Logic and Foundations Commons^™

Complexity And Decomposability Of Relations, Martin Zwick

Complex Systems Faculty Publications and Presentations

A discrete multivariate relation, defined set-theoretically, is a subset of a cartesian product of sets which specify the possible values of a number of variables. Where three or more variables are involved, the highest order relation, namely the relation between all the variables, may or may not be decomposable without loss into sets of lower order relations which involve subsets of the variables. In a completely parallel manner, the highest order relation defined information-theoretically, namely the joint probability distribution involving all the variables, may or may not be decomposed without loss into lower-order distributions involving subsets of the variables. Decomposability …

Resolution Of Local Inconsistency In Identification, Douglas Ray Anderson, Martin Zwick

Complex Systems Faculty Publications and Presentations

This paper reports an algorithm for the resolution of local inconsistency in information-theoretic identification. This problem was first pointed out by Klir as an important research area in reconstructability analysis. Local inconsistency commonly arises when an attempt is made to integrate multiple data sources, i.e., contingency tables, which have differing common margins. For example, if one ha)s an AB table and a BC table, the B margins obtained from the two tables may disagree. If the disagreement can be assigned to sampling error, then one can arrive at a compromise B margin, adjust the original AB and BC tables to …

Fuzzy Logic: An Analysis Of Logical Connectives And Their Characterizations, John F. Hamman

Dissertations and Theses @ UNI

The focus of this thesis is to determine exactly which functions serve as appropriate fuzzy negation, conjunction and disjunction functions. To this end, the first chapter serves as motivation for why fuzzy logic is needed, and includes an original demonstration of the inadequacy of many valued logics to resolve the sorites paradox. Chapter 2 serves as an introduction to fuzzy sets and logic. The canonical fuzzy set of tall men is examined as a motivating example, and the chapter concludes with a discussion of membership functions.

Four desirable conditions of the negation function are given in Chapter 3, but it …