Unrestricted solutions of arbitrary linear fuzzy systems

Solving linear fuzzy system has intrigued many researchers due to its ability to handle imprecise information of real problems. However, there are several weaknesses of the existing methods. Among the drawbacks are heavy dependence on linear programing, avoidance of near zero fuzzy numbers, lack of accurate solutions, focus on limited size of the systems, and restriction to the matrix coefficients and solutions. Therefore, this study aims to construct new methods which are associated linear systems, min-max system and absolute systems in matrix theory with triangular fuzzy numbers to solve linear fuzzy systems with respect to the aforementioned drawbacks. It is proven that the new constructed associated linear systems are equivalent to linear fuzzy systems without involving any fuzzy operation. Furthermore, the new constructed associated linear systems are effective in providing exact solution as compared to linear programming, which is subjected to a number of constraints. These methods are also able to provide accurate solutions for large systems. Moreover, the existence of fuzzy solutions and classification of possible solutions are being checked by these associated linear systems. In case of near zero fully fuzzy linear system, fuzzy operations are required to determine the nature of solution of fuzzy system and to ensure the fuzziness of the solution. Finite solutions which are new concept of consistency in linear systems are obtained by the constructed min-max and absolute systems. These developed methods can also be modified to solve advanced fuzzy systems such as fully fuzzy matrix equation and fully fuzzy Sylvester equation, and can be employed for other types of fuzzy numbers such as trapezoidal fuzzy number. The study contributes to the methods to solve arbitrary linear fuzzy systems without any restriction on the system

A weighted goal programming approach to fuzzy linear regression with quasi type-2 fuzzy input-output data

This study attempts to develop a regression model when both input data and output data are quasi type-2 fuzzy numbers. To estimate the crisp parameters of the regression model, a linear programming model is proposed based on goal programming. To handle the outlier problem, an omission approach is proposed. This approach examines the behavior of value changes in the objective function of proposed model when observations are omitted. In order to illustrate the proposed model, some numerical examples are presented. The applicability of the proposed method is tested on a real data set on soil science. The predictive performance of the model is examined by cross-validation.Publisher's Versio

AUTOMATED INTERPRETATION OF THE BACKGROUND EEG USING FUZZY LOGIC

A new framework is described for managing uncertainty and for deahng with artefact corruption to introduce objectivity in the interpretation of the electroencephalogram (EEG). Conventionally, EEG interpretation is time consuming and subjective, and is known to show significant inter- and intra-personnel variation. A need thus exists to automate the interpretation of the EEG to provide a more consistent and efficient assessment. However, automated analysis of EEGs by computers is complicated by two major factors. The difficulty of adequately capturing in machine form, the skills and subjective expertise of the experienced electroencephalbgrapher, and the lack of a reliable means of dealing with the range of EEG artefacts (signal contamination). In this thesis, a new framework is described which introduces objectivity in two important outcomes of clinical evaluation of the EEG, namely, the clinical factual report and the clinical 'conclusion', by capturing the subjective expertise of the electroencephalographer and dealing with the problem of artefact corruption. The framework is separated into two stages .to assist piecewise optimisation and to cater for different requirements. The first stage, 'quantitative analysis', relies on novel digital signal processing algorithms and cluster analysis techniques to reduce data and identify and describe background activities in the EEG. To deal with artefact corruption, an artefact removal strategy, based on new reUable techniques for artefact identification is used to ensure that artefact-free activities only are used in the analysis. The outcome is a quantitative analysis, which efficiently describes the background activity in the record, and can support future clinical investigations in neurophysiology. In clinical practice, many of the EEG features are described by the clinicians in natural language terms, such as very high, extremely irregular, somewhat abnormal etc. The second stage of the framework, 'qualitative analysis', captures the subjectivity and linguistic uncertainty expressed.by the clinical experts, using novel, intelligent models, based on fuzzy logic, to provide an analysis closely comparable to the clinical interpretation made in practice. The outcome of this stage is an EEG report with qualitative descriptions to complement the quantitative analysis. The system was evaluated using EEG records from 1 patient with Alzheimer's disease and 2 age-matched normal controls for the factual report, and 3 patients with Alzheimer's disease and 7 age-matched nonnal controls for the 'conclusion'. Good agreement was found between factual reports produced by the system and factual reports produced by qualified clinicians. Further, the 'conclusion' produced by the system achieved 100% discrimination between the two subject groups. After a thorough evaluation, the system should significantly aid the process of EEG interpretation and diagnosis

