scholarly journals A Multi-Criteria Decision-Making Method Based on the Improved Single-Valued Neutrosophic Weighted Geometric Operator

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1051 ◽  
Author(s):  
Chao Tian ◽  
Juan Juan Peng
Keyword(s):  
Decision Making ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Special Cases ◽  
Mcdm Method ◽  
Geometric Operator

The aggregation operator is one of the most common techniques to solve multi-criteria decision-making (MCDM) problems. The aim of this paper is to propose an MCDM method based on the improved single-valued neutrosophic weighted geometric (ISVNWG) operator. First, the defects of several existing single-valued neutrosophic weighted geometric aggregation operators in terms of producing uncertain results in some special cases are analyzed. Second, an ISVNWG operator is proposed to avoid the defects of existing operators. Further, the properties of the proposed ISVNWG operator, including idempotency, boundedness, monotonicity, and commutativity, are discussed. Finally, a single-valued neutrosophic MCDM method based on the developed ISVNWG operator is proposed to overcome the defects of existing MCDM methods based on existing operators. Application examples demonstrate that our proposed operator and corresponding MCDM method are effective and rational for avoiding uncertain results in some special cases.

scholarly journals A Multi-Criteria Decision-Making Method Based on Single-Valued Neutrosophic Partitioned Heronian Mean Operator

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1189
Author(s):  
Chao Tian ◽  
Juan Juan Peng ◽  
Zhi Qiang Zhang ◽  
Mark Goh ◽  
Jian Qiang Wang
Keyword(s):  
Decision Making ◽  
Selection Criteria ◽  
Aggregation Operators ◽  
Fuzzy Measure ◽  
Multi Criteria Decision Making ◽  
Special Cases ◽  
Mcdm Method ◽  
Heronian Mean

A multi-criteria decision-making (MCDM) method with single-valued neutrosophic information is developed based on the Partitioned Heronian Mean (PHM) operator and the Shapley fuzzy measure, which recognizes correlation among the selection criteria. Motivated by the PHM operator and Shapley fuzzy measure, two new aggregation operators, namely the single-valued neutrosophic PHM operator and the weighted single-valued neutrosophic Shapley PHM operator, are defined, and their corresponding properties and some special cases are investigated. An MCDM model is applied to solve the single-valued neutrosophic problem where weight information is not completely known. An example is provided to validate the proposed method.

scholarly journals Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 280 ◽  
Author(s):  
Harish Garg ◽  
Nancy
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
New Method ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Special Cases

The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

2021 ◽  
pp. 1-23
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Score Function ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Multi Criteria Decision Making ◽  
Accuracy Function ◽  
Special Cases

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

scholarly journals Complex T-spherical fuzzy Dombi aggregation operators and their applications in multiple-criteria decision-making

2021 ◽  
Author(s):  
Faruk Karaaslan ◽  
Mohammed Allaw Dawood Dawood
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Two Dimensional ◽  
Weighted Arithmetic ◽  
Mcdm Method ◽  
Dombi Operations

AbstractComplex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.

scholarly journals Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1081 ◽  
Author(s):  
Peng ◽  
Tian ◽  
Zhang ◽  
Song ◽  
Wang
Keyword(s):  
Decision Making ◽  
Programming Model ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Preference Information ◽  
Fuzzy Measures ◽  
Correlative Relationship

Single-valued neutrosophic sets (SVNSs), which involve in truth-membership, indeterminacy-membership and falsity-membership, play a significant role in describing the decision-makers’ preference information. In this study, a single-valued neutrosophic multi-criteria decision-making (MCDM) approach is developed based on Shapley fuzzy measures and power aggregation operator that takes a correlative relationship among criteria into account and also simultaneously reduces the effects of abnormal preference information. Firstly, two aggregation operators, namely, generalized weighted single-valued neutrosophic power Shapley Choquet average (GWSVNPSCA) operator and generalized weighted single-valued neutrosophic power Shapley Choquet geometric (GWSVNPSCG) operator, are accordingly defined, and the corresponding properties are discussed as well. Secondly, based on the proposed aggregation operators, an integrated MCDM approach is proposed to effectively solve single-valued neutrosophic problems where the weight information is incompletely known. A programming model is constructed to obtain the optimal Shapley fuzzy measure. Next, the proposed operators are utilized to aggregate the decision-makers’ preference information. Finally, a theoretical example with tourism attraction selection is provided to examine the efficacy of the developed approach, in which the results is found reasonable and credible.

scholarly journals Neutrosophic Cubic Einstein Geometric Aggregation Operators with Application to Multi-Criteria Decision Making Method

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 247 ◽  
Author(s):  
Majid Khan ◽  
Muhammad Gulistan ◽  
Naveed Yaqoob ◽  
Madad Khan ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Daily Life ◽  
Aggregation Operators ◽  
Scalar Multiplication ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Vague Data ◽  
Multiplication Score ◽  
Geometric Operator ◽  
Interval Neutrosophic Sets

Neutrosophic cubic sets (NCs) are amore generalized version of neutrosophic sets(Ns) and interval neutrosophic sets (INs). Neutrosophic cubic setsare better placed to express consistent, indeterminate and inconsistent information, which provides a better platform to deal with incomplete, inconsistent and vague data. Aggregation operators play a key role in daily life, and in relation to science and engineering problems. In this paper we defined the algebraic and Einstein sum, multiplication and scalar multiplication, score and accuracy functions. Using these operations we defined geometric aggregation operators and Einstein geometric aggregation operators. First, we defined the algebraic and Einstein operators of addition, multiplication and scalar multiplication. We defined score and accuracy function to compare neutrosophic cubic values. Then we definedthe neutrosophic cubic weighted geometric operator (NCWG), neutrosophic cubic ordered weighted geometric operator (NCOWG), neutrosophic cubic Einstein weighted geometric operator (NCEWG), and neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) over neutrosophic cubic sets. A multi-criteria decision making method is developed as an application to these operators. This method is then applied to a daily life problem.

