# 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