The Monotonicity And Sub-Additivity Properties Of Fuzzy Inference Systems And Their Applications

The Fuzzy Inference System (FIS) is a popular computing paradigm for undertaking modelling, control, and decision-making problems. In this thesis, the focus of investigation is on two theoretical properties of an FIS model, i.e., the monotonicity and sub-additivity properties. These properties are defined, and their applicability to tackling real-world problems is discussed. This research contributes to formulating a systematic procedure that is based on a mathematical foundation (i.e., the sufficient conditions) to develop monotonicity-preserving FIS models. A method to improve the sub-additivity property is also proposed

An Evolutionary-Based Similarity Reasoning Scheme for Monotonic Multi-Input Fuzzy Inference Systems

In this paper, an Evolutionary-based Similarity Reasoning (ESR) scheme for preserving the monotonicity property of the multi-input Fuzzy Inference System (FIS) is proposed. Similarity reasoning (SR) is a useful solution for undertaking the incomplete rule base problem in FIS modeling. However, SR may not be a direct solution to designing monotonic multi-input FIS models, owing to the difficulty in getting a set of monotonically-ordered conclusions. The proposed ESR scheme, which is a synthesis of evolutionary computing, sufficient conditions, and SR, provides a useful solution to modeling and preserving the monotonicity property of multi-input FIS models. A case study on Failure Mode and Effect Analysis (FMEA) is used to demonstrate the effectiveness of the proposed ESR scheme in undertaking real world problems that require the monotonicity property of FIS models

An Empirical Evaluation of the Inferential Capacity of Defeasible Argumentation, Non-monotonic Fuzzy Reasoning and Expert Systems

Several non-monotonic formalisms exist in the field of Artificial Intelligence for reasoning under uncertainty. Many of these are deductive and knowledge-driven, and also employ procedural and semi-declarative techniques for inferential purposes. Nonetheless, limited work exist for the comparison across distinct techniques and in particular the examination of their inferential capacity. Thus, this paper focuses on a comparison of three knowledge-driven approaches employed for non-monotonic reasoning, namely expert systems, fuzzy reasoning and defeasible argumentation. A knowledge-representation and reasoning problem has been selected: modelling and assessing mental workload. This is an ill-defined construct, and its formalisation can be seen as a reasoning activity under uncertainty. An experimental work was performed by exploiting three deductive knowledge bases produced with the aid of experts in the field. These were coded into models by employing the selected techniques and were subsequently elicited with data gathered from humans. The inferences produced by these models were in turn analysed according to common metrics of evaluation in the field of mental workload, in specific validity and sensitivity. Findings suggest that the variance of the inferences of expert systems and fuzzy reasoning models was higher, highlighting poor stability. Contrarily, that of argument-based models was lower, showing a superior stability of its inferences across knowledge bases and under different system configurations. The originality of this research lies in the quantification of the impact of defeasible argumentation. It contributes to the field of logic and non-monotonic reasoning by situating defeasible argumentation among similar approaches of non-monotonic reasoning under uncertainty through a novel empirical comparison

A Study of Membership Functions on Mamdani-Type Fuzzy Inference System for Industrial Decision-Making

The complexity of product design in industry has been continuously increasing. More factors are required to be taken into account simultaneously before a decision about the new product could be determined. For this reason, decision-making process costs much more time and it may even be impossible to determine the optimal decision by normal calculations. Therefore, Fuzzy Inference System based on Fuzzy Logic is introduced as a quick decision-making tool to arrive at a good decision within much shorter time.This thesis focuses on studying the features of membership functions in Mamdani-type fuzzy inference process. It is aimed at making the black box of fuzzy inference system to be transparent by adjusting the membership functions to control the relations between input and output variables. Systematic trial and error is implemented based on the Fuzzy Logic Toolbox from MATLAB, and conclusions developed from experiments help eliminate the uncertainties of membership functions, so that the inference process turns to be more precise and reliable. Firstly, Single-Input Single-Output (SISO) Fuzzy Inference System is discussed through the adjustment of membership functions, and the influence on input-output relations are concluded. Next, Two-Input Single-Output (TISO) Fuzzy Inference System is simulated to verify the conclusions from SISO Fuzzy Inference System, and general features of membership functions on affecting input-output relation are developed. Then, an approach using weights on input variables, for practical decision-making process, is derived. Finally, a design problem of timing system of automobile engine is chosen as case study to examine the validity of conclusions on practical decision-making problem

