Identification of interpretable and accurate fuzzy classifiers and function estimators with hybrid methods

Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: an overview.- Regaining comprehensibility of approximative fuzzy models via the use of linguistic hedges.- Identifying flexible structured premises for mining concise fuzzy knowledge.- A multiobjective genetic learning process for joint feature selection and granularity and contexts learning in fuzzy rule-based classification systems.- Extracting linguistic fuzzy models from numerical data-AFRELI algorithm.- Constrained optimization of fuzzy decision trees.- A new method for inducing a set of interpretable fuzzy partitions and fuzzy inference systems from data.- A Feature Ranking Algorithm for Fuzzy Modelling Problems.- Interpretability in multidimensional classification.- Interpretable semi-mechanistic fuzzy models by clustering, OLS and FIS model reduction.- Trade-off between approximation accuracy and complexity: TS controller design via HOSVD based complexity minimization.- Simplification and reduction of fuzzy rules.- Effect of rule representation in rule base reduction.- Singular value-based fuzzy reduction with relaxed normalization condition.- Interpretability, complexity, and modular structure of fuzzy systems.- Hierarchical genetic fuzzy systems: accuracy, interpretability and design autonomy.- About the trade-off between accuracy and interpretability of Takagi-Sugeno models in the context of nonlinear time series forecasting.- Accurate, transparent and compact fuzzy models by multi-objective evolutionary algorithms.- Transparent fuzzy systems in modeling and control.- Uniform fuzzy partitions with cardinal splines and wavelets: getting interpretable linguistic fuzzy models.- Relating the theory of partitions in MV-logic to the design of interpretable fuzzy systems.- A formal model of interpretability of linguistic variables.- Expressing relevance and interpretability of rule-based systems.- Conciseness of fuzzy models.- Exact trade-off between approximation accuracy and interpretability: solving the saturation problem for certain FRBSs.- Interpretability improvement of RBF-based neurofuzzy systems using regularized learning.- Extracting fuzzy classification rules from fuzzy clusters on the basis of separating hyperplanes.

Design of a two-stage fuzzy classification model

Error measures for fuzzy linear regression: Monte Carlo simulation approach

Takagi-Sugeno-Kang-type fuzzy model to assist with real estate appraisals is described and optimized using evolutionary algorithms Two approaches were compared in the paper. The first one consisted in learning the rule base and the second one in combining learning the rule base and tuning the membership functions in one process. Five TSK-type fuzzy models comprising 3 or 4 input variables referring to the attributes of a property were evaluated. The evolutionary algorithms were based on Pittsburgh approach with the real coded chromosomes of constant length comprising whole rule base or both the rule base and all parameters of all membership functions. The experiments were conducted using training and testing sets prepared on the basis of actual 134 sales transactions made in one of Polish cities and located in a residential section.

С.А. Глушенко - кандидат экономических наук, старший преподаватель кафедры информационных систем и прикладной информатики, Ростовский государственный экономический университет (РИНХ)Адрес: 344002, г. Ростов-на-Дону, ул. Большая Садовая, д. 69E-mail: gs-gears@yandex.ru В статье обосновывается важность применения оценки рисков при реализации системы обеспечения информационной безопасности. Рассматриваются наиболее распространенные методики оценки риска и предлагается использовать для этих целей теорию нечеткой логики. Описывается предложенная нечеткая продукционная модель (НПМ), в которой определены семь входных лингвистических переменных, характеризующих факторы риска, четыре выходных лингвистических переменных, характеризующих риски различных областей информационной безопасности, а также четыре базы правил. Отмечается, что НПМ является первым приближением для рассматриваемой предметной области и требует оптимизации с целью минимизации ошибки выходов модели. Рассматриваются наиболее распространенные методы оптимизации параметров нечетких моделей и обосновываются преимущества применения методов, основанных на использовании нейро-нечетких сетей (ННС). Описывается процесс преобразования элементов нечеткой модели, таких как блок фаззификации, блок базы правил и блок дефаззификации во фрагменты нейронной сети. Результатом данного процесса является нейро-нечеткая сеть, соответствующая нечеткой модели. Построение разработанной ННС осуществляется на основе системы нейро-нечеткого вывода (adaptive neuro-fuzzy inference system, ANFIS) посредством применения специализированного пакета Neuro-Fuzzy Designer программного средства MATLAB. Обучение модели было выполнено гибридным методом, который представляет собой комбинацию методов наименьших квадратов и обратного распространения ошибки. Результатом данного процесса является оптимизация (настройка) параметров функций принадлежности входных лингвистических переменных. Использованный подход нейро-нечеткого моделирования позволил получить более адекватную нечеткую продукционную модель, которая позволяет проводить лингвистический анализ рисков информационной безопасности организации. Полученные с ее помощью сведения позволяют ИТ-менеджерам определять приоритеты рисков и разрабатывать эффективные планы мероприятий по снижению влияния наиболее опасных угроз. [1] Исследование выполнено при финансовой поддержке РФФИ, в рамках научного проекта № 16-31-00285 «Методы и модели нечеткой логики в системах принятия решений управления рисками»

