International Journal of Neutrosophic Science

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Introduction to Neutrosophic Subtraction Algebra and Neutrosophic Subtraction Semigroup

M.A. Ibrahim, A.A.A. Agboola , E.O. Adeleke, S.A. Akinleye

The objective of this paper is to introduce and study the notion of neutrosophic subtraction algebras and neutrosophic subtraction semigroups. It also introduces the notion of neutrosophic ideals of neutrosophic subtraction semigroup and presents some of their basic properties. In addition, the notion of neutrosophic homomorphism of neutrosophic subtraction semigroups and neutrosophic quotient subtraction semigroups was also introduced.

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Vol. 2 Issue. 1 PP. 47-62, (2020)

Some Results on Single Valued Neutrosophic (Weak) Polygroups

Madeleine Al- Tahan

Polygroups are a generalized concept of groups and  the concept of single valued neutrosophic set is a generalization of the classical notion of a set. The objective of this paper is to combine the innovative concept of single valued neutrosophic sets and polygroups. In this regard, we introduce the concepts of single valued neutrosophic polygroups and anti- single valued neutrosophic polygroups. Moreover, we investigate their properties and study the relation between level sets of single valued neutrosophic polygroups and (normal) subpolygroups.  

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Vol. 2 Issue. 1 PP. 38-46, (2020)

NeutroAlgebra is a Generalization of Partial Algebra

Florentin Smarandache

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures).  Let <A> be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to <A> and <antiA>, and one corresponding to neutral (indeterminate) <neutA> (also denoted <neutroA>) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space).  A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation).  

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Vol. 2 Issue. 1 PP. 08-17, (2020)

Uncertainty: two probabilities for the three states of neutrosophy

Philippe Schweizer

Uncertainty is inherent to the real world: everything is only probable, precision like in measurements is finite, noise is everywhere... Also, science is based on a modeling of reality that can only be approximate. Therefore we postulate that uncertainty should be considered in our models, and for making this more easy we propose a simple operational conceptualization of uncertainty. Starting from the simple model of associating a probability p to a statement supposed to be true our proposed modeling bridges the gap towards the most complex representation proposed by neutrosophy as a triplet of probabilities. The neutrosophic representation consists in using a triplet of probabilities (t,i,f)  instead of just a single probability. In this triplet, t represents the probability of the statement to be true, and f it's the probability to be false. The specific point of neutrosophy it that the probability i represents  the probability of the statement to be uncertain, imprecise, or neutral among other significations according to the application. Our proposed representation uses only 2 probabilities instead of 3, and it can be easily translated into the neutrosophic representation. By being simpler we renounce to some power of representing the uncertain but we encourage the modeling of uncertainty (instead of ignoring it) by making this simpler. Briefly said, the prepare the path towards using neutrosophy. Our proposed representation of uncertainty consist, for a statement, not only to add its probability to be true p, but also a second probability pp to model the confidence we have in the first probability p. This second parameter pp represents the plausibility of p, therefore the opposite of its uncertainty. This is the confidence given to the value of p, in short pp is the probability of p (hence the name pp), This is simple to understand, and that allows calculations of combined events using classical probability such as based on the concepts of mean and variance. The stringent advantage of our modeling by the couple (p,pp) is that experts can be easily interrogated to provide their expertise by asking them simply the chance they give to an event a occur (this is p) and the confidence they have in that prediction (which is pp). We give also a formula to transform from our model to the neutrosophic representation. Finally, a short discussion on the entropy as a measure of uncertainty is done.  

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Vol. 2 Issue. 1 PP. 18-26, (2020)

Magnification of MBJ-Neutrosophic Translation on G-Algerbra

Mohsin Khalid , Young Bae Jun , Mohammad Mohseni Takallo , Neha Andaleeb Khalid

In this article, we define the MBJ-neutrosophic magnified translation (MBJNMT) on G-algebra which is the combination of multiplication and translation and study significant results of MBJ-neutrosophic ideal and MBJ-neutrosophic subalgebra by using the notion of MBJ-neutrosophic magnified translation. We investigate the conversion of MBJ-neutrosophic ideal and MBJ-neutrosophic subalgebra with one another and use the idea of  intersection and union to produce some important results of MBJ-neutrosophic magnified translation.

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Vol. 2 Issue. 1 PP. 27-37, (2020)