scholarly journals Heronian Mean Operator of Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Methods

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Changxing Fan ◽  
Jun Ye
Keyword(s):  
Decision Making ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Multiple Attribute ◽  
Decision Methods ◽  
Multiattribute Decisions ◽  
Heronian Mean

Many aggregation operators in multiattribute decisions assume that attributes are independent of each other; this leads to an unreasonable situation in information aggregation and decision-making. Heronian mean is the aggregation operator that can embody the interaction between attributes. In this paper, we merge the linguistic neutrosophic cubic number (LNCN) and the Heronian mean operator together to develop a LNCN generalized weighted Heronian mean (LNCNGWHM) operator and a LNCN three-parameter weighted Heronian mean (LNCNTPWHM) operator and then discuss their properties. Further, two multiattribute decision methods based on the proposed LNCNGWHM or LNCNTPWHM operator are introduced under LNCN environment. Finally, an example is used to indicate the effectiveness of the developed methods.

scholarly journals Hesitant Fuzzy Linguistic Hamy Mean Aggregation Operators and Their Application to Linguistic Multiple Attribute Decision-Making

2020 ◽  
Vol 2020 ◽  
pp. 1-22 ◽  
Author(s):  
Yuan Rong ◽  
Zheng Pei ◽  
Yi Liu
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Multiple Attribute ◽  
Fuzzy Linguistic

Linguistic aggregation operator is a paramount appliance to fix linguistic multiple attribute decision-making (MADM) issues. In the article, the Hamy mean (HM) operator is utilized to fuse hesitant fuzzy linguistic (HFL) information and several novel HFL aggregation operators including the hesitant fuzzy linguistic Hamy mean (HFLHM) operator, weighted hesitant fuzzy linguistic Hamy mean (WHFLHM) operator, hesitant fuzzy linguistic dual Hamy mean (HFLDHM) operator, and weighted hesitant fuzzy linguistic dual Hamy mean (WHFLDHM) operator are proposed. Besides, several paramount theorems and particular cases of these aggregation operators are investigated in detail, and then a novel MADM approach is presented by using the proposed aggregation operators. Ultimately, a practical example is utilized to manifest the effectiveness and practicability of the propounded method.

scholarly journals A Multiple Attribute Decision Making Method Based on Uncertain Linguistic Heronian Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaodi Liu ◽  
Jianjun Zhu ◽  
Guodong Liu ◽  
Jingjing Hao
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operator ◽  
Linguistic Variables ◽  
Multiple Attribute ◽  
Heronian Mean

The Heronian mean is a useful aggregation operator which can capture the interrelationship of the input arguments. In this paper, we develop some Heronian means based on uncertain linguistic variables, such as the generalized uncertain linguistic Heronian mean (GULHM) and uncertain linguistic geometric Heronian mean (ULGHM), and some of their desirable properties are also investigated. Considering the different importance of the input arguments, we define the generalized uncertain linguistic weighted Heronian mean (GULWHM) and uncertain linguistic weighted geometric Heronian mean (ULWGHM). Then, a method of multiple attribute decision making under uncertain linguistic environment is presented based on the GULWHM or the ULWGHM. In the end, an example is given to demonstrate the effectiveness and feasibility of the proposed method.

scholarly journals Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chunyong Wang ◽  
Qingguo Li ◽  
Xiaoqiang Zhou ◽  
Tian Yang
Keyword(s):  
Decision Making ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Special Cases ◽  
Fuzzy Aggregation

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

scholarly journals An Approach to Linguistic Multiple Attribute Decision-Making Based on Unbalanced Linguistic Generalized Heronian Mean Aggregation Operator

2018 ◽  
Vol 2018 ◽  
pp. 1-25 ◽  
Author(s):  
Bing Han ◽  
Huayou Chen ◽  
Jiaming Zhu ◽  
Jinpei Liu
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Low Carbon ◽  
Weighted Arithmetic ◽  
Multiple Attribute ◽  
Linguistic Assessment ◽  
Linguistic Assessment Information ◽  
Heronian Mean ◽  
Generalized Arithmetic

This paper proposes an approach to linguistic multiple attribute decision-making problems with interactive unbalanced linguistic assessment information by unbalanced linguistic generalized Heronian mean aggregation operators. First, some generalized Heronian mean aggregation operators with unbalanced linguistic information are proposed, involving the unbalanced linguistic generalized arithmetic Heronian mean operator and the unbalanced linguistic generalized geometric Heronian mean operator. For the situation that the input arguments have different degrees of importance, the unbalanced linguistic generalized weighted arithmetic Heronian mean operator and the unbalanced linguistic generalized weighted geometric Heronian mean operator are developed. Then we investigate their properties and some particular cases. Finally, the effectiveness and universality of the developed approach are illustrated by a low-carbon tourist instance and comparison analysis. A sensitivity analysis is performed as well to test the robustness of proposed methods.

