Chapter X: Introduction to Fuzzy Set Theory Uncertainty is universal ...

Another type of fuzziness in biomedical research results from the fuzzy description of biological terms.
Our descriptions of many biological concepts often have difficulty fitting into a deterministic (crisp)
explanation. As a result, our knowledge, concepts, and representations of biological terms may also be
fuzzy, and fuzzy set theory is useful to describe these terms. For example, the species definitions for
microbes can be fuzzy due to recombination of the genetic materials across species [Hanage et al., 2005].
The concept of “protein function” is sometimes fuzzy because it is often based on whimsical terms or
contradictory nomenclature [Jansen and Gerstein, 2004]. This currently presents a challenge for
functional genomics. In addition, descriptions for similarity and typicality can be fuzzy. For example,
how much do two proteins resemble each other, what properties do they (partially) share, how close is a
given protein to the prototypical sequence of a protein family, etc. Such fuzziness could result from the
limitations of classifications, natural language, or poor understanding of the underlying mechanism.
Tolerance of fuzziness allows us to explore these biological concepts effectively.
But we still ask the question: do we really need fuzziness? If the world were deterministic, the answer
would be no. Boolean logic and probability theory would clearly suffice. This is the “balls in the urn”
world; you know, where you put 12 red balls and 7 green balls into an urn and ask questions like “If you
pick out 5 balls, what’s the probability that they are all red?” If however, you put balls of varying radii
into the urn and picked out 5, what’s the probability that they are all SMALL? Here the event, SMALL
balls, is ambiguous. You can convert this into the former case if you set a threshold radius below which a
ball is considered SMALL, but then 2 balls just on each side of the threshold will feel the same, but one
will be SMALL and the other Not SMALL. So, establishing such a threshold doesn’t match well with
human intuition in ambiguous cases. It would be nice to have models and calculi that handle these
situations.
Fuzzy set theory in general and fuzzy logic specifically are natural ways to model ambiguous events that
occur in human-like reasoning. People have no trouble operating with phrases such as “large risk factor”,
“somewhat likely to be involved in cancer”, “significantly hyper methylated”, etc. As will be seen, rules
containing such ambiguous clauses can be successfully handled in a fuzzy logic system.
The beauty (and also a danger, if we are not careful) of fuzzy set theory is that it offers a multitude of
calculi for the fusion of partial support for a hypothesis under investigation, that is, flexible mechanisms
to increase or decrease confidence in a decision as evidence unfolds. In his seminal text on computer
vision, [Marr, 1982], David Marr stated two principles to be followed in the design of intelligent (vision)
algorithms. The first is called the Principle of Least Commitment (PLC). He states it simply as “Don’t do
something that later must be undone”. Hence, in a complex computing scenario, one where there are
many decision making steps, avoid making deterministic decisions for as long as is possible. It is very