North American Fuzzy Logic Processing Society (NAFIPS 1992), volume 2

This document contains papers presented at the NAFIPS '92 North American Fuzzy Information Processing Society Conference. More than 75 papers were presented at this Conference, which was sponsored by NAFIPS in cooperation with NASA, the Instituto Tecnologico de Morelia, the Indian Society for Fuzzy Mathematics and Information Processing (ISFUMIP), the Instituto Tecnologico de Estudios Superiores de Monterrey (ITESM), the International Fuzzy Systems Association (IFSA), the Japan Society for Fuzzy Theory and Systems, and the Microelectronics and Computer Technology Corporation (MCC). The fuzzy set theory has led to a large number of diverse applications. Recently, interesting applications have been developed which involve the integration of fuzzy systems with adaptive processes such a neural networks and genetic algorithms. NAFIPS '92 was directed toward the advancement, commercialization, and engineering development of these technologies

Using Pythagorean Fuzzy Sets (PFS) in Multiple Criteria Group Decision Making (MCGDM) Methods for Engineering Materials Selection Applications

The process of materials’ selection is very critical during the initial stages of designing manufactured products. Inefficient decision-making outcomes in the material selection process could result in poor quality of products and unnecessary costs. In the last century, numerous materials have been developed for manufacturing mechanical components in different industries. Many of these new materials are similar in their properties and performances, thus creating great challenges for designers and engineers to make accurate selections. Our main objective in this work is to assist decision makers (DMs) within the manufacturing field to evaluate materials alternatives and to select the best alternative for specific manufacturing purposes. In this research, new hybrid fuzzy Multiple Criteria Group Decision Making (MCGDM) methods are proposed for the material selection problem. The proposed methods tackle some challenges that are associated with the material selection decision making process, such as aggregating decision makers’ (DMs) decisions appropriately and modeling uncertainty. In the proposed hybrid models, a novel aggregation approach is developed to convert DMs crisp decisions to Pythagorean fuzzy sets (PFS). This approach gives more flexibility to DMs to express their opinions than the traditional fuzzy and intuitionistic sets (IFS). Then, the proposed aggregation approach is integrated with a ranking method to solve the Pythagorean Fuzzy Multi Criteria Decision Making (PFMCGDM) problem and rank the material alternatives. The ranking methods used in the hybrid models are the Pythagorean Fuzzy TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution) and Pythagorean Fuzzy COPRAS (COmplex PRoportional Assessment). TOPSIS and COPRAS are selected based on their effectiveness and practicality in dealing with the nature of material selection problems. In the aggregation approach, the Sugeno Fuzzy measure and the Shapley value are used to fairly distribute the DMs weight in the Pythagorean Fuzzy numbers. Additionally, new functions to calculate uncertainty from DMs recommendations are developed using the Takagai-Sugeno approach. The literature reveals some work on these methods, but to our knowledge, there are no published works that integrate the proposed aggregation approach with the selected MCDM ranking methods under the Pythagorean Fuzzy environment for the use in materials selection problems. Furthermore, the proposed methods might be applied, due to its novelty, to any MCDM problem in other areas. A practical validation of the proposed hybrid PFMCGDM methods is investigated through conducting a case study of material selection for high pressure turbine blades in jet engines. The main objectives of the case study were: 1) to investigate the new developed aggregation approach in converting real DMs crisp decisions into Pythagorean fuzzy numbers; 2) to test the applicability of both the hybrid PFMCGDM TOPSIS and the hybrid PFMCGDM COPRAS methods in the field of material selection. In this case study, a group of five DMs, faculty members and graduate students, from the Materials Science and Engineering Department at the University of Wisconsin-Milwaukee, were selected to participate as DMs. Their evaluations fulfilled the first objective of the case study. A computer application for material selection was developed to assist designers and engineers in real life problems. A comparative analysis was performed to compare the results of both hybrid MCGDM methods. A sensitivity analysis was conducted to show the robustness and reliability of the outcomes obtained from both methods. It is concluded that using the proposed hybrid PFMCGDM TOPSIS method is more effective and practical in the material selection process than the proposed hybrid PFMCGDM COPRAS method. Additionally, recommendations for further research are suggested

