A MAGDM Method Based on 2-Tuple Linguistic Heronian Mean and New Operational Laws

In this paper, we investigate the multiple attributes group decision making (MAGDM) problem with 2-tuple linguistic information. According to some closed operational laws of 2-tuple linguistic, some Algebra t-norm and s-norm based Heronian aggregation operators of 2-tuple linguistic information are put forward, the desired properties and the special cases where the parameters take different values are also discussed. Furthermore, a method of MAGDM under 2-tuple linguistic environment is proposed based on the Algebra t-norm and s-norm based 2-tuple linguistic Heronian mean operator or the Algebra t-norm and s-norm based 2-tuple linguistic weighted Heronian mean operator. Finally, a numerical example is presented to demonstrate the proposed method.

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A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment

Mathematics ◽

10.3390/math9131489 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1489

Author(s):

Shahzad Faizi ◽

Wojciech Sałabun ◽

Nisbha Shaheen ◽

Atiq ur Rehman ◽

Jarosław Wątróbski

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Weighted Average ◽

Aggregation Operators ◽

Bonferroni Mean ◽

Operational Laws ◽

Geometric Bonferroni Mean ◽

The Individual ◽

Heronian Mean

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.

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Multiple Attribute Group Decision-Making Based on Power Heronian Aggregation Operators under Interval-Valued Dual Hesitant Fuzzy Environment

Mathematical Problems in Engineering ◽

10.1155/2020/2080413 ◽

2020 ◽

Vol 2020 ◽

pp. 1-19

Author(s):

Shenqing Jiang ◽

Wei He ◽

Fangfang Qin ◽

Qingqing Cheng

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operators ◽

Fuzzy Environment ◽

Multiple Attribute ◽

Special Cases ◽

Magdm Problems ◽

Interval Valued ◽

Heronian Mean

In this paper, we focus on new methods to deal with multiple attribute group decision-making (MAGDM) problems and a new comparison law of interval-valued dual hesitant fuzzy elements (IVDHFEs). More explicitly, the interval-valued dual hesitant fuzzy 2nd-order central polymerization degree (IVDHFCP2) function is introduced, for the case that score values of different IVDHFEs are identical. This function can further compare different IVDHFEs. Then, we develop a series of interval-valued dual hesitant fuzzy power Heronian aggregation operators, i.e., the interval-valued dual hesitant fuzzy power Heronian mean (IVDHFPHM) operator, the interval-valued dual hesitant fuzzy power geometric Heronian mean (IVDHFPGHM) operator, and their weighted forms. Some desirable properties and their special cases are discussed. These proposed operators can simultaneously reflect the interrelationship of aggregated arguments and reduce the influence of unreasonable evaluation values. Finally, two approaches for interval-valued dual hesitant fuzzy MAGDM with known or unknown weight information are presented. An illustrative example and comparative studies are given to verify the advantages of our methods. A sensitivity analysis of the decision results is analyzed with different parameters.

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Some Single-Valued Neutrosophic Power Heronian Aggregation Operators and Their Application to Multiple-Attribute Group Decision-Making

Symmetry ◽

10.3390/sym11050653 ◽

2019 ◽

Vol 11 (5) ◽

pp. 653 ◽

Cited By ~ 4

Author(s):

Shuping Zhao ◽

Dong Wang ◽

Changyong Liang ◽

Yajun Leng ◽

Jian Xu

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Comparison Method ◽

Aggregation Operators ◽

Multiple Attribute ◽

Special Cases ◽

Magdm Problems ◽

Heronian Mean

The power Heronian aggregation (PHA) operator can use the advantages of power average and the Heronian mean operator, which together could take into account the interrelationship of the aggregated arguments, and therefore alleviate the effects caused by unreasonable data through considering the support degree between input arguments. However, PHA operators cannot be used to process single-valued neutrosophic numbers (SVNNs), which is significant for extending it to SVNNs. We propose some new PHA operators for SVNNs and introduce a novel MAGDM method on the basis of the proposed operators. Firstly, the definition, properties, comparison method, and operational rules of SVNNs are introduced briefly. Then, some PHA operators are proposed, such as the single-valued neutrosophic power Heronian aggregation (SVNPHA) operator, the single-valued neutrosophic weighted power Heronian aggregation (SVNWPHA) operator, single-valued neutrosophic geometric power Heronian aggregation (SVNGPHA) operator, single-valued neutrosophic weighted geometric power Heronian aggregation (SVNWGPHA) operator. Furthermore, we discuss some properties of these new aggregation operators and several special cases. Moreover, the method to solve the MAGDM problems with SVNNs is proposed, based on the SVNWPHA and SVNWGPHA operators. Lastly, we verified the application and effectiveness of the proposed method by using an example for the MAGDM problem.

