scholarly journals Some T-Spherical Fuzzy Einstein Interactive Aggregation Operators and Their Application to Selection of Photovoltaic Cells

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Shouzhen Zeng ◽  
Muhammad Munir ◽  
Tahir Mahmood ◽  
Muhammad Naeem
Keyword(s):  
Fuzzy Set ◽  
Photovoltaic Cells ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Selection Of

In this article, it is pointed out that the existing intuitionistic fuzzy and T-spherical fuzzy Einstein averaging and geometric operators have some limitations. To overcome these limitations, we proposed some new averaging and geometric operators in the T-spherical fuzzy environment instead of the intuitionistic fuzzy environment because the T-spherical fuzzy set is the most generalized form and the proposed operators can be particularized to the intuitionistic fuzzy environment. First, new operational laws for T-spherical fuzzy information are defined, on the basis of which Einstein geometric interaction operators and Einstein averaging interactive aggregation operators are then proposed. Some basic properties and advantages of proposed aggregation operators are also discussed. Moreover, the proposed operators are applied to the MADM problem to check their reliability. The superiority of the proposed operators over existing work is checked with the help of an example.

scholarly journals A Novel Multiple Attribute Satisfaction Evaluation Approach with Hesitant Intuitionistic Linguistic Fuzzy Information

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Shanghong Yang ◽  
Zhuo Sun ◽  
Yanbing Ju ◽  
Chengya Qiao
Keyword(s):  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Evaluation Approach ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Satisfaction Evaluation ◽  
Attribute Satisfaction

This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic linguistic fuzzy element (HILFE). Firstly, motivated by the idea of intuitionistic linguistic variables (ILVs) and hesitant fuzzy elements (HFEs), the concept, operational laws, and comparison laws of HILFE are defined. Then, some aggregation operators are developed for aggregating the hesitant intuitionistic linguistic fuzzy information, such as hesitant intuitionistic linguistic fuzzy weighted aggregation operators, hesitant intuitionistic linguistic fuzzy ordered weighted aggregation operators, and generalized hesitant intuitionistic linguistic fuzzy weighted aggregation operators. Moreover, some desirable properties of these operators and the relationships between them are discussed. Based on the hesitant intuitionistic linguistic fuzzy weighted average (HILFWA) operator and the hesitant intuitionistic linguistic fuzzy weighted geometric (HILFWG) operator, an approach for evaluating satisfaction degree is proposed under hesitant intuitionistic linguistic fuzzy environment. Finally, a practical example of satisfaction evaluation for milk products is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.

scholarly journals Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 218 ◽  
Author(s):  
Jinming Zhou ◽  
Tomas Baležentis ◽  
Dalia Streimikiene
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Real Life ◽  
Aggregation Operators ◽  
Harmonic Mean ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Selection Of

In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator.

scholarly journals Archimedean Copula-Based Hesitant Fuzzy Information Aggregation Operators for Multiple Attribute Decision Making

2020 ◽  
Vol 2020 ◽  
pp. 1-21 ◽  
Author(s):  
Ju Wu ◽  
Lianming Mou ◽  
Fang Liu ◽  
Haobin Liu ◽  
Yi Liu
Keyword(s):  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Archimedean Copula ◽  
Fuzzy Information ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Special Cases ◽  
Effective Use

In view of the good properties of copulas and their effective use in various fuzzy environments, the goal of the current study is to develop a series of aggregation operators for hesitant fuzzy information based on Archimedean copula and cocopula, which are applied to the MADM problems. Firstly, operational laws of hesitant fuzzy elements on the basis of copulas and cocopulas are defined which can show the relevance between hesitant fuzzy values. Secondly, four aggregation operators (AC-HFWA, AC-GHFWA, AC-HFWG, and AC-GHFWG) under hesitant fuzzy environment are developed according to the proposed operational laws. The properties of these operators are also studied in detail, including idempotence, monotonicity, boundedness, etc. Subsequently, five special cases of copula are also given and the special forms of aggregation operator are obtained. In the end, an example is used to illustrate the application of the proposed approach in MADM problems. The influences of different generated functions and parameters are shown, and the feasibility of the proposed method is validated through comparative analyses.

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.

Hesitant Trapezoid Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making

2020 ◽  
Vol 8 (6) ◽  
pp. 524-548
Author(s):  
Qian Yu ◽  
Jun Cao ◽  
Ling Tan ◽  
Yubing Zhai ◽  
Jiongyan Liu
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Definition Of

Abstract In this paper, we investigate the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant trapezoid fuzzy information. Firstly, inspired by the idea of hesitant fuzzy sets and trapezoid fuzzy numbers, the definition of hesitant trapezoid fuzzy set and some operational laws of hesitant trapezoid fuzzy elements are proposed. Then some hesitant trapezoid fuzzy aggregation operators based on Hamacher operation are developed, such as the hesitant trapezoid fuzzy Hamacher weighted average (HTrFHWA) operator, the hesitant trapezoid fuzzy Hamacher weighted geometric (HTrFHWG) operator, the hesitant trapezoid fuzzy Hamacher Choquet average (HTrFHCA), the hesitant trapezoid fuzzy Hamacher Choquet geometric (HTrFHCG), etc. Furthermore, an approach based on the hesitant trapezoid fuzzy Hamacher weighted average (HTrFHWA) operator and the hesitant trapezoid fuzzy Hamacher weighted geometric (HTrFHWG) operator is proposed for MADM problems under hesitant trapezoid fuzzy environment. Finally, a numerical example for supplier selection is given to illustrate the application of the proposed approach.

scholarly journals Redefined “Maclaurin Symmetric Mean Aggregation Operators Based on Cubic Pythagorean Linguistic Fuzzy Numbers”

