Archive for the ‘Soft Sets’ Category

Operations on soft sets revisited

Tuesday, May 15th, 2012

Operations on soft sets revisited by Ping Zhu and Qiaoyan Wen.

Abstract:

Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft sets from given soft sets, some operations on soft sets have been proposed. Unfortunately, such operations cannot keep all classical set-theoretic laws true for soft sets. In this paper, we redefine the intersection, complement, and difference of soft sets and investigate the algebraic properties of these operations along with a known union operation. We find that the new operation system on soft sets inherits all basic properties of operations on classical sets, which justifies our definitions.

An interesting paper will get you interested in soft sets if you aren’t already.

It isn’t easy going, even with the Alice and Bob examples, which I am sure the authors found immediately intuitive.

If you have data where numeric values cannot be assigned, it will be worth your while to explore this paper and the literature on soft sets.

Subjects, Identifiers, IRI’s, Crisp Sets

Sunday, September 19th, 2010

I was reading Fuzzy Sets, Uncertainty, and Information by George J. Klir and Tina A. Folger, when it occurred to me that use of IRI’s as identifiers for subjects, is by definition a “crisp set.”

Klir and Folger observe:

The crisp set is defined in such a was as to dichotomize the individuals in some given universe of discourse into two groups: members (those that certainly belong in the set) and nonmembers (those that certainly do not). A sharp, unambiguous distinction exists between the members of the class or category represented by the crisp set. (p. 3)

A subject can be assigned an IRI as an identifier, based on some set of properties.

That assignment and use as an identifier makes identification a crisp set operation.

Eliminates fuzzy, rough, soft and other non-crisp set operations, as well as other means of identification.

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What formal characteristics of crisp sets are useful for topic maps?

Are those characteristics useful for topic map design, authoring or both?

Extra credit: Any set software you would suggest to test your answers?