Crispness

Fuzzy sets and fuzzy logic. Fuzzy sets differ from the normal crisp sets in the fact that their elements have partial membership (represented by a value between 0 an 1) in the set. Fuzzy logic differs from the binary logic by the fact that the truth values are represented by fuzzy sets. 

A conventional set which contains members that satisfy such precise properties concerning theii set membership is called a crisp set. 

An important property of a fuzzy set is its cardinality. While for crisp sets the cardinality is simply the number of elements in a set, the cardinality of a fuzzy set A, CardA, gives the sum of the values of the membership function of A, as in Eq. (9). 

The principle of applying fuzzy logic to matching of spectra is that, given a sample spectrum and a collection of reference spectra, in a first step the reference spectra are unified and fuzzed, i.e., around each characteristic line at a certain wavenumber k, a certain fuzzy interval [/ o - Ak, + Afe] is laid. The resulting fuzzy set is then intersected with the crisp sample spectrum. A membership function analogous to the one in Figure 9-25 is applied. If a line of the sample spec-... 

Tempeh. DehuUed cooked soybeans are inoculated with the mold, Thi pus oligosporus packed in perforated plastic bags, and allowed to ferment for 18 h. The mold mycelium overgrows the soybean cotyledons and forms a compact cake. When sHced and deep-fried in oil, a crisp and golden brown product is obtained. Although native to Indonesia, tempeh has become popular with vegetarians in the United States and other Western countries (93). 

P. A. Fenner-Crisp, "Risk Assessment Methods for Pesticides in Food and Drinking Water," Office of Pesticide Programs, U.S. Environmental Protection Agency, presented at the Florida Pesticide Review Council Meeting, July 7, 1989. 

Sucrose is widely used in the food industry to sweeten, control water activity, add body or bulk, provide crispness, give surface glaze or frost, form a glass, provide viscosity, and impart desirable texture. It is used in a wide variety of products from bread to medicinal symps. 

Phospha.tes, Pentasodium triphosphate [7758-29-4] sodium tripolyphosphate, STPP, Na P O Q, is the most widely used and most effective builder in heavy-duty fabric washing compositions (see also Phosphoric acid and phosphates). It is a strong sequestrant for calcium and magnesium, with a p c of ca 6, and provides exceUent suspending action for soils. Because of its high sequestration power, it also finds extensive appHcation in automatic-dishwashing detergents. Sodium tripolyphosphate forms stable hydrates and thus aids in the manufacture of crisp spray-dried laundry powders. 

In this work, the crisp numerical data for the analyte and reference samples were transformed into the fuzzy form with the application of the L/ -representation. The procedure of fuzzyfication is illustrated roughly by the figure, where a and b are the nominal (crisp) measured values ... 

Conventional set theory distinguishes between those elements that are members of a set and those that are not, there being very clear, or crisp boundaries. Figure 10.2 shows the crisp set medium temperature . Temperatures between 20 and 30 °C he within the crisp set, and have a membership value of one. 

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