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

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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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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Generalized Hamacher Aggregation Operators for Intuitionistic Uncertain Linguistic Sets: Multiple Attribute Group Decision Making Methods

Information ◽

10.3390/info10060206 ◽

2019 ◽

Vol 10 (6) ◽

pp. 206 ◽

Cited By ~ 1

Author(s):

Yun Jin ◽

Hecheng Wu ◽

Jose M. Merigó ◽

Bo Peng

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Weighted Average ◽

Aggregation Operators ◽

Linguistic Variables ◽

Multiple Attribute ◽

Special Cases ◽

The Given ◽

Magdm Problems

In this paper, we consider multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables. Based on Hamacher operations, we developed several Hamacher aggregation operators, which generalize the arithmetic aggregation operators and geometric aggregation operators, and extend the algebraic aggregation operators and Einstein aggregation operators. A number of special cases for the two operators with respect to the parameters are discussed in detail. Also, we developed an intuitionistic uncertain linguistic generalized Hamacher hybrid weighted average operator to reflect the importance degrees of both the given intuitionistic uncertain linguistic variables and their ordered positions. Based on the generalized Hamacher aggregation operator, we propose a method for MAGDM for intuitionistic uncertain linguistic sets. Finally, a numerical example and comparative analysis with related decision making methods are provided to illustrate the practicality and feasibility of the proposed method.

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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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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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A NOVEL EDAS BASED METHOD FOR MULTIPLE ATTRIBUTE GROUP DECISION MAKING WITH PYTHAGOREAN 2-TUPLE LINGUISTIC INFORMATION

Technological and Economic Development of Economy ◽

10.3846/tede.2020.12733 ◽

2020 ◽

Vol 26 (6) ◽

pp. 1125-1138

Author(s):

Tingting He ◽

Guiwu Wei ◽

Jianping Lu ◽

Jiang Wu ◽

Cun Wei ◽

...

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Safety Assessment ◽

Group Decision ◽

Construction Safety ◽

Aggregation Operators ◽

Multiple Attribute ◽

Todim Method ◽

Basic Concepts ◽

Magdm Problems

In this article, we combine some fundamental theories of the Pythagorean 2-tuple linguistic sets (P2TLSs) with EDAS method and design the Pythagorean 2-tuple linguistic number (P2TLN) EDAS (P2TLN-EDAS) method for multiple attribute group decision making (MAGDM) issue. Firstly, the basic concepts of P2TLSs are introduced. Next, two aggregation operators of P2TLN are defined, and then the calculation steps of EDAS method are listed briefly. Furthermore, P2TLN-EDAS method is given for MAGDM problems and computing steps are proposed in detail. Finally, a computational example related to construction safety assessment is used to expound the effectiveness of the designed method. Meanwhile, we also carried out some comparative analysis between P2TLN-EDAS method and P2TLWA/P2TLWG operators and another P2TLN-TODIM method. The results show that P2TLN-EDAS method derives the same best alternative as P2TLWA, P2TLWG operators and P2TLN-TODIM method.

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Multiple attribute group decision-making based on interval-valued q-rung orthopair uncertain linguistic power Muirhead mean operators and linguistic scale functions

PLoS ONE ◽

10.1371/journal.pone.0258772 ◽

2021 ◽

Vol 16 (10) ◽

pp. e0258772

Author(s):

Yuan Xu ◽

Shifeng Liu ◽

Jun Wang

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Comparison Method ◽

Model Framework ◽

Scale Functions ◽

Multiple Attribute ◽

Definition Of ◽

Magdm Problems ◽

Interval Valued

Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.

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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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FUZZY POWER AGGREGATION OPERATORS AND THEIR APPLICATION TO MULTIPLE ATTRIBUTE GROUP DECISION MAKING

Technological and Economic Development of Economy ◽

10.3846/20294913.2013.821684 ◽

2013 ◽

Vol 19 (3) ◽

pp. 377-396 ◽

Cited By ~ 38

Author(s):

Guiwu Wei ◽

Xiaofei Zhao ◽

Hongjun Wang ◽

Rui Lin

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operators ◽

Fuzzy Information ◽

Multiple Attribute ◽

Magdm Problems ◽

The Ideal

The article investigates the multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of triangular fuzzy information. Motivated by the ideal of power aggregation, in this paper some power aggregation operators for aggregating triangular fuzzy information are developed and then applied in order to develop some models for multiple attribute group decision making with triangular fuzzy information. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.

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UNCERTAIN LINGUISTIC PRIORITIZED AGGREGATION OPERATORS AND THEIR APPLICATION TO MULTIPLE ATTRIBUTE GROUP DECISION MAKING

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488513500293 ◽

2013 ◽

Vol 21 (04) ◽

pp. 603-627 ◽

Cited By ~ 51

Author(s):

L. Y. ZHOU ◽

R. LIN ◽

X. F. ZHAO ◽

G. W. WEI

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operators ◽

Linguistic Information ◽

Priority Level ◽

Multiple Attribute ◽

Prioritized Aggregation Operators ◽

Magdm Problems

In this paper, we investigate the uncertain linguistic multiple attribute group decision making (MAGDM) problems in which the attributes and experts are in different priority level. Motivated by the idea of prioritized aggregation operators (R. R. Yager, Prioritized aggregation operators, Int. J. Approximate Reasoning48 (2008) 263–274.), we develop some prioritized aggregation operators for aggregating uncertain linguistic information, and then apply them to develops some models for uncertain linguistic multiple attribute group decision making (MAGDM) problems in which the attributes and experts are in different priority level. Finally, a practical example about talent introduction is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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Multiple attribute group decision-making based on cubic linguistic Pythagorean fuzzy sets and power Hamy mean

Complex & Intelligent Systems ◽

10.1007/s40747-020-00255-z ◽

2021 ◽

Author(s):

Wuhuan Xu ◽

Xiaopu Shang ◽

Jun Wang

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Group Decision Making ◽

Distance Measure ◽

Group Decision ◽

Comparison Method ◽

Aggregation Operators ◽

Decision Makers ◽

Pythagorean Fuzzy Sets ◽

Multiple Attribute

AbstractThe linguistic Pythagorean fuzzy sets (LPFSs), which employ linguistic terms to express membership and non-membership degrees, can effectively deal with decision makers’ complicated evaluation values in the process of multiple attribute group decision-making (MAGDM). To improve the ability of LPFSs in depicting fuzzy information, this paper generalized LPFSs to cubic LPFSs (CLPFSs) and studied CLPFSs-based MAGDM method. First, the definition, operational rules, comparison method and distance measure of CLPFSs are investigated. The CLPFSs fully adsorb the advantages of LPFSs and cubic fuzzy sets and hence they are suitable and flexible to depict attribute values in fuzzy and complicated decision-making environments. Second, based on the extension of power Hamy mean operator in CLPFSs, the cubic linguistic Pythagorean fuzzy power average operator, the cubic linguistic Pythagorean fuzzy power Hamy mean operator as well as their weighted forms were introduced. These aggregation operators can effectively and comprehensively aggregate attribute values in MAGDM problems. Besides, some important properties of these operators were studied. Finally, we presented a new MAGDM method based on CLPFSs and their aggregation operators. Illustrative examples and comparative analysis are provided to show the effectiveness and advantages of our proposed decision-making method.

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