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Muhammad Naeem ◽  
Shahzaib Ashraf ◽  
Saleem Abdullah ◽  
F. M. AL‐Harbi
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Pythagorean Fuzzy Set ◽  
Numerical Application ◽  
Operational Laws ◽  
Maclaurin Symmetric Mean ◽  
Definition Of ◽  
Improved Algorithm

In this study, we highlight the errors in Sections 2.3, 2.4, 3, and 4 in the article by Fahmi et al. (J Ambient Intell Human Comput (2020). https://doi.org/10.1007/s12652-020-02272-9) by counter definitions and theorems. We find that the definition of cubic Pythagorean fuzzy set (CPFS) (Definition 2.3.1) and operational laws (Definition 2.3.2) violates the rules to consider the membership and nonmembership functions, and then, we redefined the corrected definition and their operations for CPFS. Furthermore, we redefine the concept of cubic Pythagorean linguistic fuzzy set (CPLFS) and their basic operational laws. In addition, we find that Sections 3 and 4 (consist of a list of Maclaurin symmetric mean (MSM) and dual MSM aggregation operators) are invalid, and then, we redefined the list of updated MSM and dual MSM aggregation operators in correct way. Finally, we established the numerical application of the proposed improved algorithm using cubic Pythagorean linguistic fuzzy information to show the applicability and effectiveness of the proposed technique.

scholarly journals AN APPROACH TO MULTIPLE ATTRIBUTE DECISION MAKING BASED ON THE INDUCED CHOQUET INTEGRAL WITH FUZZY NUMBER INTUITIONISTIC FUZZY INFORMATION

2014 ◽  
Vol 15 (2) ◽  
pp. 277-298 ◽  
Author(s):  
Guiwu Wei ◽  
Rui Lin ◽  
Xiaofei Zhao ◽  
Hongjun Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Choquet Integral ◽  
Score Function ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Multiple Attribute

In this paper, we investigate the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. Firstly, some operational laws of fuzzy number intuitionistic fuzzy values, score function and accuracy function of fuzzy number intuitionistic fuzzy values are introduced. Then, we have developed two fuzzy number intuitionistic fuzzy Choquet integral aggregation operators: induced fuzzy number intuitionistic fuzzy choquet ordered averaging (IFNIFCOA) operator and induced fuzzy number intuitionistic fuzzy choquet ordered geometric (IFNIFCOG) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have studied some desirable properties of the IFNIFCOA and IFNIFCOG operators, such as commutativity, idempotency and monotonicity, and applied the IFNIFCOA and IFNIFCOGM operators to multiple attribute decision making with fuzzy number intuitionistic fuzzy information. Finally an illustrative example has been given to show the developed method.

scholarly journals Interval-Valued Intuitionistic Hesitant Fuzzy Aggregation Operators and Their Application in Group Decision-Making

2013 ◽  
Vol 2013 ◽  
pp. 1-33 ◽  
Author(s):  
Zhiming Zhang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Aggregation Operators ◽  
Hesitant Fuzzy Set ◽  
Mathematical Tool ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Hesitant fuzzy sets, permitting the membership of an element to be a set of several possible values, can be used as an efficient mathematical tool for modelling people’s hesitancy in daily life. In this paper, we extend the hesitant fuzzy set to interval-valued intuitionistic fuzzy environments and propose the concept of interval-valued intuitionistic hesitant fuzzy set, which allows the membership of an element to be a set of several possible interval-valued intuitionistic fuzzy numbers. The aim of this paper is to develop a series of aggregation operators for interval-valued intuitionistic hesitant fuzzy information. Then, some desired properties of the developed operators are studied, and the relationships among these operators are discussed. Furthermore, we apply these aggregation operators to develop an approach to multiple attribute group decision-making with interval-valued intuitionistic hesitant fuzzy information. Finally, a numerical example is provided to illustrate the application of the developed approach.

Some improved pythagorean fuzzy Dombi power aggregation operators with application in multiple-attribute decision making

2021 ◽  
pp. 1-21
Author(s):  
Peide Liu ◽  
Qaisar Khan ◽  
Tahir Mahmood ◽  
Rashid Ali Khan ◽  
Hidayat Ullah Khan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Pythagorean Fuzzy Set ◽  
Operational Laws ◽  
Multiple Attribute ◽  
General Parameter ◽  
Pythagorean Fuzzy Numbers

Pythagorean fuzzy set (PyFS) is an extension of various fuzzy concepts, such as fuzzy set (FS), intuitionistic FS, and it is enhanced mathematical gizmo to pact with uncertain and vague information. In this article, some drawbacks in the Dombi operational rules for Pythagorean fuzzy numbers (PyFNs) are examined and some improved Dombi operational laws for PyFNs are developed. We also find out that the value aggregated using the existing Dombi aggregation operators (DAOs) is not a PyFN. Furthermore, we developed two new aggregations, improved existing aggregation operators (AOs) for aggregating Pythagorean fuzzy information (PyFI) and are applied to multiple-attribute decision making (MADM). To acquire full advantage of power average (PA) operators proposed by Yager, the Pythagorean fuzzy Dombi power average (PyFDPA) operator, the Pythagorean fuzzy Dombi weighted power average (PyFDWPA) operator, Pythagorean fuzzy Dombi power geometric (PyFDPG) operator, Pythagorean fuzzy Dombi weighted geometric (PyFDPWG) operator, improved the existing AOs and their desirable properties are discussed. The foremost qualities of these developed Dombi power aggregation operators is that they purge the cause of discomfited data and are more supple due to general parameter. Additionally, based on these Dombi power AOs, a novel MADM approach is instituted. Finally, a numerical example is given to show the realism and efficacy of the proposed approach and judgment with the existing approaches is also specified.

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