Fuzzy logicとNonstandard Analysis

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概要

• 論文の詳細を見る

• The present paper consists of the following two parts. 1. Some ambiguous notions in our real life can be seen as ultrafilters on partially ordered sets. A fuzzy set corresponds to an ultafilter. But well known theorems show that fuzzy sets as ultrafilters are crisp sets. For a Heyting algebra H, the category H-fuzzy sets can be defined, representing a many valued logic. Since a category H-fuzzy sets is topos ⇄ H is Boolean, fuzzy logic must be rich in a category which is not topos. 2. Nonstandard analysis is constructed on the theory of ultrafilters. Let I be a countable partially ordered set. Then there is an ultrafilter F on I such that a truth-value function T can be defined and X∈F 1/2≦T(X)≦1. Defining such many valued logic with truth-function T, a proposition in mathematics is proved to be consistent.

• 明治大学の論文

著者

• 大橋 健八郎

  School Of Science And Technology Meiji University

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