Density aggregation operators for interval-valued q-rung orthopair fuzzy numbers and their application in multiple attribute decision making

2021 ◽  
pp. 1-14
Author(s):  
Huijuan Guo ◽  
Ruipu Yao
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Weighted Arithmetic ◽  
Geometric Average ◽  
Novel Approach ◽  
Multiple Attribute ◽  
Interval Valued

The symmetry between fuzzy evaluations and crisp numbers provides an effective solution to multiple attribute decision making (MADM) problems under fuzzy environments. Considering the effect of information distribution on decision making, a novel approach to MADM problems under the interval-valued q-rung orthopair fuzzy (Iq-ROF) environments is put forward. Firstly, the clustering method of interval-valued q-rung orthopair fuzzy numbers (Iq-ROFNs) is defined. Secondly, Iq-ROF density weighted arithmetic (Iq-ROFDWA) intermediate operator and Iq-ROF density weighted geometric average (Iq-ROFDWGA) intermediate operator are developed based on the density weighted intermediate operators for crisp numbers. Thirdly, combining the density weighted intermediate operators with the Iq-ROF weighted aggregation operators, Iq-ROF density aggregation operators including Iq-ROF density weighted arithmetic (Iq-ROFDWAA) aggregation operator and Iq-ROF density weighted geometric (Iq-ROFDWGG) aggregation operator are proposed. Finally, effectiveness of the proposed method is verified through a numerical example.

scholarly journals Multiple Attribute Decision-Making Based on Three-Parameter Generalized Weighted Heronian Mean

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1363
Author(s):  
Ximei Hu ◽  
Shuxia Yang ◽  
Ya-Ru Zhu
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Correlation Factor ◽  
Aggregation Operators ◽  
Practical Significance ◽  
Correlation Relationship ◽  
Multiple Attribute ◽  
Aggregation Problem ◽  
The Relationship ◽  
Heronian Mean

For the aggregation problem of attributes with a correlation relationship, it is often necessary to take the correlation factor into account in order to make the decision results more objective and reasonable. The Heronian mean is an aggregation operator which reflects the interaction between attributes. It is of great theoretical and practical significance to study and popularize the multiple attribute decision-making methods based on the Heronian mean operator. In this paper, we first give a new three-parameter generalized weighted Heronian mean (TPGWHM), which has a series of excellent properties such as idempotency, monotonicity and boundedness. At the same time, the relationship between the TPGWHM and the existing aggregation operators is given. Then, we propose the intuitionistic fuzzy three-parameter generalized weighted Heronian mean (IFTPGWHM) and give its idempotency, monotonicity, boundedness and limit properties. On this basis, a multiple attribute decision-making method based on the TPGWHM and a multiple attribute decision-making method based on the IFTPGWHM are given, and corresponding examples are given and analyzed.

scholarly journals Harmonic Aggregation Operator with Trapezoidal Picture Fuzzy Numbers and Its Application in a Multiple-Attribute Decision-Making Problem

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 135
Author(s):  
Chittaranjan Shit ◽  
Ganesh Ghorai ◽  
Qin Xin ◽  
Muhammad Gulzar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Harmonic Mean ◽  
Life Problems ◽  
Multiple Attribute ◽  
Fuzzy Order

Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.

scholarly journals Hesitant Probabilistic Fuzzy Information Aggregation Using Einstein Operations

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 226 ◽  
Author(s):  
Jin Park ◽  
Yu Park ◽  
Mi Son
Keyword(s):  
Decision Making ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multiple Attribute ◽  
Special Cases ◽  
Fuzzy Aggregation ◽  
Einstein Operations ◽  
Geometric Operator

In this paper, a hesitant probabilistic fuzzy multiple attribute group decision making is studied. First, some Einstein operations on hesitant probability fuzzy elements such as the Einstein sum, Einstein product, and Einstein scalar multiplication are presented and their properties are discussed. Then, several hesitant probabilistic fuzzy Einstein aggregation operators, including the hesitant probabilistic fuzzy Einstein weighted averaging operator and the hesitant probabilistic fuzzy Einstein weighted geometric operator and so on, are introduced. Moreover, some desirable properties and special cases are investigated. It is shown that some existing hesitant fuzzy aggregation operators and hesitant probabilistic fuzzy aggregation operators are special cases of the proposed operators. Further, based on the proposed operators, a new approach of hesitant probabilistic fuzzy multiple attribute decision making is developed. Finally, a practical example is provided to illustrate the developed approach.

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