We present a method for incremental modeling and time-varying control of unknown nonlinear systems. The method combines elements of evolving intelligence, granular machine learning, and multi-variable control. We propose a State-Space Fuzzy-set-Based evolving Modeling (SS-FBeM) approach. The resulting fuzzy model is structurally and parametrically developed from a data stream with focus on memory and data coverage. The fuzzy controller also evolves, based on the data instances and fuzzy model parameters. Its local gains are redesigned in real-time -- whenever the corresponding local fuzzy models change -- from the solution of a linear matrix inequality problem derived from a fuzzy Lyapunov function and bounded input conditions. We have shown one-step prediction and asymptotic stabilization of the Henon chaos.

Fuzzy functions based ARX model and new fuzzy basis function models for nonlinear system identification

We believe the great interpretability of fuzzy models allow fuzzy-based methods to play a very important role in Microarray gene expression data analysis, but the advantages offered by fuzzy-based techniques in this application have not yet been fully explored in the literature. In this paper, we construct Multi-Objective Evolutionary Algorithms based Interpretable Fuzzy (MOEAIF) models for microarray gene expression data analysis. Our novel fuzzy models can significantly decrease the model complexity, and automatically balance the accuracy and interpretability of the models. The experimental studies have shown that relatively simple and small fuzzy rule bases, with satisfactory classification performance, have been successful found for challenging microarray gene expression datasets.

This chapter presents two novel approaches for the identification of Takagi-Sugeno fuzzy models with time variant and time invariant features. The mixed fuzzy clustering (MFC) algorithm is used for determining the parameters of Takagi-Sugeno fuzzy models (FMs) in two different ways: (1) MFC FM, where the antecedent fuzzy sets are determined based on the partition matrix generated by the mixed fuzzy clustering algorithm; (2) FCM–UMFC FM, where the input features are transformed using MFC and the antecedent fuzzy sets are derived using fuzzy c-means (FCM). The fuzzy modeling approaches are tested on four health care applications for the classification of critically ill patients: administration of vasopressors in pancreatitis and pneumonia patients, mortality in septic shock and early readmissions. Both approaches increase the performance of Takagi-Sugeno based on FCM, in all datasets. In particular, the best performer, FCM–UMFC FM, achieves notable improvements in the four datasets.

Fuzzy systems are widely used in most fields of science and engineering, mainly because the models they produce are robust, accurate, easy to evaluate and capture real-world uncertainty better than do the classical alternatives. We propose a new methodology for structure and parameter tuning of Takagi–Sugeno–Kang fuzzy models using several optimization techniques. The output parameters are determined analytically, by finding the minimum of the root-mean-square error (RMSE) for a properly defined error function. The membership functions are simplified by considering symmetry and equispacing, to reduce the optimization problem of finding their parameters, and allow it to be carried out using the numerical method of gradient descent. Both algorithms are fast enough to finally implement a strategy based on the hill climbing approach to finding the optimal structure (number and type of membership functions) of the fuzzy system. The effectiveness of the proposed strategy is shown by comparing its performance, using four case studies found in current relevant works, to the popular adaptive network-based fuzzy inference system (ANFIS), and to other recently published strategies based on evolutionary fuzzy models. In terms of the RMSE, performance was at least 28% better in all case studies.

The immune algorithm based on clonal selection can be used for identification and optimization of the parameters of Sugeno fuzzy model extracted from numerical data. In [5] the rules of fuzzy model were extracted using clonal selection for clustering task, implemented in the MATLAB code. In this paper, the application of the clonal selection has been proposed to solve optimization problems. The algorithm of clonal selection can be used before the clustering version of identification of parameters of the fuzzy model Sugeno-type. Then the same algorithm can be adapted to solve optimization tasks. The results were applied to approximation of a test function.

