Set Theory and Logic

1004 Submissions

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

Some Characterisations of α-Cut in Intuitionistic Fuzzy Set Theory

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

A Note on Neutrosophy

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

Toward Excitation and Inhibition in Neutrosophic Logic

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

Truth and Absolute Truth in Neutrosophic Logic

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

Single Valued Neutrosophic Sets

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

Neutrosophic Diagram and Classes of Neutrosophic Paradoxes

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

N-norm and N-conorm in Neutrosophic Logic and Set, and the Neutrosophic Topologies

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

n-ary Fuzzy Logic and Neutrosophic Logic Operators

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

Strategy on T, I, F Operators.

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

Toward Dialectic Matter Element of Extenics Model

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