Data Structures and Algorithms

1004 Submissions

[2] viXra:1004.0015 [pdf] submitted on 8 Mar 2010

Neutrosophic Relational Data Model

Authors: Haibin Wang, Rajshekhar Sunderraman, Florentin Smarandache, André Rogatko
Comments: 25 pages

In this paper, we present a generalization of the relational data model based on interval neutrosophic set [1]. Our data model is capable of manipulating incomplete as well as inconsistent information. Fuzzy relation or intuitionistic fuzzy relation can only handle incomplete information. Associated with each relation are two membership functions one is called truth-membership function T which keeps track of the extent to which we believe the tuple is in the relation, another is called falsity-membership function F which keeps track of the extent to which we believe that it is not in the relation. A neutrosophic relation is inconsistent if there exists one tuple a such that T(α) + F(α) > 1. In order to handle inconsistent situation, we propose an operator called "split" to transform inconsistent neutrosophic relations into pseudo-consistent neutrosophic relations and do the set-theoretic and relation-theoretic operations on them and finally use another operator called "combine" to transform the result back to neutrosophic relation. For this data model, we define algebraic operators that are generalizations of the usual operators such as intersection, union, selection, join on fuzzy relations. Our data model can underlie any database and knowledge-base management system that deals with incomplete and inconsistent information.
Category: Data Structures and Algorithms

[1] viXra:1004.0007 [pdf] replaced on 12 Apr 2010

Algebraic Generalization of Venn Diagram

Authors: Florentin Smarandache
Comments: 3 pages

It is easy to deal with a Venn Diagram for 1 ≤ n ≤ 3 sets. When n gets larger, the picture becomes more complicated, that's why we thought at the following codification. That's why we propose an easy and systematic algebraic way of dealing with the representation of intersections and unions of many sets.
Category: Data Structures and Algorithms