Living in the era of deluge demands for an increase in the application and development of machine learning methods, both in basic and applied research. Among these methods, in the last decades fuzzy inference systems carved out their own niche as (light) grey box models, which are considered more interpretable and transparent than other commonly employed methods, such as artificial neural networks. Although commercially distributed alternatives are available, software able to assist practitioners and researchers in each step of the estimation of a fuzzy model from data are still limited in scope and applicability. This is especially true when looking at software developed in Python, a programming language that quickly gained popularity among data scientists and it is often considered their language of choice. To fill this gap, we introduce pyFUME, a Python library for automatically estimating fuzzy models from data. pyFUME contains a set of classes and methods to estimate the antecedent sets and the consequent parameters of a Takagi-Sugeno fuzzy model from data, and then create an executable fuzzy model exploiting the Simpful library. pyFUME can be beneficial to practitioners, thanks to its pre-implemented and user-friendly pipelines, but also to researchers that want to fine-tune each step of the estimation process.

The dynamic nature and increasing complexity of the construction industry have led to increased conflicts in construction projects. An accurate prediction of the outcome of a dispute resolution in courts could effectively reduce the number of disputes that would otherwise conclude by spending more money through litigation. This study aims to introduce a two-layered fuzzy logic model for predicting court decisions in construction contract disputes. 100 cases of construction contract disputes are selected from the courts of Iran. A questionnaire survey is then conducted to extract a set of fuzzy rules for identifying important decision parameters and expert knowledge. Accordingly, a two-layered fuzzy logic-based decision-making architecture is proposed for the prediction model. Furthermore, the fuzzy system is trained based on 10-fold cross-validation. Analysis of results indicates that 51 out of the 100 cases are filed after the dissolution and termination of the contract show a significant impact of these clauses as the root cause in construction contract disputes. Our results present a proposed hierarchical fuzzy system that can correctly predict nearly 60% of the test data. Also, we demonstrate a methodology of using argument before ML to establish interpretable AI models. Based on our findings, a fuzzy model with a hierarchical structure may be used as a simple and efficient method for predicting court decisions in construction contract disputes.

An approach to construct interpretable and precise fuzzy models from data is proposed. Interpretability, which is one of the most important features of fuzzy models, is analyzed first. Then a modified fuzzy clustering algorithm, combined with the least square method, is used to identify the initial fuzzy model. Third, the multi-objective genetic algorithm and interpretability-driven simplification techniques are proposed to evolve the initial fuzzy model to optimize its structure and parameters iteratively, thus interpretability and precision of the fuzzy model are improved. Finally, the proposed approach is applied to the Mackey-Glass tine series, and the results show its validity

One of the most important physical properties of the soil is its mechanical strength. Increasing soil mechanical strength will lead to increments in the draft, fuel consumption, work duration and equipment wear, but will follow the reduction in the root growth. Awareness of the soil cone index (as a criterion of the arable soil compaction) in order to production management in connection with the soil physical properties have high importance, especially in precision farming. On the other hand, finding the methods and models that be able to create the best function or model to estimate the soil cone index at the least cost and use of available data are crucial for researchers. The aim of this study was predicting arable soils cone index values by effective parameters on the soil cone index, including bulk density, soil moisture content and soil electrical conductivity by using Fuzzy and neuro-fuzzy systems. In this study, for measurement and determination of the influencing factors on the soil cone index value, the experimental design was the factorial experiment based on a randomized complete block design with five replications. The experimental field had three types of loam, sandy loam and loamy sand soils. The modeling of soil cone index was performed by using effective parameters such as bulk density, moisture content and soil electrical conductivity in the fuzzy and adaptive neuro-fuzzy inference system (ANFIS) systems. For fuzzification of input and output parameters, the linguistic variables, including very low (VL), low (L), medium (M), high (H) and very high (VH) were used. Since determining the type and number of membership functions was conducted experimentally, the triangular membership function for both input and output variables was used due to the high accuracy and convenience in system design. In ANFIS model, 80% and 20% of total data were considered as training and test data, respectively. The numbers of membership functions were selected 5 for each input parameters. ANFIS training was done by the hybrid method. The average of coefficients of determination (R2) were obtained 80.1% and 97.9% for the fuzzy and ANFIS models, respectively. The obtained model through ANFIS presented the high accuracy of 2.54% rather than the fuzzy models with the accuracy of 9.68%. Also in comparison with regression models, ANFIS model has high accuracy and can be used to estimate the soil cone index in agricultural land.