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An axiom or law which deals with indeterminacy is called neutrosophic axiom or law. We introduce these new structures because in the world we do not always know exactly or completely the space we work in; and because the axioms or laws are not always well defined on this space, or may have indeterminacies when applying them. Indeterminate Space due to Unknown Element.

And Neutrosophic Number included. Indeterminate Space due to Partially Known Element. Indeterminacy Axiom Law. Let us reconsider the same neutrosophic set D as above. We combine the ideas from Examples 5 and 6 and we construct the following example.

Therefore, N3 G 2;2;3 is a refined 2; 2; 3 -neutrosophic groupoid and a 3-refined I-neutrosophic groupoid. Indeterminate Space.

Or we might know that a point Q only partially belongs to the space S and partially does not belong to the space S [for example Q. Such situations occur when the space has vague or unknown frontiers, or the space contains ambiguous not well defined regions. We can extend this hybrid geometry adding a new space So the law defined on the set NG has the properties that: region where one does not know if there are or there are.

We can construct many such algebraic structures where at least one axiom has such behavior such indeterminacy in principal. The author would like to thank Mr. Neutrosophic Algebraic Structures A. I, EuropaNova, Brussels, Belgium, p. Vasantha Kandasamy, Florentin Smarandache, A.

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Selected logic papers - [PDF Document]

Vasantha Kandasamy, F. Florentin Smarandache editor , Neutrosoph-. Smarandache, V. Florentin Smarandache, V. Florentin Smarandache, D. Rabounski, L. Florentin Smarandache, H. Florentin Smarandache, W. Vasantha Kandasamy, K. Florentin Smarandache, Neutrosophy. Liu, Xiquan Chinese Branch, p. Neutrosophic Algebraic Structures - Edited Books. Neutrosophic Geometries Chimienti and M.

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Kuciuk and M. China, June , Press, Rehoboth, VIII, pp. Iseri, Smarandache Manifolds, Am. II, p.

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L1, In October , he repented and renewed his faith in Jesus Christ, and then he works only for Jesus Christ until now as an independent researcher. He is now studying theology in a local college in East Java graduate course , besides lecturing in a local college. He loves science as well as theology topics.

His particular interests are gravitation and cosmology.


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He has published more than nine books together with Prof. Florentin Smarandache and other scientists, including: a. Profile viewed times. Brawijaya University Engineer,. Faculty of Mathematics-Physics. Publishing Books He has published more than nine scientific books in various fields from astrophysics to quantum physics.

15. Particle Description, Liouville & Boltzmann Equations

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