In this paper, we extend the notion of classical soft expert sets to possibility neutrosophic vague soft expert sets by applying the theory of soft expert sets to possibility neutrosophic vague soft sets. The subset, complement, union , intersection, AND and OR operations as well as some related concepts pertaining to this notion are defined.
Journal: AIP Conference Proceedings 1830, 010001 (2017); doi: 10.1063/1.4980863
We introduce the mapping on complex neutrosophic soft expert sets. Further, we investigated the basic operations and
other related properties of complex neutrosophic soft expert image and complex neutrosophic soft expert inverse image of
complex neutrosophic soft expert sets.
Journal: AIP Conference Proceedings 1940, 020111 (2018); doi: 10.1063/1.5028026
Recently, vague sets and neutrosophic sets have received great attention among the scholars and have been applied in many applications. But, the actual theoretical impacts of the combination of these two sets in dealing uncertainties are still not fully explored until now. In this paper, a new generalized mathematical model called interval neutrosophic vague sets is proposed, which is a combination of vague sets and interval neutrosophic sets and a generalization of interval neutrosophic vague sets. Some definitions of interval neutrosophic vague set such as union, complement and intersection are presented. Furthermore, the basic operations, the derivation of its properties and related example are included.
Journal: (Neutrosophic Sets and Systems: 25(2019
The notion of classical soft sets is extended to neutrosophic vague soft sets
by applying the theory of soft sets to neutrosophic vague sets to be more
effective and useful. We also define its null, absolute and basic operations,
namely complement, subset, equality, union and intersection along with
illustrative examples, and study some related properties with supporting
proofs. Lastly, this notion is applied to a decision making problem and
its effectiveness is demonstrated using an illustrative example.
Journal: (MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES:11(2
The notion of classical soft sets is extended to neutrosophic vague soft sets
by applying the theory of soft sets to neutrosophic vague sets to be more
effective and useful. We also define its null, absolute and basic operations,
namely complement, subset, equality, union and intersection along with
illustrative examples, and study some related properties with supporting
proofs. Lastly, this notion is applied to a decision making problem and
its effectiveness is demonstrated using an illustrative example
Journal: (Malaysian Journal of Mathematical Sciences: 11(2
The notion of classical soft multisets is extended to neutrosophic vague soft multisets by applying the theory of soft
multisets to neutrosophic vague sets to be more effective and useful. We also define its basic operations, namely complement,
subset, union, intersection along with illustrative examples, and study some related properties with supporting proofs. Lastly, this
notion is applied to a decision making problem and its effectiveness is demonstrated using an illustrative example
Journal: (Songklanakarin Journal of Science and Technology:40(2
In this paper, we propose the theory of fuzzy parameterized single
valued neutrosophic soft expert set by giving an importance degree for each
element in the set of parameters and define some related concepts pertaining
to this notion as well as the basic operations of complement, subset, union,
intersection, AND and OR along with illustrative examples. The basic properties
and relevant laws pertaining to this concept such as the De Morgan’s laws are
proved. A comparison between our proposed method and other methods is made
to illustrate the advantages of our proposed method and its ability to handle
problems involving imprecise, indeterminacy and inconsistent data, which makes
it more accurate and realistic than other methods. Lastly, this concept is applied
to a decision making problem and its effectiveness is demonstrated using an
illustrative example.
Journal: (International Journal of Applied Decision Sciences:9(2
The basic aim of soft computing is to trade precision for a tractableness and reduction
in solution cost by pushing the limits of tolerance for imprecision and uncertainty. This paper
introduces a novel soft computing technique called complex neutrosophic relation (CNR) to evaluate
the degree of interaction between two complex neutrosophic sets (CNSs). CNSs are used to
represent two-dimensional information that are imprecise, uncertain, incomplete and indeterminate.
The Cartesian product of CNSs and subsequently the complex neutrosophic relation is formally
defined. This relation is generalised from a conventional single valued neutrosophic relation (SVNR),
based on CNSs, where the ranges of values of CNR are extended to the unit circle in complex plane
for its membership functions instead of [0, 1] as in the conventional SVNR. A new algorithm is
created using a comparison matrix of the SVNR after mapping the complex membership functions
from complex space to the real space. This algorithm is then applied to scrutinise the impact of some
teaching strategies on the student performance and the time frame(phase) of the interaction between
these two variables. The notion of inverse, complement and composition of CNRs along with some
related theorems and properties are introduced. The performance and utility of the composition
concept in real-life situations is also demonstrated. Then, we define the concepts of projection and
cylindric extension for CNRs along with illustrative examples. Some interesting properties are also
obtained. Finally, a comparison between different existing relations and CNR to show the ascendancy
of our proposed CNR is provided.
Journal: (Axioms:11(384
In this paper, we first introduce the concept of neutrosophic vague soft expert sets (NVSESs for short) which
combines neutrosophic vague sets and soft expert sets to be more effective and useful. We also define its basic operations,
namely complement, union, intersection, AND and OR along with illustrative examples, and study some related properties
with supporting proofs. Lastly, this concept is applied to a decision making problem and its effectiveness is demonstrated
using a hypothetical example.
Journal: (Journal of Intelligent & Fuzzy Systems 30 (2016
To handle indeterminate and incomplete data, neutrosophic logic/set/probability were
established. The neutrosophic truth, falsehood and indeterminacy components exhibit symmetry
as the truth and the falsehood look the same and behave in a symmetrical way with respect to the
indeterminacy component which serves as a line of the symmetry. Soft set is a generic mathematical
tool for dealing with uncertainty. Rough set is a new mathematical tool for dealing with vague,
imprecise, inconsistent and uncertain knowledge in information systems. This paper introduces a
new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of
rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data. The idea
of neutrosophic right neighborhood is utilised to define the concepts of neutrosophic soft rough
(NSR) lower and upper approximations. Properties of suggested approximations are proposed and
subsequently proven. Some of the NSR set concepts such as NSR-definability, NSR-relations and
NSR-membership functions are suggested and illustrated with examples. Further, we demonstrate
the feasibility of the newly rough set model with decision making problems involving neutrosophic
soft set. Finally, a discussion on the features and limitations of the proposed model is provided.
Journal: (Symmetry 11(3
