Prioritized weighted aggregation operators under complex pythagorean fuzzy information

2020 ◽  
Vol 39 (3) ◽  
pp. 4763-4783
Author(s):  
Muhammad Akram ◽  
Xindong Peng ◽  
Ahmad N. Al-Kenani ◽  
Aqsa Sattar
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Two Dimensional ◽  
Fuzzy Information ◽  
Pythagorean Fuzzy Set ◽  
Priority Level ◽  
Prioritized Aggregation Operators

Complex Pythagorean fuzzy (CPF), a worthwhile generalization of Pythagorean fuzzy set, is a powerful tool to deal with two-dimensional or periodic information. In this paper, we develop two prioritized aggregation operators (AOs) under CPF environment, namely, complex Pythagorean fuzzy prioritized weighted averaging (CPFPWA) operator and complex Pythagorean fuzzy prioritized weighted geometric (CPFPWG) operator. We consider the prioritization relationship among criteria and decision makers (DMs) to make our result more accurate as in real decision making (DM) problems, the criteria and DMs have different priority level. Further, we discuss remarkable properties of our proposed AOs. Moreover, we promote the evolution of MCDM problem by investigating an algorithm in CPF environment with its flow chart. Finally, to check the superiority and validity of proposed operators, we compare the computed results with the different existing techniques.

Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

2018 ◽  
Vol 29 (1) ◽  
pp. 393-408 ◽  
Author(s):  
Khaista Rahman ◽  
Saleem Abdullah ◽  
Muhammad Sajjad Ali Khan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Interval Valued

Abstract In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.

Protraction of Einstein operators for decision-making under q-rung orthopair fuzzy model

2020 ◽  
pp. 1-20
Author(s):  
Muhammad Akram ◽  
Gulfam Shahzadi ◽  
Sundas Shahzadi
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Fuzzy Model ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Pythagorean Fuzzy Set ◽  
Career Selection ◽  
Ordered Weighted Averaging ◽  
Multi Attribute Decision Making

An q-rung orthopair fuzzy set is a generalized structure that covers the modern extensions of fuzzy set, including intuitionistic fuzzy set and Pythagorean fuzzy set, with an adjustable parameter q that makes it flexible and adaptable to describe the inexact information in decision making. The condition of q-rung orthopair fuzzy set, i.e., sum of q th power of membership degree and nonmembership degree is bounded by one, makes it highly competent and adequate to get over the limitations of existing models. The basic purpose of this study is to establish some aggregation operators under the q-rung orthopair fuzzy environment with Einstein norm operations. Motivated by innovative features of Einstein operators and dominant behavior of q-rung orthopair fuzzy set, some new aggregation operators, namely, q-rung orthopair fuzzy Einstein weighted averaging, q-rung orthopair fuzzy Einstein ordered weighted averaging, generalized q-rung orthopair fuzzy Einstein weighted averaging and generalized q-rung orthopair fuzzy Einstein ordered weighted averaging operators are defined. Furthermore, some properties related to proposed operators are presented. Moreover, multi-attribute decision making problems related to career selection, agriculture land selection and residential place selection are presented under these operators to show the capability and proficiency of this new idea. The comparison analysis with existing theories shows the superiorities of proposed model.

Extensions of prioritized weighted aggregation operators for decision-making under complex q-rung orthopair fuzzy information

2020 ◽  
Vol 39 (5) ◽  
pp. 7469-7493 ◽  
Author(s):  
Peide Liu ◽  
Muhammad Akram ◽  
Aqsa Sattar
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Weighted Averaging ◽  
Human Judgment ◽  
Pythagorean Fuzzy Set ◽  
Priority Level ◽  
Special Cases ◽  
Complex Intuitionistic Fuzzy Set ◽  
A New Technique