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SOME HERONIAN MEAN OPERATORS WITH 2-TUPLE LINGUISTIC INFORMATION AND THEIR APPLICATION TO MULTIPLE ATTRIBUTE GROUP DECISION MAKING

Technological and Economic Development of Economy ◽

10.3846/20294913.2015.1055614 ◽

2015 ◽

Vol 21 (5) ◽

pp. 797-814 ◽

Cited By ~ 16

Author(s):

Ye Ye ◽

Peide LIU

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operators ◽

Linguistic Information ◽

Multiple Attribute ◽

Heronian Mean

With respect to multi-attribute group decision-making problems, in which attribute values take the form of 2-tuple linguistic information, a new decision making method that considers the interrelationships of attribute values is proposed. Firstly, some new aggregation operators of 2-tuple linguistic information based on Heronian mean are proposed, such as 2-tuple linguistic Heronian mean operator (2TLHM) and 2-tuple linguistic weighted Heronian mean operator (2TLWHB), and some desired properties of the proposed operators are studied. Then, a method based on the 2TLHM and 2TLWHB operators for multiple attribute group decision making is developed. In this approach, the interrelationships of attribute values are considered. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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T-Spherical Fuzzy Rough Interactive Power Heronian Mean Aggregation Operators for Multiple Attribute Group Decision-Making

Symmetry ◽

10.3390/sym13122422 ◽

2021 ◽

Vol 13 (12) ◽

pp. 2422

Author(s):

Haolun Wang

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Distance Measure ◽

Group Decision ◽

Aggregation Operators ◽

Membership Degree ◽

Symmetric Information ◽

Multiple Attribute ◽

Special Cases ◽

Heronian Mean

In this article, to synthesize the merits of interaction operational laws (IOLs), rough numbers (RNs), power average (PA) and Heronian mean (HM), a new notion of T-spherical fuzzy rough numbers (T-SFRNs) is first introduced to describe the intention of group experts accurately and take the interaction between individual experts into account with complete and symmetric information. The distance measure and ordering rules of T-SFRNs are proposed, and the IOLs of T-SFRNs are extended. Next, the PA and HM are combined based on the IOLs of T-SFRNs, and the T-Spherical fuzzy rough interaction power Heronian mean operator and its weighted form are proposed. These aggregation operators can accurately express both individual and group uncertainty using T-SFRNs, capture the interaction among membership degree, abstinence degree and non-membership degree of T-SFRNs by employing IOLs, ensure the overall balance of variable values by the PA in the process of information fusion, and realize the interrelationship between attribute variables by the HM. Several properties and special cases of these aggregation operators are further presented and discussed. Subsequently, a new approach for dealing with T-spherical fuzzy multiple attribute group decision-making problems based on proposed aggregation operator is developed. Lastly, in order to validate the feasibility and reasonableness of the proposed approach, a numerical example is presented, and the superiorities of the proposed method are illustrated by describing a sensitivity analysis and a comparative analysis.

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Uncertain Linguistic Aggregation Distance Measures and Their Application to Group Decision Making

Journal of Applied Mathematics ◽

10.1155/2013/563650 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9

Author(s):

Wei Li ◽

Shouzhen Zeng

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Distance Measures ◽

University Faculty ◽

Linguistic Information ◽

Weighted Distance ◽

Special Cases ◽

Decision Making Problem

We introduce a method based on distance measures for group decision making under uncertain linguistic environment. We develop some uncertain linguistic aggregation distance measures called the uncertain linguistic weighted distance (ULWD) measure, the uncertain linguistic ordered weighted distance (ULOWD) measure, and the uncertain linguistic hybrid weighted distance (ULHWD) measure. We study some of their characteristic, and we prove that the ULWD and the ULOWD are special cases of the ULHWD measure. Finally, we develop an application of the ULHWD measure in a group decision making problem concerning the evaluation of university faculty for tenure and promotion with uncertain linguistic information.

