Lawry J. Modelling and Reasoning with Vague Concepts

Springer, 2006. — 260.Vague concepts are intrinsic to human communication. Somehow it would seems that vagueness is central to the flexibility and robustness of natural language descriptions. If we were to insist on precise concept definitions then we would be able to assert very little with any degree of confidence. In many cases our perceptions simply do not provide sufficient information to allow us to verify that a set of formal conditions are met. Our decision to describe an individual as 'tall' is not generally based on any kind of accurate measurement of their height. Indeed it is part of the power of human concepts that they do not require us to make such fine judgements. They are robust to the imprecision of our perceptions, while still allowing us to convey useful, and sometimes vital, information. The study of vagueness in Artificial Intelligence (AI) is therefore motivated by the desire to incorporate this robustness and flexibility into intelligent computer systems. This goal, however, requires a formal model of vague concepts that will allow us to quantify and manipulate the uncertainty resulting from their use as a means of passing information between autonomous agents.
I first became interested in these issues while working with Jim Baldwin to develop a theory of the probability of fuzzy events based on mass assignments. Fuzzy set theory has been the dominant theory of vagueness in AI since its introduction by Lotfi Zadeh in 1965 and its subsequent successful application in the area of automatic control. Mass assignment theory provides an attractive model of fuzzy sets, but I became increasingly frustrated with a range of technical problems and unintuitive properties that seemed inherent to both theories. For example, it proved to be very difficult to devise a measure of conditional probability for fuzzy sets, that satisfied all of a minimal set of intuitive properties. Also, mass assignment theory provides no real justification for the truth-functionality assumption central to fuzzy set theory.
This volume is the result of my attempts to understand and resolve some of these fundamental issues and problems, in order to provide a coherent framework for modelling and reasoning with vague concepts. It is also an attempt to develop such a framework as can be applied in practical problems concerning automated reasoning, knowledge representation, learning and fusion. I do not believe AI research should be carried out in isolation from potential applications. In essence AI is an applied subject. Instead, I am committed to the idea that theoretical development should be informed by complex practical problems, through the direct application of theories as they are developed. Hence, I have dedicated a significant proportion of this book to presenting the application of the proposed framework in the areas of data analysis, data mining and information fusion, in the hope that this will give the reader at least some indication as to the utility of the more theoretical ideas.
Finally, I believe that much of the controversy in the AI community surrounding fuzzy set theory and its application arises from the lack of a clear operational semantics for fuzzy membership functions, consistent with their truth-functional calculus. Such an interpretation is important for any theory to ensure that its not based on an ad hoc, if internally consistent, set of inference processes. It is also vital in knowledge elicitation, to allow for the translation of uncertainty judgements into quantitative values. For this reason there will be a semantic focus throughout this volume, with the aim of identifying possible operational interpretations for the uncertainty measures discussed.Vague Concepts and Fuzzy Sets
Label Semantics
Multi-Dimensional and Multi-Instance Label Semantics
Information from Vague Concepts
Learning Linguistic Models from Data
Fusing Knowledge and Data
Non-Additive Appropriateness Measures