scholarly journals Picture Hesitant Fuzzy Set and Its Application to Multiple Criteria Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 295 ◽  
Author(s):  
Rui Wang ◽  
Yanlai Li
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Real Life ◽  
Multiple Criteria Decision Making ◽  
Service Selection ◽  
Aggregation Operators ◽  
Multiple Criteria ◽  
Hesitant Fuzzy Set ◽  
Web Service Selection ◽  
Picture Fuzzy Set

To address the complex multiple criteria decision-making (MCDM) problems in practice, this article proposes the picture hesitant fuzzy set (PHFS) theory based on the picture fuzzy set and the hesitant fuzzy set. First, the concept of PHFS is put forward, and its operations are presented, simultaneously. Second, the generalized picture hesitant fuzzy weighted aggregation operators are developed, and some theorems and reduced operators of them are discussed. Third, the generalized picture hesitant fuzzy prioritized weighted aggregation operators are put forward to solve the MCDM problems that the related criteria are at different priorities. Fourth, two novel MCDM methods combined with the proposed operators are constructed to determine the best alternative in real life. Finally, two numerical examples and an application of web service selection are investigated to illustrate the effectiveness of the proposed methods. The sensitivity analysis shows that the different values of the parameter λ affect the ranking of alternatives, and the proposed operators are compared with several existing MCDM methods to illustrate their advantages.

scholarly journals Interval Valued T-Spherical Fuzzy Soft Average Aggregation Operators and Their Applications in Multiple-Criteria Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 829
Author(s):  
Tahir Mahmood ◽  
Jabbar Ahmmad ◽  
Zeeshan Ali ◽  
Dragan Pamucar ◽  
Dragan Marinkovic
Keyword(s):  
Decision Making ◽  
Asymmetric Information ◽  
Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Multiple Criteria ◽  
Soft Set ◽  
Operator Interval ◽  
Interval Valued

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. Multiple-criteria decision making (MCDM) is a very effective and well-known tool to investigate fuzzy information more effectively. However, the selection of houses cannot be done by utilizing symmetry information, because enterprises do not have complete information, so asymmetric information should be used when selecting enterprises. In this paper, the notion of soft set (SftS) and interval-valued T-spherical fuzzy set (IVT-SFS) are combined to produce a new and more effective notion called interval-valued T-spherical fuzzy soft set (IVT-SFSftS). It is a more general concept and provides more space and options to decision makers (DMs) for making their decision in the field of fuzzy set theory. Moreover, some average aggregation operators like interval-valued T-spherical fuzzy soft weighted average (IVT-SFSftWA) operator, interval-valued T-spherical fuzzy soft ordered weighted average (IVT-SFSftOWA) operator, and interval-valued T-spherical fuzzy soft hybrid average (IVT-SFSftHA) operators are explored. Furthermore, the properties of these operators are discussed in detail. An algorithm is developed and an application example is proposed to show the validity of the present work. This manuscript shows how to make a decision when there is asymmetric information about an enterprise. Further, in comparative analysis, the established work is compared with another existing method to show the advantages of the present work.

scholarly journals A Single-Valued Extended Hesitant Fuzzy Score-Based Technique for Probabilistic Hesitant Fuzzy Multiple Criteria Decision-Making

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Bahram Farhadinia ◽  
Atefeh Taghavi
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Quantitative Assessment ◽  
Dimensional Space ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Splitting Algorithm ◽  
Score Functions

The probabilistic hesitant fuzzy set (PHFS) is a worthwhile extension of the hesitant fuzzy set (HFS) which allows people to improve their quantitative assessment with the corresponding probability. Recently, in order to address the issue of difficulty in aggregating decision makers’ opinions, a probability splitting algorithm has been developed that drives an efficient probabilistic-unification process of PHFSs. Adopting such a unification process allows decision makers to disregard the probability part in developing fruitful theories of comparison of PHFSs. By keeping this feature in mind, we try to introduce a class of score functions for the notion of the single-valued extended hesitant fuzzy set (SVEHFS) as a novel deformation of PHFS. Interestingly, a SVEHFS not only belongs to a less dimensional space compared to that of PHFSs but also the proposed SVEHFS-based score functions satisfy a number of interesting properties. Eventually, some case studies of multiple criteria decision-making (MCDM) techniques under the PHFS environment are provided to demonstrate the effectiveness of proposed SVEHFS-based score functions.

scholarly journals Complex T-spherical fuzzy Dombi aggregation operators and their applications in multiple-criteria decision-making

2021 ◽  
Author(s):  
Faruk Karaaslan ◽  
Mohammed Allaw Dawood Dawood
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Two Dimensional ◽  
Weighted Arithmetic ◽  
Mcdm Method ◽  
Dombi Operations

AbstractComplex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.

scholarly journals Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 280 ◽  
Author(s):  
Harish Garg ◽  
Gagandeep Kaur
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Weight Vector ◽  
Aggregation Operators ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Maximum Deviation ◽  
Dual Hesitant Fuzzy Set ◽  
Deviation Method

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

scholarly journals A Q-RUNG ORTHOPAIR FUZZY GLDS METHOD FOR INVESTMENT EVALUATION OF BE ANGEL CAPITAL IN CHINA

2020 ◽  
Vol 26 (1) ◽  
pp. 103-134 ◽  
Author(s):  
Huchang Liao ◽  
Hongrun Zhang ◽  
Cheng Zhang ◽  
Xingli Wu ◽  
Abbas Mardani ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Investment Evaluation ◽  
Dominance Score ◽  
Do So

As a generalized form of both intuitionistic fuzzy set and Pythagorean fuzzy sets, the q-rung orthopair fuzzy set (q-ROFS) has strong ability to handle uncertain or imprecision decisionmaking problems. This paper aims to introduce a new multiple criteria decision making method based on the original gain and lost dominance score (GLDS) method for investment evaluation. To do so, we first propose a new distance measure of q-rung orthopair fuzzy numbers (q-ROFNs), which takes into account the hesitancy degree of q-ROFNs. Subsequently, two methods are developed to determine the weights of DMs and criteria, respectively. Next, the original GLDS method is improved from the aspects of dominance flows and order scores of alternatives to address the multiple criteria decision making problems with q-ROFS information. Finally, a case study concerning the investment evaluation of the BE angle capital is given to illustrate the applicability and superiority of the proposed method.

scholarly journals Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 608 ◽  
Author(s):  
Saifullah Khan ◽  
Saleem Abdullah ◽  
Lazim Abdullah ◽  
Shahzaib Ashraf
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Vital Role ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making

The objective of this study was to create a logarithmic decision-making approach to deal with uncertainty in the form of a picture fuzzy set. Firstly, we define the logarithmic picture fuzzy number and define the basic operations. As a generalization of the sets, the picture fuzzy set provides a more profitable method to express the uncertainties in the data to deal with decision making problems. Picture fuzzy aggregation operators have a vital role in fuzzy decision-making problems. In this study, we propose a series of logarithmic aggregation operators: logarithmic picture fuzzy weighted averaging/geometric and logarithmic picture fuzzy ordered weighted averaging/geometric aggregation operators and characterized their desirable properties. Finally, a novel algorithm technique was developed to solve multi-attribute decision making (MADM) problems with picture fuzzy information. To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method, and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable.

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.

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