The complex q-rung orthopair fuzzy set (Cq-ROFS), an efficient generalization of complex intuitionistic fuzzy set (CIFS) and complex Pythagorean fuzzy set (CPFS), is potent tool to handle the two-dimensional information and has larger ability to translate the more uncertainty of human judgment then CPFS as it relaxes the constrains of CPFS and thus the space of allowable orthopair increases. To solve the multi-criteria decision making (MCDM) problem by considering that criteria are at the same priority level may affect the results because in realistic situations the priority level of criteria is different. In this manuscript, we propose some useful prioritized AOs under Cq-ROF environment by considering the prioritization among attributes. We develop two prioritized AOs, namely complex q-rung orthropair fuzzy prioritized weighted averaging (C-qROFPWA) operator and complex q-rung orthropair fuzzy prioritized weighted geometric (Cq-ROFPWG) operator. We also consider their desirable properties and two special cases with their detailed proofs. Moreover, we investigate a new technique to solve the MCDM problem by initiating an algorithm along with flowchart on the bases of proposed operators. Further, we solve a practical example to reveal the importance of proposed AOs. Finally, we apply the existing operators on the same data to compare our computed result to check the superiority and validity of our proposed operators.

scholarly journals Linear Diophantine Fuzzy Einstein Aggregation Operators for Multi-Criteria Decision-Making Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Aiyared Iampan ◽  
Gustavo Santos García ◽  
Muhammad Riaz ◽  
Hafiz Muhammad Athar Farid ◽  
Ronnason Chinram
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Cerebrovascular Diseases ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Uncertain Information ◽  
Health Administration ◽  
Pythagorean Fuzzy Set

The linear Diophantine fuzzy set (LDFS) has been proved to be an efficient tool in expressing decision maker (DM) evaluation values in multicriteria decision-making (MCDM) procedure. To more effectively represent DMs’ evaluation information in complicated MCDM process, this paper proposes a MCDM method based on proposed novel aggregation operators (AOs) under linear Diophantine fuzzy set (LDFS). A q -Rung orthopair fuzzy set ( q -ROFS), Pythagorean fuzzy set (PFS), and intuitionistic fuzzy set (IFS) are rudimentary concepts in computational intelligence, which have diverse applications in modeling uncertainty and MCDM. Unfortunately, these theories have their own limitations related to the membership and nonmembership grades. The linear Diophantine fuzzy set (LDFS) is a new approach towards uncertainty which has the ability to relax the strict constraints of IFS, PFS, and q –ROFS by considering reference/control parameters. LDFS provides an appropriate way to the decision experts (DEs) in order to deal with vague and uncertain information in a comprehensive way. Under these environments, we introduce several AOs named as linear Diophantine fuzzy Einstein weighted averaging (LDFEWA) operator, linear Diophantine fuzzy Einstein ordered weighted averaging (LDFEOWA) operator, linear Diophantine fuzzy Einstein weighted geometric (LDFEWG) operator, and linear Diophantine fuzzy Einstein ordered weighted geometric (LDFEOWG) operator. We investigate certain characteristics and operational laws with some illustrations. Ultimately, an innovative approach for MCDM under the linear Diophantine fuzzy information is examined by implementing suggested aggregation operators. A useful example related to a country’s national health administration (NHA) to create a fully developed postacute care (PAC) model network for the health recovery of patients suffering from cerebrovascular diseases (CVDs) is exhibited to specify the practicability and efficacy of the intended approach.

scholarly journals Hamacher Interactive Hybrid Weighted Averaging Operators under Fermatean Fuzzy Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Gulfam Shahzadi ◽  
G. Muhiuddin ◽  
Muhammad Arif Butt ◽  
Ather Ashraf
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Pythagorean Fuzzy Set ◽  
Averaging Operators ◽  
Research Article ◽  
Individual Evaluation ◽  
The Given

