[6] **viXra:1207.0062 [pdf]**
*submitted on 2012-07-16 23:17:12*

**Authors:** Florentin Smarandache

**Comments:** 8 Pages.

In this paper we extend Prof. Yang Chunyan and Prof. Cai Wen’s dependent function of a point P with respect to two nested sets X0 X, for the case the sets X0 and X have common ending points, from 1D-space to n-D-space. We give several examples in 2D- and 3D-spaces. When computing the dependent function value k(.) of the optimal point O, we take its maximum possible value.
Formulas for computing k(O), and the geometrical determination the Critical Zone are also given.

**Category:** Artificial Intelligence

[5] **viXra:1207.0058 [pdf]**
*submitted on 2012-07-16 05:14:14*

**Authors:** Florentin Smarandache

**Comments:** 7 Pages.

In this paper we introduce the indeterminate models in
information fusion, which are due either to the existence of some
indeterminate elements in the fusion space or to some
indeterminate masses. The best approach for dealing with such
models is the neutrosophic logic.

**Category:** Artificial Intelligence

[4] **viXra:1207.0057 [pdf]**
*submitted on 2012-07-16 05:15:50*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 8 Pages.

In most of classical fusion problems modeled from
belief functions, the frame of discernment is considered as static.
This means that the set of elements in the frame and the
underlying integrity constraints of the frame are fixed forever
and they do not change with time. In some applications, like in
target tracking for example, the use of such invariant frame is
not very appropriate because it can truly change with time. So it
is necessary to adapt the Proportional Conflict Redistribution
fusion rules (PCR5 and PCR6) for working with dynamical
frames. In this paper, we propose an extension of PCR5 and
PCR6 rules for working in a frame having some non-existential
integrity constraints. Such constraints on the frame can arise in
tracking applications by the destruction of targets for example.
We show through very simple examples how these new rules can
be used for the belief revision process.

**Category:** Artificial Intelligence

[3] **viXra:1207.0056 [pdf]**
*submitted on 2012-07-16 05:17:47*

**Authors:** Florentin Smarandache, Deqiang Han, Arnaud Martin

**Comments:** 7 Pages.

Uncertainty measures in the theory of belief functions
are important for the uncertainty representation and
reasoning. Many measures of uncertainty in the theory of belief
functions have been introduced. The degree of discord (or
conflict) inside a body of evidence is an important index for
measuring uncertainty degree. Recently, distance of evidence
is used to define a contradiction measure for quantifying the
degree of discord inside a body of evidence. The contradiction
measure is actually the weighted summation of the distance
values between a given basic belief assignment (bba) and the
categorical bba’s defined on each focal element of the given bba
redefined in this paper. It has normalized value and can well
characterize the self-discord incorporated in bodies of evidence.
We propose here, some numerical examples with comparisons
among different uncertainty measures are provided, together
with related analyses, to show the rationality of the proposed
contradiction measure.

**Category:** Artificial Intelligence

[2] **viXra:1207.0040 [pdf]**
*submitted on 2012-07-11 05:41:10*

**Authors:** Gurpinder Singh

**Comments:** 1 Page. this is only existing proof of this problem

t

**Category:** Artificial Intelligence

[1] **viXra:1207.0026 [pdf]**
*submitted on 2012-07-06 10:56:56*

**Authors:** Mitra Ganguly, Timothy Eller

**Comments:** 5 Pages. technical report in NUI, #551

In this paper, we address consensus seeking problem of dynamical agents on random sector graphs. Random sector graphs are directed
geometric graphs and have been investigated extensively. Each agent randomly walks on these graphs and communicates with each other if
and only if they coincide on a node at the same time. Extensive simulations are performed to show that global consensus can be reached.

**Category:** Artificial Intelligence