Hamacher heronian mean operators for multi-critria decision-making under multi-valued picture fuzzy uncertain lingsuitic environment

2021 ◽  
pp. 1-22
Author(s):  
Baolin Li ◽  
Lihua Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Comparison Method ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Picture Fuzzy Set ◽  
Linguistic Term ◽  
Cognitive Information ◽  
Evaluation Information ◽  
Heronian Mean

Picture fuzzy set (PFS) and linguistic term set (LTS) are two significant notions in multi-criteria decision-making (MCDM). In practice, decision-makers sometimes need utilize the multiple probable membership degrees for an uncertain linguistic term to express evaluation information. Motivated by these, to better convey the vagueness and uncertainty of cognitive information, multi-valued picture fuzzy uncertain linguistic set combining picture hesitant fuzzy set with uncertain linguistic term set is proposed. We firstly define the concepts of multi-valued picture fuzzy uncertain linguistic set and multi-valued picture fuzzy uncertain linguistic number. Hamacher operations are more general and flexible in information fusion, thus, Hamacher operations and comparison method are developed at the same time. Improved generalized Heronian Mean operator can simultaneously reflect correlations between values and prevent the redundant calculation. Then, two operators of improved generalized weighted Heronian mean and improved generalized geometric weighted Heronian mean in view of Hamacher operations are proposed. Meanwhile, some distinguished properties and instances of two operators are explored as well. Moreover, a novel MCDM approach applying the developed operators is constructed. Ultimately, an illustrative example on vendor selection is performed, and sensitivity analysis and comparison analysis are provided to verify the powerfulness of the proposed method.

scholarly journals Some Novel Picture 2-Tuple Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple Attribute Decision Making

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 943
Author(s):  
Min Feng ◽  
Yushui Geng
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Linguistic Variable ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Picture Fuzzy Set ◽  
Input Parameters ◽  
Cognitive Information

When solving multiple attribute decision making (MADM) problems, the 2-tuple linguistic variable is an effective tool that can not only express complex cognitive information but also prevent loss of information in calculation. The picture fuzzy set (PFS) has three degrees and has more freedom to express cognitive information. In addition, Archimedean t-conorm and t-norm (ATT) can generalize most existing t-conorms and t-norms and Maclaurin symmetric mean (MSM) operators can catch the relationships among the multi-input parameters. Therefore, we investigate several novel aggregation operators, such as the picture 2-tuple linguistic MSM (2TLMSM) operator based on the ATT (ATT-P2TLMSM) and the picture 2-tuple linguistic generalized MSM (2TLGMSM) operator based on ATT (ATT-P2TLGMSM). Considering that the input parameters have different importance, we proposed picture 2-tuple linguistic weighted MSM (2TLWMSM) operators based on ATT (ATT-P2TLWMSM) and picture 2-tuple linguistic weighted generalized MSM (2TLWGMSM) operators based on ATT (ATT-P2TLWGMSM). Finally, a MADM method is introduced, and an expositive example is presented to explain the availability and applicability of the developed operators and methods.

Interval-Valued Dual Hesitant Fuzzy Heronian Mean Aggregation Operators and their Application to Multi-Attribute Decision Making

2018 ◽  
Vol 17 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Yuqi Zang ◽  
Xiaodong Zhao ◽  
Shiyong Li
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Aggregation Operators ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
New Approach ◽  
Dual Hesitant Fuzzy Set ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Heronian Mean

The interval-valued dual hesitant fuzzy set (IVDHFS) can depict the imprecise, vague and indeterminate information and Heronian mean (HM) has the prominent characteristic of capturing the correlation of the aggregated arguments. In this paper, we investigate multi-attribute decision making (MADM) problems based on HM, in which the attribute values are assumed in the form of interval-valued dual hesitant fuzzy information. Firstly, we briefly present some concepts of IVDHFS and HM. Then, we propose the interval-valued dual hesitant fuzzy Heronian mean (IVDHFHM) operator and the interval-valued dual hesitant fuzzy geometric Heronian mean (IVDHFGHM) operator. We also prove that they satisfy some desirable properties. Further, we consider the importance of the input arguments and derive the interval-valued dual hesitant fuzzy weighted Heronian mean (IVDHFWHM) operator and the interval-valued dual hesitant fuzzy weighted geometric Heronian mean (IVDHFWGHM) operator, and then develop the procedure of MADM. Finally, an illustrate example is given to demonstrate the practicality and effectiveness of the new approach.