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Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator and Its Application to Decision Making

Symmetry ◽

10.3390/sym10110658 ◽

2018 ◽

Vol 10 (11) ◽

pp. 658 ◽

Cited By ~ 16

Author(s):

Aliya Fahmi ◽

Fazli Amin ◽

Florentin Smarandache ◽

Madad Khan ◽

Nasruddin Hassan

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operators ◽

Weighted Averaging ◽

Linguistic Information ◽

Ordered Weighted Averaging ◽

Averaging Operator ◽

Multiple Attribute ◽

The Relationship

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach.

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Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators

Complexity ◽

10.1155/2018/9531064 ◽

2018 ◽

Vol 2018 ◽

pp. 1-24 ◽

Cited By ~ 15

Author(s):

Mingwei Lin ◽

Jiuhan Wei ◽

Zeshui Xu ◽

Riqing Chen

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Bonferroni Mean ◽

Fuzzy Environment ◽

Operational Laws ◽

Special Cases ◽

Geometric Bonferroni Mean ◽

Decision Making Model ◽

Pythagorean Fuzzy Numbers

The partitioned Bonferroni mean (PBM) operator can efficiently aggregate inputs, which are divided into parts based on their interrelationships. To date, it has not been used to aggregate linguistic Pythagorean fuzzy numbers (LPFNs). In this paper, we extend the PBM operator and partitioned geometric Bonferroni mean (PGBM) operator to the linguistic Pythagorean fuzzy sets (LPFSs) and use them to develop a novel multiattribute group decision-making model under the linguistic Pythagorean fuzzy environment. We first define some novel operational laws for LPFNs, which take into consideration the interactions between the membership degree (MD) and nonmembership degree (NMD) from two different LPFNs. Based on these novel operational laws, we put forward the interaction PBM (LPFIPBM) operator, the weighted interaction PBM (LPFWIPBM) operator, the interaction PGBM (LPFIPGBM) operator, and the weighted interaction PGBM (LPFWIPGBM) operator. Then, we study some properties of these proposed operators and discuss their special cases. Based on the proposed LPFWIPBM and LPFWIPGBM operators, a novel multiattribute group decision-making model is developed to process the linguistic Pythagorean fuzzy information. Finally, some illustrative examples are introduced to compare our proposed methods with the existing ones.

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An Approach to Group Making Problems Based on Two-Tuple Linguistic Theory

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.472.456 ◽

2014 ◽

Vol 472 ◽

pp. 456-459

Author(s):

Jun Wei ◽

Xiao Jun Zhong ◽

Jun Gong

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Linguistic Theory ◽

Linguistic Information ◽

Numerical Example ◽

Judgement Matrix ◽

The World

The group decision-making is a new way recent years in the world which is based on the analysis of linguistic information.A method for this kind of group problems based on two-tuple linguistic theory is proposed in this paper.First,the method transforms initial linguistic information into group judgement matrix,and then give the select process of optimal alternative based on an operator.Finally,a numerical example is given to illustrate the validity of the proposed method.

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Induced Interval-Valued Intuitionistic Fuzzy Hybrid Aggregation Operators with TOPSIS Order-Inducing Variables

Journal of Applied Mathematics ◽

10.1155/2012/245732 ◽

2012 ◽

Vol 2012 ◽

pp. 1-24 ◽

Cited By ~ 4

Author(s):

Jun-Ling Zhang ◽

Xiao-Wen Qi

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operators ◽

Intuitionistic Fuzzy ◽

Multiple Attribute ◽

Special Cases ◽

Wide Range ◽

Induced Aggregation ◽

Interval Valued

Two induced aggregation operators with novelly designed TOPSIS order-inducing variables are proposed: Induced Interval-valued Intuitionistic Fuzzy Hybrid Averaging (I-IIFHA) operator and Induced Interval-valued Intuitionistic Fuzzy Hybrid Geometric (I-IIFHG) operator. The merit of two aggregation operators is that they can consider additional preference information of decision maker’s attitudinal characteristics besides argument-dependent information and argument-independent information. Some desirable properties of I-IIFHA and I-IIFHG are studied and theoretical analysis also shows that they can include a wide range of aggregation operators as special cases. Further, we extend these operators to form a novel group decision-making method for selecting the most desirable alternative in multiple attribute multi-interest group decision-making problems with attribute values and decision maker’s interest values taking the form of interval-valued intuitionistic fuzzy numbers, and application research to real estate purchase selection shows its practicality.

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