Some Generalized Intuitionistic Fuzzy Geometric Aggregation Operators with Applications in Multi-Criteria Decision Making Process

2016 ◽  
pp. 159-179 ◽  
Author(s):  
Bhagawati Prasad Joshi
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Decision Making Process ◽  
Additional Parameter ◽  
Multi Criteria Decision Making ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Special Cases ◽  
Multidimensional Information

The aggregation operators play an important role in the fusion of multidimensional information in decision making process. In this study, a series of generalized aggregation operators such as: the generalized intuitionistic fuzzy weighted geometric (GIFWG) operator, the generalized intuitionistic fuzzy ordered weighted geometric (GIFOWG) operator and the generalized intuitionistic fuzzy hybrid geometric (GIHG) operator are proposed under intuitionistic fuzzy environment by controlling the power of the argument values with an additional parameter p. Some of the important properties and some special cases of these operators are also included in this study. Further, the developed approach is utilized to deal with multi-criteria decision making (MCDM) problems. Numerical examples are constructed to illustrate the developed approach effectively.

scholarly journals Multi-criteria decision making based on induced generalized interval neutrosophic Choquet integral

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0242449
Author(s):  
Yangyang Jiao ◽  
Lu Wang ◽  
Jianxia Liu ◽  
Gang Ma
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Investment Decision ◽  
Aggregation Operators ◽  
Optimal Decision ◽  
Multi Criteria Decision Making ◽  
Investment Decision Making ◽  
Decision Making Problem ◽  
Geometric Operator ◽  
Integral Average

In this paper, two new aggregation operators based on Choquet integral, namely the induced generalized interval neutrosophic Choquet integral average operator(IGINCIA) and the induced generalized interval neutrosophic Choquet integral geometric operator(IG-INCIG), are proposed for multi-criteria decision making problems (MCDM). Firstly, the criteria are dependent to each other and the evaluation information of the criteria are expressed by interval neutrosophic numbers. Moreover, two indices which are inspired by the geometrical structure are established to compare the interval neutrosophic numbers. Then, a MCDM method is proposed based on the proposed aggregation operators and ranking indices to cope with MCDM with interactive criteria. Lastly, an investment decision making problem is provided to illustrate the practicality and effectiveness of the proposed approach. The validity and advantages of the proposed method are analyzed by comparing with some existing approaches. By a numerical example in company investment to expand business though five alternatives with considering four criteria, the optimal decision is made.

scholarly journals Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 3 ◽  
Author(s):  
Suizhi Luo ◽  
Lining Xing
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Sensitivity Analyses ◽  
Special Cases ◽  
Different Parts

Picture fuzzy numbers (PFNs), as the generalization of fuzzy sets, are good at fully expressing decision makers’ opinions with four membership degrees. Since aggregation operators are simple but powerful tools, this study aims to explore some aggregation operators with PFNs to solve practical decision-making problems. First, new operational rules, the interaction operations of PFNs, are defined to overcome the drawbacks of existing operations. Considering that interrelationships may exist only in part of criteria, rather than all of the criteria in reality, the partitioned Heronian aggregation operator is modified with PFNs to deal with this condition. Then, desirable properties are proved and several special cases are discussed. New decision-making methods with these presented aggregation operators are suggested to process hotel selection issues. Last, their practicability and merits are certified by sensitivity analyses and comparison analyses with other existing approaches. The results indicate that our methods are feasible to address such situations where criteria interact in the same part, but are independent from each other at different parts.

Some Generalized Intuitionistic Fuzzy Geometric Aggregation Operators With Applications in Multi-Criteria Decision Making Process

2018 ◽  
pp. 1190-1211
Author(s):  
Bhagawati Prasad Joshi
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Decision Making Process ◽  
Additional Parameter ◽  
Multi Criteria Decision Making ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Special Cases ◽  
Multidimensional Information

The aggregation operators play an important role in the fusion of multidimensional information in decision making process. In this study, a series of generalized aggregation operators such as: the generalized intuitionistic fuzzy weighted geometric (GIFWG) operator, the generalized intuitionistic fuzzy ordered weighted geometric (GIFOWG) operator and the generalized intuitionistic fuzzy hybrid geometric (GIHG) operator are proposed under intuitionistic fuzzy environment by controlling the power of the argument values with an additional parameter p. Some of the important properties and some special cases of these operators are also included in this study. Further, the developed approach is utilized to deal with multi-criteria decision making (MCDM) problems. Numerical examples are constructed to illustrate the developed approach effectively.

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