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Solving problems in Library and Information Science using Fuzzy Set Theory.

Article Excerpt
ABSTRACT

VARIOUS MATHEMATICAL TOOLS AND THEORIES have found application in Library and Information Science (LIS). One of these is Fuzzy Set Theory (FST). FST is a generalization of classical Set Theory, designed to better model situations where membership of a set is not discrete but is "fuzzy." The theory dates from 1965, when Lotfi Zadeh published his seminal paper on the topic. As well as mathematical developments and extensions of the theory itself, there have been many applications of FST to such diverse areas as medical diagnoses and washing machines. The theory has also found application in a number of aspects of LIS. Information Retrieval (IR) is one area where FST can prove useful; this paper reviews IR applications of FST. Another major area of Information Science in which FST has found application is Informetrics; these studies are also reviewed. A few examples of the use of this theory in non-LIS domains are also examined.

BACKGROUND

When an information professional is confronted with a problem, there may be many different ways to tackle it. In the armoury of the profession, there are a number of tools and techniques that can be drawn upon to address the situation. A good problem solver needs to be aware of a wide range of tools that can be used in that particular situation. Tools developed for one specific situation may be applicable to others, though they be quite different. One class of tools that can be applied to library problems are mathematical tools. Mathematical tools are indispensable for solving a whole range of different types of problems. These tools include statistics, probability theory, operations research (including, for example, queuing theory), and cluster analysis.

Mathematical tools that are used to solve real-world problems fall into the category of applied mathematics. The essence of applied mathematics is abstraction and modeling. Some aspect of the real world may be modeled by a mathematical theory, which is an approximation of the reality. Development can take place in the mathematical theory, independent of any applications, and the results can then be applied back to the real world. How useful this is depends on how well the mathematical model captures the essence of the reality, and also how well the model has been formulated and developed. A good model will be able to provide useful insights into the real life situation, and will be a good tool for problem solving.

Set Theory is one theory or model that has proved enormously useful in a wide range of situations. Any collection of objects can be regarded as a set. Operations, such as union, intersection, and complementation, can be carried out on these sets. In fact, most of mathematics has Set Theory as its theoretical underpinning. The classical formulation of Set Theory applies to situations where membership of a set is discrete. The "set of red balls" or the "set of white cars" are situations where membership (or not) of the set from a universe of objects is definite. The "set of documents in a filing cabinet" or "the set of books on the library shelf" are also discrete and clear-cut sets. Set Theory has been applied in many situations that can be modeled by discrete membership, and has proven to be a useful tool.

However, there are many situations where classical Set Theory does not provide a good model. If there is some vagueness or fuzziness about the membership of a set, then classical Set Theory may not be useful. The "set of tall people" has the problem of defining exactly what constitutes a tall person: Where do you make the boundary of "tallness" and what happens if someone is marginally shorter than this boundary? The "set of relevant documents" also suffers from this problem. In Library and Information Science, "relevance" is sometimes regarded as dichotomous, but in reality, relevance is a graded concept with documents ranging from highly relevant for a particular purpose, to highly irrelevant, and every degree of relevance in between. (1)

In a seminal paper on what he defined as Fuzzy Sets, Zadeh (1965) attempted to provide a mathematical model that would be better suited to these vague situations. Fuzzy Set Theory (FST) has become a branch of mathematics that generalizes the concept of a set (2) to provide better tools for dealing with the sorts of situations described in the previous paragraph. Though designed to model fuzziness, the theory itself is not fuzzily defined. This essay will give an introduction to what FST is, as well as provide some of the applications for which it has been used. The material for this article has been developed from the first author's Ph.D. thesis (Hood, 1998).

Basic Idea Behind Fuzzy Set Theory

The basic idea behind FST is to generalize the concept of membership of a set. In classical (or crisp) sets, membership of a set can be regarded as a function with only two possible values. That is, an item either belongs to the set or does not. The generalization that is made to produce Fuzzy Sets is to allow the membership function to be multivalued. This allows an item to have a degree of membership in a set. An item can belong to a Fuzzy Set with any degree of membership from none to full. Let us consider the example of a "Fuzzy Set of Relevant Documents" for a particular query. In this case, a highly relevant document may belong to this set with high degree of membership; whereas a marginally relevant document will still belong to the set, but with only a small degree of membership. A totally nonrelevant document will not belong to this set at all.

The concept of...