"Fuzzy" Sets and Blue Eyes
Submitted by Kim Blutreich
Adapted from a series of posts in SHOWDALS, the mailing list for Show Dalmatians.
by: Jim Seltzer email@example.com Willowind Dalmatians
As we all know, virtually all faults discussed in various breed standards are not clearly defined, and each judge and exhibitor evaluates them independently. -- This is prelude and simply provides a launching point for what follows.
In the early '60s, Prof. Zadeh, U.C. Berkeley, was a guest lecturer at a symposium at the government research lab where I then worked. He introduced the mathematical concept of the "Fuzzy Set", which has become a well-known and widely applied concept in this day of computerized decision making and system control.
Quoting from a recent book, "Advances in Fuzzy Systems":
"While classical methodology only admits precise descriptions, fuzzy logic extends to subjective and vague phenomena. It includes the use of approximate reasoning, by which we model how humans obtain information from imprecise information. A major goal is to obtain a description of human knowledge and experience in a way that can be implemented on machines.The field has come a long way since fuzzy set theory was first propounded by Lotfi Zadeh in the mid-1960s. Within thirty years, it had developed from an abstract extension of conventional logic into a field with a whole range of practical applications. Initially, many of these arose in the field of process control, with Japan as pioneer. In recent years however fuzzy logic has found its way into even the commonest household appliances."
The fuzzy logic industry has it's own language; I list a few of the terms.
Fuzzification - The process of decomposing a system input and/or output into one or more qualitative groupings called fuzzy sets. Fuzzy set - A defined range of measured or calculated values. For example, a "long-back dog" fuzzy set may range from a length/height ratio of 1.5 to 1 .0, a "square dog" fuzzy set may range from 1.2 to 0.9 and a "short-back dog" fuzzy set may range from 1.0 to 0.7. Note that there is generally overlap in these sets. Each fuzzy set consists of 3 parts; domain, membership function, and degree of membership. Degree of membership - This is the degree to which a value belongs to a fuzzy set. For example, a length/height measurement may be 40% long-back dog and 20% square dog. Membership function - The curve used in a fuzzy set which maps a system input or output value, i.e., the actual measurement, to a degree of membership value.
The breed standard is "supposed" to provide the judge with a sort of "membership function", and the judge then determines the "degree of membership" by evaluating each dog in the ring according to its degree of membership. Using the breed standards weightings for each characteristic, the judge should be able to select the "best" dog shown, i.e., WD, WB, etc.
Several years ago I tried to very loosely introduce the Fuzzy Set concept to the development of a pictorial Dalmatian breed standard. The picture sets I developed were morphed sequences of well-known Dals of historic prominence in the breed that served as paradigms for the sequences which ran from ghastly on one extreme to the paradigm in the middle to preposterous on the other extreme. Unfortunately, the Fuzzy Set approach was deemed too confusing, and technical difficulties have delayed the completion of this venture.
By the way, the characteristic, "Blue Eyes", is also a fuzzy set -- and more on that subject follows:
The animal world is pretty limited in the variety of colors that can be produced (though the interplay of light reflection and diffraction makes it APPEAR that the variety is more extensive). Other than the red blood hemoglobin, pigment production is virtually limited to the melanins: eumelanin and phaeomelanin. Eumelanin is the set of dark pigments: blacks and browns; phaeomelanin is the lighter red-yellow pigment. Other shades are produced as variations and/or combinations of these pigments.
Blue is NOT among the pigments that result directly from pigment production in the pigment-producing cells.
A very concise description of eye color comes from Andre Henriksson of the University of Leeds:
"The iris is a disk shaped muscle with a hole (the pupil) in the center. It is responsible for adjusting the amount of light entering the eye. There are , in addition, optical effects created by the diameter of the pupil opening. The muscle fibers of the iris contain various amounts of melanin pigment deposited on the back (inside) surface and on the front. The purpose of the brown pigment is to absorb reflected light scatter inside the eye. A minimal amount of pigment on the back surface results in the appearance of "blue eyes", a larger amount of brown pigment on the rear makes for "hazel eyes". Add some pigment to the front and you get "green eyes" and more dense pigment on the front yields "brown eyes". The color of iris doesn't matter, though it has to be opaque enough to work as a diaphragm."
Hence, any discussion that talks about only two types of blue,i.e., "blue eyes" and "wall eyes", is too limiting. TOTAL lack of pigment results in the pink, extreme albino eye where the blood vessels are reflected through the iris. Various shades of pale blue, gray, dark blue, green, yellow, brown, etc. are caused by the varying amounts of BROWN (melanin) pigment occurring in the various layers of the iris -- and this is what makes eye color a "fuzzy set". Add to this the parti-colored blue/brown eyes and the situation becomes even more complex.
Willis, "Genetics of the Dog", cites some work by Burns and Fraser (1966), who propose that there are three eye color genes that interact to produce various shades of eye color. Willis also notes that some coat-color genes will also influence eye color. It is clear, however, that much more remains to be discovered in this area than is now known, and the importance of the subject is compounded by the strong relationship to Dal deafness -- manifested by absence of melanocytes in the stria vascularis of the inner ear.
The Dalmatian Club of the Piedmont is grateful to Jim Seltzer for allowing us to reprint this material, and even more grateful that he would trust us enough to allow us to edit it. This material is copyrighted. Please contact the author for permission to reprint.