Some Maclaurin Symmetric Mean Aggregation Operators Based on Cloud Model and Their Application to Decision-Making

2019 ◽  
Vol 18 (03) ◽  
pp. 981-1007 ◽  
Author(s):  
Peide Liu ◽  
Hongyu Yang ◽  
Haiquan Wu ◽  
Meilong Ju ◽  
Fawaz E. Alsaadi
Keyword(s):  
Decision Making ◽  
Quantitative Method ◽  
Group Decision ◽  
Cloud Model ◽  
Aggregation Operators ◽  
Linguistic Variables ◽  
Qualitative Information ◽  
New Approach ◽  
Maclaurin Symmetric Mean ◽  
Magdm Problems

The cloud model (CM) is an important tool to describe qualitative concept by the quantitative method, and the Maclaurin symmetric mean (MSM) can capture the interrelationship among the multi-inputs and it can generalize most of existing operators. In this paper, we firstly convert the uncertain linguistic variables (ULVs), which are easily used to express the qualitative information, to CM. Then, we combine the MSM with the CM, and propose the cloud MSM (CMSM) operator and cloud weighted MSM (CWMSM) operator. In addition, we explore some of their desirable features and develop a new approach to deal with some multi-attribute group decision-making (MAGDM) problems under the uncertain environment based on the proposed operators. Finally, by comparing with other approaches, an illustrative example is arranged to demonstrate the usability of the proposed method.

scholarly journals Some Partitioned Maclaurin Symmetric Mean Based on q-Rung Orthopair Fuzzy Information for Dealing with Multi-Attribute Group Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 383 ◽  
Author(s):  
Kaiyuan Bai ◽  
Xiaomin Zhu ◽  
Jun Wang ◽  
Runtong Zhang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Negative Influence ◽  
Fuzzy Information ◽  
New Approach ◽  
Maclaurin Symmetric Mean ◽  
Magdm Problems ◽  
Different Parts

In respect to the multi-attribute group decision making (MAGDM) problems in which the evaluated value of each attribute is in the form of q-rung orthopair fuzzy numbers (q-ROFNs), a new approach of MAGDM is developed. Firstly, a new aggregation operator, called the partitioned Maclaurin symmetric mean (PMSM) operator, is proposed to deal with the situations where the attributes are partitioned into different parts and there are interrelationships among multiple attributes in same part whereas the attributes in different parts are not related. Some desirable properties of PMSM are investigated. Then, in order to aggregate the q-rung orthopair fuzzy information, the PMSM is extended to q-rung orthopair fuzzy sets (q-ROFSs) and two q-rung orthopair fuzzy partitioned Maclaurin symmetric mean (q-ROFPMSM) operators are developed. To eliminate the negative influence of unreasonable evaluation values of attributes on aggregated result, we further propose two q-rung orthopair fuzzy power partitioned Maclaurin symmetric mean (q-ROFPPMSM) operators, which combine the PMSM with the power average (PA) operator within q-ROFSs. Finally, a numerical instance is provided to illustrate the proposed approach and a comparative analysis is conducted to demonstrate the advantage of the proposed approach.

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

Information ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 206 ◽  
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.

scholarly journals Some Trapezoid Intuitionistic Fuzzy Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple-Attribute Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1778
Author(s):  
Zheng Dong ◽  
Yushui Geng
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Intuitionistic Fuzzy ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Multiple Input ◽  
Fuzzy Linguistic ◽  
Magdm Problems

In order to solve multiple-attribute group decision-making (MAGDM) problems under a trapezoid intuitionistic fuzzy linguistic (TIFL) environment and the relationships between multiple input parameters needed, in this paper, we extend the Maclaurin symmetric mean (MSM) operators to TIFL numbers (TIFLNs). Some new aggregation operators are proposed, including the trapezoid intuitionistic fuzzy linguistic Maclaurin symmetric mean (TIFLMSM) operator, trapezoid intuitionistic fuzzy linguistic generalized Maclaurin symmetric mean (TIFLGMSM) operator, trapezoid intuitionistic fuzzy linguistic weighted Maclaurin symmetric mean (TIFLWMSM) operator and trapezoid intuitionistic fuzzy linguistic weighted generalized Maclaurin symmetric mean (TIFLWGMSM) operator. Next, based on the TIFLWMSM and TIFLWGMSM operators, two methods are presented to deal with MAGDM problems. Finally, there is a numerical example to verify the effectiveness and feasibility of the proposed approaches.

scholarly journals Uncertain Linguistic Power Geometric Operators and Their Use in Multiattribute Group Decision Making

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Huimin Zhang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Linguistic Variables ◽  
Triangular Norm ◽  
Operational Laws ◽  
Linguistic Power ◽  
Magdm Problems

