The aim of this paper is to combine the notions of ordered algebraic structures and neutrosophy. In this regard, we define for the first time single valued neutrosophic sets in ordered groupoids. More precisely, we study single valued neutrosophic subgroupoids of ordered groupoids, single valued neutrosophic ideals of ordered groupoids, and single valued neutrosophic filters of ordered groupoids. Finally, we present some remarks on single valued neutrosophic subgroups (ideals) of ordered groups.
Read MoreDoi: https://doi.org/10.54216/IJNS.0100201
Vol. 10 Issue. 2 PP. 73-83, (2020)
The NeutroGroups as alternatives to the classical groups are of different types with different algebraic prop- erties. In this paper, we are going to study a class of NeutroGroups of type-NG[1,2,4]. In this class of Neu- troGroups, the closure law, the axiom of associativity and existence of inverse are taking to be either partially true or partially false for some elements; while the existence of identity element and axiom of commutativity are taking to be totally true for all the elements. Several examples of NeutroGroups of type-NG[1,2,4] are presented along with their basic properties. It is shown that Lagrange’s theorem holds for some NeutroSub- groups of a NeutroGroup and failed to hold for some NeutroSubgroups of the same NeutroGroup. It is also shown that the union of two NeutroSubgroups of a NeutroGroup can be a NeutroSubgroup even if one is not contained in the other; and that the intersection of two NeutroSubgroups may not be a NeutroSubgroup. The concepts of NeutroQuotientGroups and NeutroGroupHomomorphisms are presented and studied. It is shown that the fundamental homomorphism theorem of the classical groups is holding in the class of NeutroGroups of type-NG[1,2,4].
Read MoreDoi: https://doi.org/10.54216/IJNS.0100202
Vol. 10 Issue. 2 PP. 84-95, (2020)
The notion of fuzzy sets initiated to overcome the uncertainty of an object. Fuzzy topological space, in- tuitionistic fuzzy sets in topological structure space, vagueness in topological structure space, rough sets in topological space, theory of hesitancy and neutrosophic topological space, etc. are the extension of fuzzy sets. Soft set is a family of parameters which is also a set. Fuzzy soft topological space, intuitionistic fuzzy soft and neutrosophic soft topological space are obtained by incorporating soft sets with various topological structures. This motivates to write a review and study on various soft set concepts. This paper shows the detailed review of soft topological spaces in various sets like fuzzy, Intuitionistic fuzzy set and neutrosophy. Eventually, we compared some of the existing tools in the literature for easy understanding and exhibited their advantages and limitations.
Read MoreDoi: https://doi.org/10.54216/IJNS.0100203
Vol. 10 Issue. 2 PP. 96-104, (2020)
In this paper, we have proposed an Interval-valued triangular neutrosophic number (IV-TNN) as a key factor to solve the neutrosophic linear programming problem. In the present neutrosophic linear programming problem IV-TNN is expressed in lower, upper truth membership function, indeterminacy membership function, and falsity membership function. Here, we try the compare our proposed method with existing methods.
Read MoreDoi: https://doi.org/10.54216/IJNS.0100204
Vol. 10 Issue. 2 PP. 105-115, (2020)
COVID-19 is pandemic affecting most of the country globally. It is an infectious disease that is affecting most of the people and it is very difficult to diagnose and treat the diseased patient. Generally asymptotic patients recover without any treatment. Patients with other illness such as Hypertension, Heart and Lung problems, Diabetic patients require intense care and treatment. In such cases, a team of doctors work together. The combination of all the experts’ opinions is needed for efficient treatment. Often, the opinion of doctors depends on their experience and involves some differences. Further, the expert’s opinion is in linguistic terms. Plithogenic sets provide a mathematical tool for aggregation of the experts’ opinion expressed in linguistic terms. Thus, this work aims to employ plithogenic neutrosophic number to rank the diseased patients affected with COVID-19. Hence, we propose an Order Preference Technique by Similarity to Ideal Solutions (TOPSIS) using Plithogenic sets.
Read MoreDoi: https://doi.org/10.54216/IJNS.0100205
Vol. 10 Issue. 2 PP. 116-125, (2020)