Division, crisp

Objective knowledge can be used to place objects into classes or sets. A class could be defined that consists of all the organic molecules that contain exactly three carbon atoms. If all objects in a group can be allocated to classes in a way that involves no uncertainty, so that the division is sharp and unambiguous, we call this a crisp division. Every organic molecule either contains... 

Thus, propanol, C3H70H, has a membership of 1 in the three-carbon molecule class, while ethanol, C2H5OH, has a membership of 0 in the same class. As the membership in a crisp set must take one of only two possible values, Boolean (two-valued) logic can be used to manipulate crisp sets. If all the knowledge that we have can be described by placing objects in sets that are separated by crisp divisions, the sort of rule-based approach to the development of an expert system described in the previous chapter is appropriate. 

CRISP. 1993. Computer Retrieval of Information on Scientific Projects. National Institutes of Health, Division of Research Grants, Bethesda, MD. May 13, 1993. 

This chapter was prepared for the International Agency for Research on Cancer Symposium on Evaluation of Human Health Risks from Drinking Water (December 14, 1984). The opinions expressed in this chapter are those of the author. They do not necessarily reflect the position of the USEPA. The authors perspectives are derived from the assessment activities and interactions with many members of the Criteria and Standards Division and others in the USEPA Office of Drinking Water. These include Larry Anderson, Ambika Bathija, Paul Berger, Richard Cothem, William Coniglio, Penelope Fenner-Crisp,... 

CRISP. 1992. Crisp Data Base. National Institute of Health, National Institute of Health, Division of Research Resources. 

The extension principle The extension principle, introduced by Zadeh, is one of the basic ideas related to fuzzy set theory. This principle provide an extension of the mathematical relationship between fuzzy sets and crisp sets. In this paper only the concepts associated with addition, multiplication, subtraction and division will be considered. 

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