Evaluation of Adaptive FRIFS Method through Several Classification Comparisons

International audienceAn iterative method to select suitable features for pattern recognition context has been proposed (FRIFS). It combines a global feature selection method based on the Choquet integral and a fuzzy linguistic rule classifier. In this paper, enhancements of this method are presented. An automatic step has been added to make it adaptive to process numerous features. The experimental study, made in a wood defect recognition context, is based on several classifier result analysis. They show the relevancy of the remaining set of selected features. The recognition rates are also considered for each class separately, showing the good behavior of the proposed method

Fuzzy model identification and self learning with smooth compositions

This Paper Develops A Smooth Model Identification And Self-Learning Strategy For Dynamic Systems Taking Into Account Possible Parameter Variations And Uncertainties. We Have Tried To Solve The Problem Such That The Model Follows The Changes And Variations In The System On A Continuous And Smooth Surface. Running The Model To Adaptively Gain The Optimum Values Of The Parameters On A Smooth Surface Would Facilitate Further Improvements In The Application Of Other Derivative Based Optimization Control Algorithms Such As Mpc Or Robust Control Algorithms To Achieve A Combined Modeling-Control Scheme. Compared To The Earlier Works On The Smooth Fuzzy Modeling Structures, We Could Reach A Desired Trade-Off Between The Model Optimality And The Computational Load. The Proposed Method Has Been Evaluated On A Test Problem As Well As The Non-Linear Dynamic Of A Chemical Process.This publication was supported in part by project MINECO, TEC2017-88048-C2-2-

Architectural Uncertainty Analysis for Access Control Scenarios in Industry 4.0

Industrie 4.0-Systeme zeichnen sich durch ihre hohe Komplexität, Konnektivität und ihren hohen Datenaustausch aus. Aufgrund dieser Eigenschaften ist es entscheidend, eine Vertraulichkeit der Daten sicher zu stellen. Ein häufig verwendetes Verfahren zum Sicherstellen von Vertraulichkeit ist das Verwenden von Zugriffskontrolle. Basierend auf modellierter Softwarearchitektur, kann eine Zugriffskontrolle bereits während der Entwurfszeit konzeptionell auf das System angewendet werden. Dies ermöglicht es, potentielle Vertraulichkeitsprobleme bereits früh zu identifizieren und bietet die Möglichkeit, die Auswirkungen von Was-wäre-wenn-Szenarien auf die Vertraulichkeit zu analysieren, bevor entsprechende Änderungen umgesetzt werden. Ungewissheiten der Systemumgebung, die sich aus Unklarheiten in den frühen Phasen der Entwicklung oder der abstrakten Sicht des Softwarearchitekturmodells ergeben, können sich jedoch direkt auf bestehende Zugriffskontrollrichtlinien auswirken und zu einer reduzierten Vertraulichkeit führen. Um dies abzuschwächen, ist es wichtig, Ungewissheiten zu identifizieren und zu behandeln. In dieser Arbeit stellen wir unseren Ansatz zum Umgang mit Ungewissheiten der Zugriffskontrolle während der Entwurfszeit vor. Wir erstellen eine Charakterisierung von Ungewissheiten in der Zugriffskontrolle auf der Architekturebene, um ein besseres Verständnis über die existierenden Arten von Ungewissheiten zu erhalten. Darauf basierend definieren wir ein Konzept des Vertrauens in die Gültigkeit von Eigenschaften der Zugriffskontrolle. Dieses Konzept bietet die Möglichkeit mit Ungewissheiten umzugehen, die bereits in Publikationen zu Zugriffskontrollmodellen beschrieben wurden. Das Konzept des Vertrauens ist eine Zusammensetzung von Umgebungsfaktoren, die die Gültigkeit von und folglich das Vertrauen in Zugriffskontrolleigenschaften beeinflussen. Um Umgebungsfaktoren zu kombinieren und so Vertrauenswerte von Zugriffskontrolleigenschaften zu erhalten, nutzen wir Fuzzy-Inferenzsysteme. Diese erhaltenen Vertrauenswerte werden von einem Analyseprozess mit in Betracht gezogen, um Probleme zu identifizieren, die aus einem Mangel an Vertrauen entstehen. Wir erweitern einen bestehenden Ansatz zur Analyse von Informationsfluss und Zugriffskontrolle zur Entwurfszeit, basierend auf Datenflussdiagrammen. Das Wissen, welches wir mit unserem Konzept des Vertrauens hinzufügen, soll Softwarearchitekten die Möglichkeit geben, die Qualität ihrer Modelle zu erhöhen und Anforderungen an die Zugriffskontrolle ihrer Systeme bereits in frühen Phasen der Softwareentwicklung, unter Berücksichtigung von Ungewissheiten zu verifizieren. Die Anwendbarkeit unseres Ansatzes evaluieren wir anhand der Verfügbarkeit der notwendigen Daten in verschiedenen Phasen der Softwareentwicklung, sowie des potenziellen Mehrwerts für bestehende Systeme. Wir messen die Genauigkeit der Analyse beim Identifizieren von Problemen und die Skalierbarkeit hinsichtlich der Ausführungszeit, wenn verschiedene Modellaspekte individuell vergrößert werden

