The notion of AntiGroups is formally presented in this paper. A particular class of AntiGroups of type-AG[4] is studied with several examples and basic properties presented. In AntiGroups of type-AG[4], the existence of an inverse is taking to be totally false for all the elements while the closure law, the existence of identity element, the axioms of associativity and commutativity are taking to be either partially true, partially indeterminate or partially false for some elements. It is shown that some algebraic properties of the classical groups do not hold in the class of AntiGroups of type-AG[4]. Specifically, it is shown that intersection of two AntiSubgroups is not necessarily an AntiSubgroup and the union of two AntiSubgroups may be an AntiSubgroup. Also, it is shown that distinct left(right) cosets of AntiSubgroups of AntiGroups of type-AG[4] do not partition the AntiGroups; and that Lagranges’ theorem and fundamental theorem of homomorphisms of the classical groups do not hold in the class of AntiGroups of type-AG[4].
Read MoreDoi: https://doi.org/10.54216/IJNS.120201
Vol. 12 Issue. 2 PP. 71-80, (2020)
Neutrosophic overset, neutrosophic underset and neutrosophic offset introduced by Smarandache are the special kinds of neutrosophic sets with values beyond the range [0,1] and these sets are pragmatic in nature as it represents the real life situations. This paper introduces the concept of saturated refined neutrosophic sets and extends the same to the special kinds of neutrosophic sets. The proposed concept is applied in decision making on Teacher’s adaptation to cybergogy. The decision making environment is characterized by different types of teachers, online teaching skills and various training methods. Fuzzy relation is used to match the most suitable method to the different kinds of teachers with the intervention of saturated interval valued neutrosophic refined oversets, offsets and undersets. The results obtained by applying the notion of saturated refined sets using various distance measures represent the effect of training methods on teacher’s adaptation to learner-centred teaching methods, which certainly give space to gain many insights on the relationship between quality of training and teacher’s adaptation rate. The proposed concept has wide scope and few limitations.
Read MoreDoi: https://doi.org/10.54216/IJNS.120202
Vol. 12 Issue. 2 PP. 58-70, (2020)
Refining the indeterminate I into many levels of indeterminacy is a way to explore many neutrosophic algebraic structures.This paper introduces the concept of n-cyclic refined algebraic system of sub-indeterminacies as a new way to refine a neutrosophic indeterminate I. This idea will be used to introduce the notion of n-cyclic refined neutrosophic ring and to study its AH-substructures. Also, this work presents the concept of n-cyclic refined neutrosophic modules with many related structures.
Read MoreDoi: https://doi.org/10.54216/IJNS.120203
Vol. 12 Issue. 2 PP. 81-95, (2020)
In a recent paper, we have introduced the notion of standard single valued neutrosophic metric space as a generalization of standard fuzzy metric spaces given by J.R. Kider and Z.A. Hussain. In this paper, we continue our previous work by introducing the notions of complete standard single valued neutrosophic metric space and compact standard single valued neutrosophic metric space. Furthermore, we give a number of properties and characterizations of these notions and relationship between them.
Read MoreDoi: https://doi.org/10.54216/IJNS.120204
Vol. 12 Issue. 2 PP. 96-104, (2020)
This study presents a smart agriculture mechanism model equipped with neutrosophy theory for the first time. The model is created by meticulously bringing together the fields of decision making, IoT and cloud computing. We have demonstrated that smart agriculture can be used in integration with neutrosophic, integrated with IoT. This integration is a model created by making much more detailed calculations by taking into account and using the uncertainty situations in neutrosophic numbers and logic, by automating both the geometric analysis of the soil and surface control and the numerical data of the environment for smart agriculture.
Read MoreDoi: https://doi.org/10.54216/IJNS.120205
Vol. 12 Issue. 2 PP. 105-115, (2020)