scholarly journals A New Multi-Attribute Decision Making Method with Single-Valued Neutrosophic Graphs

2020 ◽  
pp. 76-86
Author(s):  
admin admin ◽  
◽  
◽  
◽  
Wenhui Bai ◽  
...  
Keyword(s):  
Decision Making ◽  
Graph Theory ◽  
Comparative Analysis ◽  
Fuzzy Graph ◽  
Neutrosophic Sets ◽  
Inconsistent Information ◽  
Operational Laws ◽  
Engineering Economy ◽  
Multi Attribute Decision Making

In most realistic situations, the theory and method of multi-attribute decision-making have been widely used in different fields, such as engineering, economy, management, military, and others. Although many studies in some extended fuzzy contexts have been explored with multi-attribute decision-making, it is widely recognized that single-valued neutrosophic sets can describe incomplete, indeterminate and inconsistent information more easier. In this paper, aiming at addressing multi-attribute decision-making problems with single-valued neutrosophic information, related models and multi-attribute decision-making approaches based on the fuzzy graph theory are studied. In specific, the notion of single-valued neutrosophic sets and graphs is firstly introduced together with several common operational laws. Then a multi-attribute decision making method based on single-valued neutrosophic graphs is established. Finally, an illustrative example and a comparative analysis are conducted to verify the feasibility and efficiency of the proposed method.

scholarly journals Multi-Attribute Decision Making Based on Interval Neutrosophic Trapezoid Linguistic Aggregation Operators

2016 ◽  
pp. 344-365
Author(s):  
Broumi Said ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Numerical Example ◽  
Inconsistent Information ◽  
Weighted Arithmetic ◽  
Multi Attribute Decision Making ◽  
Interval Neutrosophic Sets

Multi-attribute decision making (MADM) play an important role in many applications, due to the efficiency to handle indeterminate and inconsistent information, interval neutrosophic sets is widely used to model indeterminate information. In this paper, a new MADM method based on interval neutrosophic trapezoid linguistic weighted arithmetic averaging aggregation (INTrLWAA) operator and interval neutrosophic trapezoid linguistic weighted geometric aggregation (INTrLWGA) operatoris presented. A numerical example is presented to demonstrate the application and efficiency of the proposed method.

scholarly journals Complex pythagorean fuzzy aggregation operators based on confidence levels and their applications

2021 ◽  
Vol 19 (1) ◽  
pp. 1078-1107
Author(s):  
Tahir Mahmood ◽  
◽  
Zeeshan Ali ◽  
Kifayat Ullah ◽  
Qaisar Khan ◽  
...  
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Comparative Analysis ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Confidence Levels ◽  
Ordered Weighted Averaging ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making

<abstract> <p>The most important influence of this assessment is to analyze some new operational laws based on confidential levels (CLs) for complex Pythagorean fuzzy (CPF) settings. Moreover, to demonstrate the closeness between finite numbers of alternatives, the conception of confidence CPF weighted averaging (CCPFWA), confidence CPF ordered weighted averaging (CCPFOWA), confidence CPF weighted geometric (CCPFWG), and confidence CPF ordered weighted geometric (CCPFOWG) operators are invented. Several significant features of the invented works are also diagnosed. Moreover, to investigate the beneficial optimal from a large number of alternatives, a multi-attribute decision-making (MADM) analysis is analyzed based on CPF data. A lot of examples are demonstrated based on invented works to evaluate the supremacy and ability of the initiated works. For massive convenience, the sensitivity analysis and merits of the identified works are also explored with the help of comparative analysis and they're graphical shown.</p> </abstract>

scholarly journals Exponential Laws and Aggregation Operators on Neutrosophic Cubic Sets

2020 ◽  
pp. 47-71
Author(s):  
Majid .. ◽  
◽  
◽  
◽  
Ismat .. ◽  
...  
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Aggregation Operators ◽  
Operational Laws ◽  
Cosine Measure ◽  
Multi Attribute Decision Making ◽  
Interval Value

This paper presents operational laws along with their cosine measure for the numbers whose base is an interval value and study their properties. Consequent upon these definitions and properties neutrosophic cubic weighted exponential averaging and dual neutrosophic cubic weighted exponential averaging aggregation operators are defined. A multi attribute decision making method is then developed for proposed aggregation operators. An example is constructed as an application. The validity of multi attribute decision making method is also tested and comparative analysis is provided to compare these aggregation operators with existing results.

scholarly journals Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 459 ◽  
Author(s):  
Qaisar Khan ◽  
Peide Liu ◽  
Tahir Mahmood ◽  
Florentin Smarandache ◽  
Kifayat Ullah
Keyword(s):  
Decision Making ◽  
Hybrid Structure ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Geometric Bonferroni Mean ◽  
Dombi Operations ◽  
The Impact

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

scholarly journals Multi-Attribute Multi-Perception Decision-Making Based on Generalized T-Spherical Fuzzy Weighted Aggregation Operators on Neutrosophic Sets

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 780 ◽  
Author(s):  
Quek ◽  
Selvachandran ◽  
Munir ◽  
Mahmood ◽  
Ullah ◽  
...  
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Do So

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

scholarly journals Algorithm for T-Spherical Fuzzy Multi-Attribute Decision Making Based on Improved Interactive Aggregation Operators

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 670 ◽  
Author(s):  
Harish Garg ◽  
Muhammad Munir ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Naeem Jan
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Counter Example ◽  
Operational Laws ◽  
Special Cases ◽  
Multi Attribute Decision Making ◽  
Picture Fuzzy Sets

The objective of this manuscript is to present some new, improved aggregation operators for the T-spherical fuzzy sets, which is an extension of the several existing sets, such as intuitionistic fuzzy sets, picture fuzzy sets, neutrosophic sets, and Pythagorean fuzzy sets. In it, some new, improved operational laws and their corresponding properties are studied. Further, based on these laws, we propose some geometric aggregation operators and study their various relationships. Desirable properties, as well as some special cases of the proposed operators, are studied. Then, based on these proposed operators, we present a decision-making approach to solve the multi-attribute decision-making problems. The reliability of the presented decision-making method is explored with the help of a numerical example and the proposed results are compared with several prevailing studies’ results. Finally, the superiority of the proposed approach is explained with a counter example to show the advantages of the proposed work.

scholarly journals Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 145
Author(s):  
Yun Jin ◽  
Zareena Kousar ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Nimet Yapici Pehlivan ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Evaluation Process ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

Neutrosophic Soft Block Matrices And Some Of Its Properties

2020 ◽  
pp. 39-49
Author(s):  
admin admin ◽  
Keyword(s):  
Decision Making ◽  
Crucial Role ◽  
Real Life ◽  
Decision Making Process ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Neutrosophic Sets ◽  
Block Matrices ◽  
Inconsistent Information

In real life situations, there are many issues in which there are uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant and inconsistent information during decision making process. The main focus of this article is to discuss the concept of neutrosophic sets, neutrosophic soft sets, neutrosophic soft matrices theory and finally to discuss about neutrosophic soft block matrics which are very useful and applicable in various situations involving uncertainties and imprecisions. In this article, neutrosophic soft block matrices, various types of neutrosophic soft block matrices, some operations on it along with some properties associated with it are discussed in details.

scholarly journals TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1739
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Miin-Shen Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Unit Interval ◽  
Polar Coordinates ◽  
Topsis Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Special Cases ◽  
Order Preference ◽  
Multi Attribute Decision Making

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.

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