An Introduction to Neutro-Fine Topology with Separation Axioms and Decision Making

2020 ◽  
pp. 13-28
Author(s):  
admin admin ◽  
◽  
◽  
M. P. Sindhu
Keyword(s):  
Decision Making ◽  
Topological Space ◽  
Positive Solution ◽  
Real Life ◽  
Neutrosophic Set ◽  
Fine Topology ◽  
Stepwise Mechanism ◽  
The Real ◽  
Separation Axioms ◽  
Decision Making Problem

The set which describes the uncertainty incident with three levels of attributes is entitled as a neutrosophic set. The unique collection of open sets which contains all types of open sets is termed as fine-open sets. The current study introduces a topology on merging these two sets, called neutro-fine topological space. Additionally, the approach of separation axioms is implemented in such space. Furthermore, the real-life application is examined as a decision-making problem in this space. The problem is to make an unfavorable query into a favorable one by determining the complement and absolute complement of such issued neutro-fine open sets. This problem desires to find a positive solution. The solving stepwise mechanism reveals in the algorithm, also formulae provide to compute the outcome with explanatory examples.

scholarly journals A note on different types of product of neutrosophic graphs

2021 ◽  
Author(s):  
Kartick Mohanta ◽  
Arindam Dey ◽  
Anita Pal
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Real World ◽  
Real Life ◽  
Neutrosophic Set ◽  
Total Degree ◽  
Decision Making Problem ◽  
Different Types ◽  
Neutrosophic Graph ◽  
Real World Problems

AbstractFuzzy set and neutrosophic set are two efficient tools to handle the uncertainties and vagueness of any real-world problems. Neutrosophic set is more capable than fuzzy set to deal the uncertainties of a real-life problem. This research paper introduces some new concept of single-valued neutrosophic graph (SVNG). We have also presented some different operations on SVNG such as rejection, symmetric difference, maximal product, and residue product with appropriate examples, and some of their important theorems are also described. Then, we have described the concept of total degree of a neutrosophic graph with some interesting examples. We have also presented an efficient approach to solve a decision-making problem using SVNG.

scholarly journals An Approach toward a Q-Neutrosophic Soft Set and Its Application in Decision Making

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 139 ◽  
Author(s):  
Majdoleen Abu Qamar ◽  
Nasruddin Hassan
Keyword(s):  
Decision Making ◽  
Uncertain Data ◽  
Real Life ◽  
Soft Set ◽  
Neutrosophic Set ◽  
Uncertain Information ◽  
Soft Sets ◽  
Independent Functions ◽  
Axis Of Symmetry ◽  
Set Aggregation

A neutrosophic set was proposed as an approach to study neutral uncertain information. It is characterized through three memberships, T , I and F, such that these independent functions stand for the truth, indeterminate, and false-membership degrees of an object. The neutrosophic set presents a symmetric form since truth enrolment T is symmetric to its opposite false enrolment F with respect to indeterminacy enrolment I that acts as an axis of symmetry. The neutrosophic set was further extended to a Q-neutrosophic soft set, which is a hybrid model that keeps the features of the neutrosophic soft set in dealing with uncertainty, and the features of a Q-fuzzy soft set that handles two-dimensional information. In this study, we discuss some operations of Q-neutrosophic soft sets, such as subset, equality, complement, intersection, union, AND operation, and OR operation. We also define the necessity and possibility operations of a Q-neutrosophic soft set. Several properties and illustrative examples are discussed. Then, we define the Q-neutrosophic-set aggregation operator and use it to develop an algorithm for using a Q-neutrosophic soft set in decision-making issues that have indeterminate and uncertain data, followed by an illustrative real-life example.

scholarly journals On Soft Separation Axioms and Their Applications on Decision-Making Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
T. M. Al-shami
Keyword(s):  
Decision Making ◽  
Topological Spaces ◽  
Topological Properties ◽  
Finite Product ◽  
Separation Axioms ◽  
Decision Making Problem ◽  
Weak Structure

In this work, we introduce new types of soft separation axioms called p t -soft α regular and p t -soft α T i -spaces i = 0,1,2,3,4 using partial belong and total nonbelong relations between ordinary points and soft α -open sets. These soft separation axioms enable us to initiate new families of soft spaces and then obtain new interesting properties. We provide several examples to elucidate the relationships between them as well as their relationships with e -soft T i , soft α T i , and t t -soft α T i -spaces. Also, we determine the conditions under which they are equivalent and link them with their counterparts on topological spaces. Furthermore, we prove that p t -soft α T i -spaces i = 0,1,2,3,4 are additive and topological properties and demonstrate that p t -soft α T i -spaces i = 0,1,2 are preserved under finite product of soft spaces. Finally, we discuss an application of optimal choices using the idea of p t -soft T i -spaces i = 0,1,2 on the content of soft weak structure. We provide an algorithm of this application with an example showing how this algorithm is carried out. In fact, this study represents the first investigation of real applications of soft separation axioms.

