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IMI/Publicaţii/CSJM/Ediţii/CSJM v.6, n.3 (18), 1998/

Fuzzy Multi-dimensional Analysis and Resolution Operation

Authors: Savinov Alexandr

Abstract

In this paper a new original approach to the analysis of fuzzy multi- dimensional distributions is described. A uniform method for representing fuzzy multi-dimensional distributions by means of sectioned vectors and matrices is proposed. Sectioned matrix is interpreted as fuzzy conjunctive normal form, while its line vectors are interpreted as fuzzy disjunctions. Several useful characteristics of fuzzy distributions and disjunctions are defined and studied. The main operation for manipulating fuzzy multi-dimensional distributions is an original fuzzy resolution which is applied to any two disjunctions on some variable and results in a third disjunction called resolvent. The property of adjacency of two disjunctions is defined and the criterion of adjacency is formulated. It is shown that the proposed resolution operation is a generalization of the conventional resolution and the whole approach can be viewed as a generalization of propositional logic. Methods for finding prime disjunctions, projection on a variable (thus solving the satisfiability problem) and transforming into the dual form are proposed.

A.A. Savinov,
Institute of Mathematics
Moldavian Academy of Sciences
5, Academiei str., Kishinev
MD-2028, Moldova
Phone: 3732-73-81-30,
E-mail: , ,
web-site: http://www.geocities.com/ResearchTriangle/7220/

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