by Chow Kan Shing. / Includes questionnaire in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 100-103). / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- A Brief Review on Fuzzy Set Theory --- p.3 / Chapter 2.1. --- The Concept of Fuzzy Set Theory --- p.3 / Chapter 2.2. --- Fundamental Operations on Fuzzy Sets --- p.4 / Chapter 2.3. --- Two Approaches to Investigate Fuzzy Set Theory --- p.6 / Chapter Chapter 3. --- The Interpretation of the Membership Function --- p.7 / Chapter 3.1. --- Review and Comparison of the Interpretation of the Membership Values --- p.7 / Chapter 3.1.1. --- Interpretation in terms of Betting / Chapter 3.1.2. --- Interpretation in terms of Payoff Function / Chapter 3.1.3. --- Interpretation in terms of Amount of Relevant Attribute / Chapter 3.1.4. --- Interpretation in terms of the TEE Model / Chapter 3.1.5. --- Interpretation in terms of a Measurement Model / Chapter 3.1.6. --- Interpretation in terms of Prototype Theory / Chapter 3.2. --- Discussion about Membership Function --- p.29 / Chapter Chapter 4. --- Estimation of the Membership Function --- p.33 / Chapter 4.1. --- The Data Collection Methods for the Estimation of the Membership Function --- p.34 / Chapter 4.1.1. --- Direct Rating / Chapter 4.1.2. --- Polling / Chapter 4.1.3. --- Set-valued Statistics / Chapter 4.1.4. --- Reverse Rating / Chapter 4.2. --- Estimation Procedures for the Membership Function and their Characteristics --- p.36 / Chapter 4.2.1. --- Non-parametric Estimation Procedures / Chapter 4.2.2. --- The Characteristics of the Non-parametric Estimation Procedures / Chapter 4.2.3. --- Parametric Estimation Procedures / Chapter 4.3. --- Connections between the Four Data Collection Methods --- p.58 / Chapter 4.3.1. --- Connection between Direct Rating and Polling / Chapter 4.3.2. --- Connection between Polling and Reverse Rating / Chapter 4.3.3. --- Connection between Reverse Rating and Set-valued Statistics / Chapter 4.4. --- Other Estimation Procedures --- p.71 / Chapter 4.4.1. --- Procedure based on Saaty's Matrix / Chapter 4.4.2. --- Procedure based on Mabuchi's Interpretation of the Membership Function / Chapter 4.5. --- The Survey --- p.77 / Chapter 4.5.1. --- Introduction of the Survey / Chapter 4.5.2. --- The Result of the Survey / Chapter 4.5.3. --- An Approach to reduce the 'bias' in Polling / Chapter 4.5.4. --- Advice to Researchers / Chapter Chapter 5. --- Discussion --- p.97 / References --- p.100 / Appendix: Questionnaire

Thesis--M. Phil., University of Hong Kong, 1986.

published_or_final_version / Mathematics / Master / Master of Philosophy

Thesis (M.A.)--Boston University

M.Ing. (Electrical & Electronic Engineering) / A dynamic process is considered modelled and identified when the model can predict its future behaviour as a result of a known stimulus. However, practical reality is complex and it is quite difficult to totally encompass a model representing a physical phenomenon in a mathematical formulation. Besides, to keep such formulations tractable, certain restrictive assumptions such as, for example, linearity, are often required. The common feature of general control-theoretic methods used for modelling is that they presuppose the valid and accurate knowledge of the processes to be controlled. If, however, one does not understand the inner workings of a complex process that one wishes to model, traditional techniques rarely yield satisfactory results. As systems become more complex it becomes increasingly difficult to make mathematical statements about them which are both meaningful and precise. Thus one is compelled to concede that imprecision and inexactness must be accepted in any real system application. The theory of fuzzy sets is a methodology for the handling of qualitative, inexact, imprecise, information in a systematic and rigorous way. This approach provides an excellent tool for the modelling of human-centered systems, especially because fuzziness seems to be an important facet of the human thinking process. Instead of using a precisely defined or measured value of a variable, a human being tends to summarize available information by classifying into vague and imprecise categories such as, for example, low, medium, high. In this way, the information received from the outside world is reduced to just what is needed to perform the task on hand with the required precision. Thus there is no need for precise mathematical models and thereby the human (i.e. fuzzy) decision-making mechanism has considerably less computational overhead and is thus faster and more conducive to biological survival than an equivalent precise mathematical model...

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Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Mavris, Dimitri; Committee Member: Bishop, Carlee; Committee Member: Brown, David; Committee Member: Costello, Mark; Committee Member: Schrage, Daniel. Part of the SMARTech Electronic Thesis and Dissertation Collection.

This paper is a small remark on the analyticity of a limit of analytic sets in a particular case: when the sets are complex discs.

The purpose of this paper is to present a study of partly ordered sets. It includes a rigorous development of relations based on the notion of a relation as a set, lattices, and theorems concerning the lattice of subgroups of a group.

No description available.