Graded Soft Expert Set as a Generalization of Hesitant Fuzzy Set

2018 ◽  
Vol 29 (1) ◽  
pp. 223-236
Author(s):  
Afshan Qayyum ◽  
Tanzeela Shaheen
Keyword(s):  
Decision Making ◽  
Decision Analysis ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Vital Role ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Relative Importance ◽  
Hesitant Fuzzy Sets

Abstract Hesitant fuzzy sets play a vital role in decision analysis. Although they have been proved to be a landmark in evaluating information, there are certain deficiencies in their structure. Also, in decision analysis with the aid of hesitant fuzzy sets, the relative importance of the decision makers according to their area of expertise is ignored completely, which may be misleading in some situations. These sorts of issues have been resolved in this work by using graded soft expert (GSE) sets. The proposed structure is a modified form of soft expert sets. Some basic operations have been introduced, and certain laws satisfied by them have carefully been investigated. With the aid of GSE sets, a decision-making algorithm (accompanied with an example) has been developed in which experts have been given due weightage according to their area of expertise.

Research on hesitant fuzzy clustering method based on fuzzy matroids

2021 ◽  
pp. 1-9
Author(s):  
Hui-Min Xiao ◽  
Mei-Qi Wang ◽  
Yan-Li Cao ◽  
Yu-Jie Guo
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Clustering Algorithm ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Job Seekers ◽  
Clustering Method ◽  
Fuzzy Clustering Method ◽  
Cut Set ◽  
R Value

In this paper, to improve the situation of singleness of selecting results in hesitant fuzzy set decision-making and expand the range of choices for decision makers, we construct a hesitant fuzzy set clustering algorithm combined with fuzzy matroid operation. The algorithm synthesizes the r-cut set, fuzzy shrinking matroids in the fuzzy matroids and the operational properties of the fuzzy derived matroids, the r value also is used to connect the two types of fuzzy matroids to form a clustering algorithm. Finally, we apply the algorithm to the hesitant fuzzy set decision-making of job seekers choosing recruitment websites, each recruitment website as an optional scheme is divided into three categories of excellent to inferior schemes to provide job seekers with ideas and methods for favorably selecting recruitment websites.

scholarly journals Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 593 ◽  
Author(s):  
Hongran Zhang ◽  
Runtong Zhang ◽  
Huiqun Huang ◽  
Jun Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operators ◽  
Fuzzy Decision Making ◽  
Good Ability ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Heronian Mean

As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy decision-making environment. Hence, in this paper our main work is to introduce novel picture fuzzy aggregation operators. Firstly, we propose new picture fuzzy operational rules based on Dombi t-conorm and t-norm (DTT). Secondly, considering the existence of a broad and widespread correlation between attributes, we use Heronian mean (HM) information aggregation technology to fuse picture fuzzy numbers (PFNs) and propose new picture fuzzy aggregation operators. The proposed operators not only fuse individual attribute values, but also have a good ability to model the widespread correlation among attributes, making them more suitable for effectively solving increasingly complicated MADM problems. Hence, we introduce a new algorithm to handle MADM based on the proposed operators. Finally, we apply the newly developed method and algorithm in a supplier selection issue. The main novelties of this work are three-fold. Firstly, new operational laws for PFSs are proposed. Secondly, novel picture fuzzy aggregation operators are developed. Thirdly, a new approach for picture fuzzy MADM is proposed.

scholarly journals Cubic q-Rung Orthopair Fuzzy Heronian Mean Operators and Their Applications to Multi-Attribute Group Decision Making

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1125
Author(s):  
Baosheng Zhang ◽  
Tahir Mahmood ◽  
Jabbar Ahmmad ◽  
Qaisar Khan ◽  
Zeeshan Ali ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Decision Makers ◽  
The Given ◽  
Interval Valued ◽  
Heronian Mean ◽  
Selection Of

The cubic q-rung orthopair fuzzy set (Cq-ROFS) contains much more information to determine the interval valued q-rung orthopair fuzzy sets (IVq-ROFSs) and q-rung orthopair fuzzy sets (q-ROFSs) simultaneously for coping with the vagueness in information. It provides more space for decision makers (DMs) to describe their opinion in the environment of fuzzy set (FS) theory. In this paper, firstly, we introduce the conception of Cq-ROFS and their characteristics. Further, the Heronian mean (HM) operator based on Cq-ROFS, called the weighted HM operator, are explored. To overcome the deficiency of HM operator and keeping in mind the partitioned structure in real decision situations, we offer Cubic q-rung orthopair fuzzy partitioned HM operator and its weighted shape. An algorithm of the proposed operators based on multi-attribute group decision making (MAGDM) problems for the selection of best alternative among the given ones is established. Lastly, we provide an example to depict the authenticity and advantages of the exposed methods by contrasting with other existing drawbacks.