Development of Interactive Support Systems for Multiobjective Decision Analysis under Uncertainty

This paper presents interactive multiobjective decision analysis support systems, called MIDASS, which is a newly developed interactive computer program for strategic use of expected utility theory. Decision analysis based on expected utility hypothesis is an established prescriptive approach for supporting business decisions under uncertainty, which embodies an effective procedure for seeking the best choice among alternatives. It is usually difficult, however, for the decision maker (DM) to apply it for the strategic use in the realistic business situations. MIDASS provides an integrated interactive computer system for supporting multiobjective decision analysis under uncertainty, which assists to derive an acceptable business solution for DM with the construction of his/her expected multiattribute utility fuction (EMUF).expected multiobjective decision analysis, MIDASS, expected multiattribute utility function (EMUF), intelligent decision support systems (IDSS).

Hand (Motor) Movement Imagery Classification of EEG Using Takagi-Sugeno-Kang Fuzzy-Inference Neural Network

Approximately 20 million people in the United States suffer from irreversible nerve damage and would benefit from a neuroprosthetic device modulated by a Brain-Computer Interface (BCI). These devices restore independence by replacing peripheral nervous system functions such as peripheral control. Although there are currently devices under investigation, contemporary methods fail to offer adaptability and proper signal recognition for output devices. Human anatomical differences prevent the use of a fixed model system from providing consistent classification performance among various subjects. Furthermore, notoriously noisy signals such as Electroencephalography (EEG) require complex measures for signal detection. Therefore, there remains a tremendous need to explore and improve new algorithms. This report investigates a signal-processing model that is better suited for BCI applications because it incorporates machine learning and fuzzy logic. Whereas traditional machine learning techniques utilize precise functions to map the input into the feature space, fuzzy-neuro system apply imprecise membership functions to account for uncertainty and can be updated via supervised learning. Thus, this method is better equipped to tolerate uncertainty and improve performance over time. Moreover, a variation of this algorithm used in this study has a higher convergence speed. The proposed two-stage signal-processing model consists of feature extraction and feature translation, with an emphasis on the latter. The feature extraction phase includes Blind Source Separation (BSS) and the Discrete Wavelet Transform (DWT), and the feature translation stage includes the Takagi-Sugeno-Kang Fuzzy-Neural Network (TSKFNN). Performance of the proposed model corresponds to an average classification accuracy of 79.4 % for 40 subjects, which is higher than the standard literature values, 75%, making this a superior model

An investigation into the merits of fuzzy logic control versus classical control.

A project report submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering.Up to now the benefits and problems with fuzzy control have not been fully identified and its role in the control domain needs investigation. The past trend has been to show that a fuzzy controller can provide better control than classical control, without examining what is actually being achieved. The aim in this project report is to give a fair comparison between classical and fuzzy control. Robustness, disturbance rejection, noise suppression" nonminimurn phase and dead time are examined for both controllers. The comparison is performed through computer simulation of classical and fuzzy controlled plant models. Fuzzy control has the advantage of non-linear performance and the ability to capture linguistic information. Translating quantitative information into the fuzzy domain is difficult; therefore when the system is easily mathematically modelled and linear, classical control is usually better. Which controller should be used depends on the application, control designer and information available.Andrew Chakane 201

Parameterizing and Aggregating Activation Functions in Deep Neural Networks

The nonlinear activation functions applied by each neuron in a neural network are essential for making neural networks powerful representational models. If these are omitted, even deep neural networks reduce to simple linear regression due to the fact that a linear combination of linear combinations is still a linear combination. In much of the existing literature on neural networks, just one or two activation functions are selected for the entire network, even though the use of heterogenous activation functions has been shown to produce superior results in some cases. Even less often employed are activation functions that can adapt their nonlinearities as network parameters along with standard weights and biases. This dissertation presents a collection of papers that advance the state of heterogenous and parameterized activation functions. Contributions of this dissertation include three novel parametric activation functions and applications of each, a study evaluating the utility of the parameters in parametric activation functions, an aggregated activation approach to modeling time-series data as an alternative to recurrent neural networks, and an improvement upon existing work that aggregates neuron inputs using product instead of sum