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.

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.

Decision Making Approach using Weighted Coefficient of Correlation along with Generalized Parametric Fuzzy Entropy Measure

2016 ◽  
Vol 5 (3) ◽  
pp. 30-41 ◽  
Author(s):  
Priti Gupta ◽  
Pratiksha Tiwari
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Entropy Measure ◽  
Managerial Decision ◽  
Coefficient Of Correlation ◽  
Different Types ◽  
Segmentation Of Images ◽  
Real World Problems

Decision making involves various attributes along with several decision takers. Recently it has become more complex. This gives raise to uncertainty and associated with the information provided. So it may be appropriate to suggest that uncertainty demonstrates itself in numerous forms and of different types. Uncertainties may arise due to human behaviour, fluctuations of information, unknown facts. Fuzzy set theory is tool to deal with uncertainty in a better way. Both Fuzzy set theory and information theory are involved in dealing with various real-world problems such as segmentation of images, medical diagnosis, managerial decision making etc. Several methods and concepts dealing with imprecision and uncertainty have been proposed by many researchers. In the present communication, the authors have proposed a parametric generalization of entropy introduced by De Luca and Termini along with its basic properties. Further, a new measure of weighted coefficient of correlation is developed and applied to solve decision making problems involving uncertainty.

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 Some Root Level Modifications in Interval Valued Fuzzy Graphs and Their Generalizations Including Neutrosophic Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 72 ◽  
Author(s):  
Naeem Jan ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Harish Garg ◽  
Bijan Davvaz ◽  
...  
Keyword(s):  
Decision Making ◽  
Essential Role ◽  
Real Life ◽  
Current Definition ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Decision Making Problem ◽  
Neutrosophic Graph ◽  
Definition Of ◽  
Interval Valued

Fuzzy graphs (FGs) and their generalizations have played an essential role in dealing with real-life problems involving uncertainties. The goal of this article is to show some serious flaws in the existing definitions of several root-level generalized FG structures with the help of some counterexamples. To achieve this, first, we aim to improve the existing definition for interval-valued FG, interval-valued intuitionistic FG and their complements, as these existing definitions are not well-defined; i.e., one can obtain some senseless intervals using the existing definitions. The limitations of the existing definitions and the validity of the new definitions are supported with some examples. It is also observed that the notion of a single-valued neutrosophic graph (SVNG) is not well-defined either. The consequences of the existing definition of SVNG are discussed with the help of examples. A new definition of SVNG is developed, and its improvement is demonstrated with some examples. The definition of an interval-valued neutrosophic graph is also modified due to the shortcomings in the current definition, and the validity of the new definition is proved. An application of proposed work is illustrated through a decision-making problem under the framework of SVNG, and its performance is compared with existing work.

Mathematical Explorations: Variables and Spreadsheets Connect with Real-World Problems

2008 ◽  
Vol 13 (7) ◽  
pp. 423-431
Author(s):  
Margaret L. Niess ◽  
Pejmon Sadri ◽  
Kwangho Lee
Keyword(s):  
Decision Making ◽  
Real World ◽  
Real Life ◽  
Wide Spread ◽  
Monthly Income ◽  
Mathematical Connections ◽  
The World ◽  
The Impact ◽  
Spreadsheet Software ◽  
Real World Problems

Spreadsheet software is generally available in schools and is in wide-spread use in business. The use of spreadsheets can help students make mathematical connections with problems in the world around them. Many real-life quantitative problems require algebra for decision making. Examples include the impact of rising gas prices on family budgets; the amount of gasoline left in the tank of a car and the distance to the nearest gas station; and the level of monthly income versus money needed to pay for food, rent, utilities, and clothing. Although these issues do not require complex mathematics, they do require knowledge of basic algebra involving variables and equations.

scholarly journals A Decision-making Problem as an Applications of Intuitionistic Fuzzy Set

2019 ◽  
Vol 9 (2) ◽  
pp. 5259-5261
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Real World Problems

The fuzzy sets and Intuitionistic fuzzy sets are very useful concepts to elaborate the vagueness in real world problems. The objective of our study is to apply fuzzy set theory and Intuitionistic fuzzy set theory in decision making process. In this paper, we identify in which society a person has to purchase a house in order to fulfil his requirement to maximum extent. In our study we use intuitionistic fuzzy sets to find a relation between the societies and the parameters. And then we find a relation between a person and the parameters. We calculate Normalized Euclidean distance between two Intuitionistic fuzzy sets to make a decision of purchasing house in a society.

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

scholarly journals Generalised Interval-Valued Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

scholarly journals Cross-disciplinary Science and the Structure of Scientific Perspectives

2014 ◽  
Vol 1 (1) ◽  
pp. 7 ◽  
Author(s):  
Hugo Fjelsted Alrøe ◽  
Egon Noe
Keyword(s):  
Nature Of Science ◽  
Real World ◽  
Scientific Research ◽  
Second Order ◽  
Philosophical Analysis ◽  
Different Types ◽  
Real World Problems

<p>Cross-disciplinary use of science is needed to solve complex, real-world problems, but carrying out scientific research with multiple very different disciplines is in itself a non-trivial problem. Perspectives matter. In this paper we carry out a philosophical analysis of the perspectival nature of science, focusing on the synchronic structure of scientific perspectives across disciplines and not on the diachronic, historical structure of shifting perspectives within single disciplines that has been widely discussed since Kuhn and Feyerabend. We show what kinds of cross-disciplinary disagreement to expect due to the perspectival structure of science, suggest how to handle different scientific perspectives in cross-disciplinary work through perspectives of a second order, and discuss some fundamental epistemic differences between different types of science.</p>

scholarly journals Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment

2015 ◽  
Vol 24 (1) ◽  
pp. 23-36 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Fuzzy Environment ◽  
Cosine Measure ◽  
Multiple Attribute

AbstractOn the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator and investigate their properties. Furthermore, a multiple-attribute decision-making method is established on the basis of the SVNHFWA and SVNHFWG operators and the cosine measure under a single-valued neutrosophic hesitant fuzzy environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

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