scholarly journals Bipolar quadripartitioned single valued neutrosophic sets

2020 ◽  
Vol 39 (6) ◽  
pp. 1597-1614
Author(s):  
Kalyan Sinha ◽  
Pinaki Majumdar
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Neutrosophic Set ◽  
Entropy Measure ◽  
Neutrosophic Sets ◽  
Basic Set ◽  
Decision Making Problem ◽  
Different Types ◽  
Measure Technique

The notion of simple bipolar quadripartition is presented valuable neutrosophic set. Some basic set theoretic terminologies, operations and properties of bipolar quadripartitioned single valued neutrosophic set are given here. Also different types of distances, similarity measures and entropy measure are discussed. Finally a decision making problem using the similarity measure technique of bipolar quadripartitioned single valued neutrosophic sets has been solved.

scholarly journals Logarithmic Divergence Measure for Fuzzy Matrix and Application

2021 ◽  
Vol 8 ◽  
pp. 1-20
Author(s):  
Alka Rani ◽  
Omdutt Sharma ◽  
Priti Gupta
Keyword(s):  
Decision Making ◽  
Real Life ◽  
Divergence Measure ◽  
Logarithmic Divergence ◽  
Fuzzy Matrix ◽  
Decision Making Problem ◽  
Fuzzy Divergence

This paper introduces a new divergence measure for a fuzzy matrix with proof of its validity. In addition, the properties are proved for the new fuzzy divergence measure. A method to solve decision making problem is developed by using the proposed fuzzy divergence measure. Finally, the application of this fuzzy divergence measure to decision making is shown using real-life example

scholarly journals Type-2 Multi-Fuzzy Sets and Their Applications in Decision Making

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 170 ◽  
Author(s):  
Mohuya B. Kar ◽  
Bikashkoli Roy ◽  
Samarjit Kar ◽  
Saibal Majumder ◽  
and Dragan Pamucar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Imperfect Information ◽  
Real Life ◽  
Distance Measures ◽  
Expert Assessment ◽  
Decision Making Problem ◽  
Medical Diagnosis System

In a real-life scenario, it is undoable and unmanageable to solve a decision-making problem with the single stand-alone decision-aid method, expert assessment methodology or deterministic approaches. Such problems are often based on the suggestions or feedback of several experts. Usually, the feedback of these experts are heterogeneous imperfect information collected from various more or less reliable sources. In this paper, we introduce the concept of multi-sets over type-2 fuzzy sets. We have tried to propose an extension of type-1 multi-fuzzy sets into a type-2 multi-fuzzy set (T2MFS). After defining T2MFS, we discuss the algebraic properties of these sets including set-theoretic operations such as complement, union, intersection, and others with examples. Subsequently, we define two distance measures over these sets and illustrate a decision-making problem which uses the idea of type-2 multi-fuzzy sets. Furthermore, an application of a medical diagnosis system based on multi-criteria decision making of T2MFS is illustrated with a real-life case study.

scholarly journals A Novel Dynamic Multi-Criteria Decision Making Method Based on Generalized Dynamic Interval-Valued Neutrosophic Set

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 618 ◽  
Author(s):  
Nguyen Tho Thong ◽  
Florentin Smarandache ◽  
Nguyen Dinh Hoa ◽  
Le Hoang Son ◽  
Luong Thi Hong Lan ◽  
...  
Keyword(s):  
Decision Making ◽  
Evaluation Model ◽  
Real Life ◽  
Decision Makers ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Proposed Model ◽  
Interval Valued ◽  
Knowledge Evaluation

Dynamic multi-criteria decision-making (DMCDM) models have many meaningful applications in real life in which solving indeterminacy of information in DMCDMs strengthens the potential application of DMCDM. This study introduces an extension of dynamic internal-valued neutrosophic sets namely generalized dynamic internal-valued neutrosophic sets. Based on this extension, we develop some operators and a TOPSIS method to deal with the change of both criteria, alternatives, and decision-makers by time. In addition, this study also applies the proposal model to a real application that facilitates ranking students according to attitude-skill-knowledge evaluation model. This application not only illustrates the correctness of the proposed model but also introduces its high potential appliance in the education domain.

THE EVOLUTION OF SPIN-OFF VENTURES: AN INTEGRATED MODEL

2010 ◽  
Vol 07 (01) ◽  
pp. 53-70 ◽  
Author(s):  
SVEN H. DE CLEYN ◽  
JOHAN BRAET
Keyword(s):  
Decision Making ◽  
Case Studies ◽  
Real Life ◽  
Integrated Model ◽  
Research Field ◽  
Integrative Model ◽  
Life Situation ◽  
Dynamic Nature ◽  
The Real ◽  
Real Life Situation

The article aims to give an overview of the main models in the spin-off research field. The main evolution models known in literature will be analyzed. The evolution models will be discussed in increasing order of complexity. However, the existing models will prove to be inadequate to reflect the real-life situation. Therefore, a new integrative model will be discussed in detail, illustrated by using 17 case studies of Belgian academic spin-offs. The model incorporates the dynamic nature of academic spin-off evolution and the major peripheral aspects. It can be used by practitioners and academics to enhance reproducibility and decision making.

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