scholarly journals Fuzzy Multi-Criteria Decision Making Algorithm under Intuitionistic Hesitant Fuzzy Set with Novel Distance Measure

2020 ◽  
Vol 5 (3) ◽  
pp. 473-487 ◽  
Author(s):  
Rupjit Saikia ◽  
Harish Garg ◽  
Palash Dutta
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Decision Makers ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Crucial Issue ◽  
Decision Making Problem

Decision making under uncertainty is a crucial issue and most demanding area of research now a days. Intuitionistic hesitant fuzzy set plays important role in dealing with the circumstances in which decision makers judge an alternative with a collection membership grades and a collection of non-membership grades. This paper contributes a novel and advanced distance measure between Intuitionistic Hesitant fuzzy sets (IHFSs). A comparative analysis of the present distance measure with existing measures is performed first. Afterwards, a case study is carried in multi-criteria decision making problem to exhibit the applicability and rationality of the proposed distance measure. The advantage of the proposed distance measure over the existing distance measures is that in case of deficit number of elements in IHFs, a decision maker can evaluate distance measure without adding extra elements to make them equivalent and furthermore, it works in successfully in all the situations.

scholarly journals Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 419 ◽  
Author(s):  
Songtao Shao ◽  
Xiaohong Zhang ◽  
Yu Li ◽  
Chunxin Bo
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Comparison Method ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Probability Interval ◽  
New Approach ◽  
Main Research ◽  
Multi Attribute Decision Making ◽  
Special Case

The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced. By definition, we know that the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) is a special case of the probabilistic interval neutrosophic hesitant fuzzy set (PINHFS). PSVNHFSs can satisfy all the properties of PINHFSs. An example is given to illustrate that PINHFS compared to PSVNHFS is more general. Then, PINHFS is the main research object. The basic operational relations of PINHFS are studied, and the comparison method of probabilistic interval neutrosophic hesitant fuzzy numbers (PINHFNs) is proposed. Then, the probabilistic interval neutrosophic hesitant fuzzy weighted averaging (PINHFWA) and the probability interval neutrosophic hesitant fuzzy weighted geometric (PINHFWG) operators are presented. Some basic properties are investigated. Next, based on the PINHFWA and PINHFWG operators, a decision-making method under a probabilistic interval neutrosophic hesitant fuzzy circumstance is established. Finally, we apply this method to the issue of investment options. The validity and application of the new approach is demonstrated.

scholarly journals Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 344 ◽  
Author(s):  
Tang ◽  
Wang ◽  
Lu ◽  
Wei ◽  
Wei ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multiple Attribute Decision Making ◽  
Decision Makers ◽  
Pythagorean Fuzzy Set ◽  
Multiple Attribute ◽  
Pythagorean Fuzzy Numbers ◽  
Evaluation Information ◽  
Heronian Mean ◽  
Real Multiple

On account of the indeterminacy and subjectivity of decision makers (DMs) in complexity decision-making environments, the evaluation information over alternatives presented by DMs is usually fuzzy and ambiguous. As the generalization of intuitionistic fuzzy sets (IFSs), the Pythagorean fuzzy set (PFS) is more useful in expressing fuzzy and ambiguous information. Meanwhile, in order to consider human hesitance, dual hesitant Pythagorean fuzzy sets (DHPFSs) are presented, which can be more valid for handling real multiple attribute decision-making (MADM) problems. To fuse the information in DHPFSs more effectively, in this article, some dual hesitant Pythagorean fuzzy Heronian mean operators, which can consider the relationships between arguments being fused, are defined and studied. Evidently, the new proposed operators can obtain more exact results than other existing methods. In addition, some important properties of these Heronian mean (HM) operators are discussed. Subsequently, the defined aggregation operators are used in MADM with dual hesitant Pythagorean fuzzy numbers (DHPFNs), and the MADM model is developed. In accordance with the defined operators and the built model, the dual hesitant Pythagorean fuzzy generalized weighted Heronian mean (DHPFGWHM) operator and dual hesitant Pythagorean fuzzy generalized geometric weighted Heronian mean (DHPFGGWHM) operator are applied to deal with the green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing them with some existing approaches. The method presented in this paper can effectively solve the MADM problems in which the decision-making information is expressed by DHPFNs and the attributes are interactive.

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