Based on the extended triangular norm, several new operational laws for linguistic variables and uncertain linguistic variables (ULVs) are defined. To avoid the limitations of existing linguistic aggregation operators, a series of extended uncertain linguistic (UL) geometric aggregation operators are proposed on the basis of the extended triangular norm. In addition, a multiattribute group decision making (MAGDM) method dealing with UL information is developed based on the extended UL geometric aggregation operators. Finally, an example is presented to show the efficiency of the developed approach in solving MAGDM problems.

scholarly journals A Novel Approach to Multi-Attribute Group Decision-Making based on Interval-Valued Intuitionistic Fuzzy Power Muirhead Mean

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 441 ◽  
Author(s):  
Wuhuan Xu ◽  
Xiaopu Shang ◽  
Jun Wang ◽  
Weizi Li
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Intuitionistic Fuzzy ◽  
Novel Approach ◽  
Maclaurin Symmetric Mean ◽  
Magdm Problems ◽  
Interval Valued

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method.

scholarly journals A Method of Multiple Attribute Group Decision Making Based on 2-Tuple Linguistic Dependent Maclaurin Symmetric Mean Operators

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 31 ◽  
Author(s):  
Min Feng ◽  
Peide Liu ◽  
Yushui Geng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
New Method ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Magdm Problems

Aiming at multiple attribute group decision making (MAGDM) problems, especially the attribute values of 2-tuple linguistic numbers and the interrelationships between each attribute needing to be considered, this paper proposes a new method of analysis. Firstly, we developed a few new aggregation operators, like the 2-tuple linguistic dependent weighted Maclaurin symmetric mean (2TLDWMSM) operator, the 2-tuple linguistic dependent weighted generalized Maclaurin symmetric mean (2TLDWGMSM) operator, and the 2-tuple linguistic dependent weighted geometric Maclaurin symmetric mean (2TLDWGeoMSM) operator. In the above operators, Maclaurin symmetric mean (MSM) operators can take the relationships between each attribute into account and dependent operators can mitigate the unfair parameters’ impact on the overall outcome, in which those ‘‘incorrect’’ and ‘‘prejudiced’’ parameters are distributed with low weights. Next, a method used by the 2TLDWMSM, 2TLDWGMSM, and 2TLDWGeoMSM operators for MAGDM is introduced. Finally, there is an explanative example to confirm the proposed approach and explain its availability and usefulness.

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

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.

Research on Evaluating Theory and Application to Design of Mechanism Scheme with Uncertain Linguistic Information

2012 ◽  
Vol 201-202 ◽  
pp. 749-752
Author(s):  
Tie Jun Wang ◽  
Chang Zhong Hao
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Primary Phase ◽  
Harmonic Mean ◽  
Linguistic Variables ◽  
Product Lifecycle ◽  
Linguistic Information ◽  
Multiple Attribute ◽  
Magdm Problems

The design of mechanism scheme is the primary phase and the creative and challenging part in product lifecycle. In this paper, we research the multiple attribute group decision making (MAGDM) problems for evaluating the design of mechanism scheme with uncertain linguistic variables. We employ the uncertain linguistic weighted harmonic mean (ULWHM) operator to aggregate the uncertain linguistic information corresponding to each alternative and get the overall value of the alternatives, then rank the alternatives and select the most desirable one(s) by using the formula of the degree of possibility for the comparison between two uncertain linguistic variables. Finally, a practical example for evaluating the design of mechanism scheme is used to illustrate the developed procedures.

Multiple Attribute Decision-Making Methods with Unbalanced Linguistic Variables Based on Maclaurin Symmetric Mean Operators

2019 ◽  
Vol 18 (01) ◽  
pp. 105-146 ◽  
Author(s):  
Fei Teng ◽  
Peide Liu ◽  
Li Zhang ◽  
Juan Zhao
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Linguistic Variables ◽  
Numerical Example ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Linguistic Term

In this paper, we firstly introduced the unbalanced linguistic term sets, the linguistic transforming methodology, the Maclaurin symmetric mean (MSM) operator and dual MSM (DMSM) operator. Then, we proposed the closed operational rules of unbalanced linguistic variables, and several new MSM aggregation operators, including unbalanced linguistic MSM (ULMSM) operator, weighted unbalanced linguistic MSM (WULMSM) operator, unbalanced linguistic DMSM (ULDMSM) operator and weighted unbalanced linguistic DMSM (WULDMSM) operator. Further, we proposed two multiple attribute decision-making (MADM) methods under unbalanced linguistic environments based on the WULMSM operator and WULDMSM operator, respectively. Finally, a numerical example is used to show the applicability and effectiveness of the proposed MADM methods and to reveal their advantages by comparing with the existing methods.

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