life-forms and photosynthetic types to a global framework. Novel application of fuzzy logic and related mathematic method to plant distribution and characteristics has been shown on a global scale. Quantification of the uncertainty gives novel insight through consequent trophic levels of biological systems, with great relevance to mathematic and geographic subject development. Informative value of Z matrices of plant distribution is increased substantiating sustainability and conservation policy value to ecosystems and human populations dependent upon them for their needs.Key words: sustainability, conservation policy, Boolean and logic-based, fuzzy logic, genetic programming, multi-objective dispersal, strategies, metabolism, life-forms