Monotonicity aspects of linguistic fuzzy models

Their interpretable model structure sets linguistic fuzzy m models apart from other modelling techniques and is considered their greatest asset. Therefore, in the identification process of a linguistic fuzzy model, the interpretability of the model should be safeguarded or at least be balanced against its accuracy. A good trade-off between accuracy and interpretability can be obtained by including as much qualitative knowledge as possible in the data-driven model identification process. Monotonicity is the type of qualitative knowledge that plays a central role in this dissertation. Monotone is hereby interpreted as order-preserving. This dissertation contributes to the ecological modelling domain by the application of fuzzy ordered classifiers to a habitat suitability modelling problem of river sites along springs to small rivers in the Central and Western Plains of Europe for 86 macroinvertebrate species. Furthermore, it contributes to the fuzzy modelling domain by (1) introducing an accurate and fast computational method for determining the crisp output of Mamdani-Assilian models applying the Center of Gravity defuzzification method and using fuzzy output partitions of trapezial membership functions, (2) presenting a new performance measure for fuzzy ordered classifiers, referred to as the average deviation (AD) as it takes the ordering of the output classes into account, (3) formulating guidelines for designers of monotone linguistic fuzzy models and (4) introducing a new inference procedure, called ATL-ATM inference, for linguistic fuzzy models with a monotone rule base

Multivalued logic systems for technical applications

Velmi často je vyžadováno, aby automatizovaná zařízení byla jistým způsobem "inteligentní", tedy aby jejich řídicí systémy uměly emulovat rozhodovací proces. Tato diplomová práce poskytuje obecný formální popis vícehodnotových logických systémů schopných zmíněné emulace a jejich souvislost s teorií fuzzy množin. Jsou uvedeny způsoby vytváření matematických modelů založených na lingvistických datech. Dále se práce zabývá znalostními bázemi a jejich vlastnostmi. Součástí této práce je také počítačový program sloužící k tvorbě slovních modelů.Automated devices are very often required to exhibit some kind of an intelligent behaviour, which means that their control systems must be able to emulate the reasoning process. This diploma thesis provides a general formal description of multivalued logic systems capable of such an emulation and their connection with the fuzzy set theory. Ways of constructing mathematical models based on linguistic data are described. Also, knowledge bases and their properties are discussed. A computer program serving as a linguistic model development tool is a part of this thesis.

Fuzzy Natural Logic in IFSA-EUSFLAT 2021

The present book contains five papers accepted and published in the Special Issue, “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”, of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference “The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences”, which took place in Bratislava (Slovakia) from September 19 to September 24, 2021. Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF–THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented. This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications