[10] **viXra:1004.0112 [pdf]**
*submitted on 21 Apr 2010*

**Authors:** V. Veeramani, Roque Batulan

**Comments:** 7 pages

This paper contains the Basic Definitions of an Intuitionstic Fuzzy Set theory and
operations on it. Mainly we discussed the basic concepts of α - cut with examples
and Characterisations.

**Category:** Set Theory and Logic

[9] **viXra:1004.0096 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Cheng-Gui Huang

**Comments:** 1 pages.

I claim that Neutrosophy, by Professor Florentin Smarandache, is a deep thought in human culture.
That gives advantage to break the mechanical understanding of human culture. For example,
according to the mechanical theory: existence and non-existence could not be simultaneously.
Actually existence and non-existence are simultaneously. Everyone knows that human life is
like a way in the empty space of a bird flying. Everyone can not see himself a second ago,
everyone can not see himself for the time being and everyone can not see himself a second
future. Everyone could not know what is the existence of self. Everyone is also difficult to
say the non-existence of self. So the existence and non-existence of self are simultaneously.
And the existence and nonexistence of everything are simultaneously, where, the law of excluded
middle does not apply. These basic facts express the depth of Smarandache's Neutrosophy. He
has a lot of friends in ancient and in nowadays, in the West and in the East.

**Category:** Set Theory and Logic

[8] **viXra:1004.0092 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Feng Liu

**Comments:** 8 pages.

Logic should have been defined as the unity of contradiction between logic director and logic
implementation. Chinese Daoism asserts that everything is defined in the unity of opposites,
namely yin and yang, accordingly yang conducts change and yin brings it up (I-Ching, also known
as Book of Changes). In this way logic is redefined in an indeterminate style to facilitate
"both A and Anti-A" etc. in neutrosophics of logic. The unity of opposites is also described
as neutrality in neutrosophy. An intermediate multi-referential model of excitation and inhibition
is developed to derive a multiagent architecture of logic, based on Chinese yin-yang philosophy.
This methodology of excitation/inhibition suggests a rhymed way of logic, leading to a dynamic
methodology of weight strategy that links logic with neural network approach. It also confirms
the crucial role of indeterminacy in logic as a fatal criticism to classical mathematics and
current basis of science.

**Category:** Set Theory and Logic

[7] **viXra:1004.0091 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Feng Liu

**Comments:** 12 pages.

As a philosophical analysis of some fatal paradoxes, the paper distinguishes the conceptual difference
between representation of truth and source of truth, and leads to the conclusion that in order to acquire
the genuine source of truth, independently of specific representations possibly belonging to different
worlds, one is necessary to ignore all the ideas, logics, conceptions, philosophies and representable
knowledge even himself belonging to those misleading worlds, returning to his infant nature, as a
preliminary step for his cultivation of unconstrained wisdom. It also carries out some coordinative
crucial issues as natural-doctrine, minded-unwitting, logic-infancy, conception-deconception,
determinacy-indeterminacy. The paper tries to verify the role of neutrosophy and neutrosophic logic in
religious issues and open a gateway toward the oriental classics, excavating the lost treasure.

**Category:** Set Theory and Logic

[6] **viXra:1004.0051 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Haibin Wang, Florentin Smarandache, Yan-Qing Zhang, Rajshekhar Sunderraman

**Comments:** 4 pages

Neutrosophic set is a part of neutrosophy which
studies the origin, nature, and scope of neutralities, as
well as their interactions with different ideational
spectra. Neutrosophic set is a powerful general formal
framework that has been recently proposed. However,
neutrosophic set needs to be specified from a technical
point of view. To this effect, we define the settheoretic
operators on an instance of neutrosophic set,
we call it single valued neutrosophic set (SVNS). We
provide various properties of SVNS, which are
connected to the operations and relations over SVNS.

**Category:** Set Theory and Logic

[5] **viXra:1004.0026 [pdf]**
*replaced on 22 Apr 2010*

**Authors:** Florentin Smarandache

**Comments:** 14 pages

These paradoxes are called "neutrosophic" since they are based on indeterminacy (or neutrality,
i.e. neither true nor false), which is the third component in neutrosophic logic. We generalize the
Venn Diagram to a Neutrosophic Diagram, which deals with vague, inexact, ambiguous, illdefined
ideas, statements, notions, entities with unclear borders. We define the neutrosophic truth
table and introduce two neutrosophic operators (neuterization and antonymization operators)
give many classes of neutrosophic paradoxes.

**Category:** Set Theory and Logic

[4] **viXra:1004.0016 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 11 pages

In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of
T-norms/T-conorms in fuzzy logic and set.
Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic
Topologies.

**Category:** Set Theory and Logic

[3] **viXra:1004.0013 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache, V. Christianto

**Comments:** 15 pages

We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic
logic binary operators. Then we generalize them to n-ary fuzzy logic and neutrosophic logic
operators using the smarandache codification of the Venn diagram and a defined vector
neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built.

**Category:** Set Theory and Logic

[2] **viXra:1004.0010 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 6 pages

The paper presents an initial explorations on T, I, F operations based on genetic concept
hierarchy and genetic referential hierarchy, as a novel proposal to the indeterminacy issue in
neutrosophic logic, in contrast to the T, I, F values inherited from conventional logics in which
those values would fail to demonstrate the genetic aspect of a concept and accordingly loose the
connection between generality and practicality. Based on the novel definition of logic and on the
relativity of T, F concept, it illustrates that T, F are hierarchical operations which inter-consist and
inter-complement each other, that "I" relates to a learning behavior profiled by an inspiration from
I-ching, and that the neutralization operation, as the means to solve contradictions, will eventually
come to the unification of opposites, leading to the fundamental issues in Buddhism and such alike.
It also implies that Buddhism and Daoism are not religions.

**Category:** Set Theory and Logic

[1] **viXra:1004.0006 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 10 pages

Based on the authors intensive investigation on the oriental dialectics, the paper presents a novel
theoretical frame of matter element in the world leading science, extenics dealing with inconsistency or
incompatibility, covering the widest range of application area from informatics, system engineering to
management and finance. The dialectic matter-element is defined as the integral of all existing and prospecting
ones based on all the infinite possible cognitive models. The novel model serves as the origin of constraint
matter elements, the unity of both state description and cognitive action (cognition force with respect to neural
science), a latent part of extenics, and possibly as essence of matter element. It explains, in a novel perspective,
the origin of a name, and uncovers the source of contradiction and even the impetus of cognition.

**Category:** Set Theory and Logic