A Fermatean fuzzy set is a more powerful tool to deal with uncertainties in the given information as compared to intuitionistic fuzzy set and Pythagorean fuzzy set and has energetic applications in decision-making. Aggregation operators are very helpful for assessing the given alternatives in the decision-making process, and their purpose is to integrate all the given individual evaluation values into a unified form. In this research article, some new aggregation operators are proposed under the Fermatean fuzzy set environment. Some deficiencies of the existing operators are discussed, and then, new operational law, by considering the interaction between the membership degree and nonmembership degree, is discussed to reduce the drawbacks of existing theories. Based on Hamacher’s norm operations, new averaging operators, namely, Fermatean fuzzy Hamacher interactive weighted averaging, Fermatean fuzzy Hamacher interactive ordered weighted averaging, and Fermatean fuzzy Hamacher interactive hybrid weighted averaging operators, are introduced. Some interesting properties related to these operators are also presented. To get the optimal alternative, a multiattribute group decision-making method has been given under proposed operators. Furthermore, we have explicated the comparison analysis between the proposed and existing theories for the exactness and validity of the proposed work.

scholarly journals Some Improved q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications to Multiattribute Group Decision-Making

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Lei Xu ◽  
Yi Liu ◽  
Haobin Liu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Pythagorean Fuzzy Set ◽  
Fuzzy Aggregation

As a generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), q-rung orthopair fuzzy set (q-ROFS) is a new concept in describing complex fuzzy uncertainty information. The present work focuses on the multiattribute group decision-making (MAGDM) approach under the q-rung orthopair fuzzy information. To begin with, some drawbacks of the existing MAGDM methods based on aggregation operators (AOs) are firstly analyzed. In addition, some improved operational laws put forward to overcome the drawbacks along with some properties of the operational law are proved. Thirdly, we put forward the improved q-rung orthopair fuzzy-weighted averaging (q-IROFWA) aggregation operator and improved q-rung orthopair fuzzy-weighted power averaging (q-IROFWPA) aggregation operator and present some of their properties. Then, based on the q-IROFWA operator and q-IROFWPA operator, we proposed a new method to deal with MAGDM problems under the fuzzy environment. Finally, some numerical examples are provided to illustrate the feasibility and validity of the proposed method.

scholarly journals A Novel Approach to MADM Problems Using Fermatean Fuzzy Hamacher Prioritized Aggregation Operators

2021 ◽  
Author(s):  
Asmatullah Jan ◽  
Asghar Khan ◽  
Waqar Khan ◽  
Minhaj Afridi
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operators ◽  
Pythagorean Fuzzy Set ◽  
Novel Approach ◽  
Special Cases ◽  
Cognitive Information ◽  
Prioritized Aggregation Operators ◽  
Working Parameter

Abstract A generalized form of union and intersection on FFS can be formulated from a generalized t-norm (TN) and t-conorm (TCN). Hamacher operations such as Hamacher product and Hamacher sum, are good alternatives to produce such product and sum. The Hamacher operations can generate more flexible and more accurate results in decision making process due to the working parameter involved in these operations. The intuitionistic fuzzy set, brifely as; IFS and its extension involving Pythagorean fuzzy set (PFS) and Fermatean fuzzy set (FFS), are all effective tools to express uncertain and incomplete cognitive information with membership, nonmembership and hesitancy degrees. The Fermatean fuzzy set (FF-set) carries out uncertain and imprecise information smartly in exercising decision-making than IFS and PFS. By adjusting the prioritization of attributes in FF-environment, in this course of this article, we first device new operations on FF information using prioritized attributes and by employing HTN and HTCN, we discuss the basic operations. Induced by the Hamacher operations and FF-set, we propose FF Hamacher arithmetic and also geometric aggregation operators (AOs). In the first section, we introduce the concepts of an FF Hamacher prioritized AO, and FF Hamacher prioritized weighted AO. In the second part, we develop FF Hamacher prioritized geometric operator (GO), and FF Hamacher prioritized weighted GO. We study essential properties and a few special cases of our newly proposed operators. Then, we make use of these proposed operators in developing tools which are key factors in solving the FF multi-attribute decision-making situations with prioritization. The university selection phenomena is considered as a direct application for analysis and to demonstrate the practicality and efficacy of our proposed model. The working parameter considered in these AOs is analyzed in different existing and proposed AOs. Further, comparison analysis is conducted for the authenticity of proposed & existing operators.

scholarly journals Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 594 ◽  
Author(s):  
Mi Jung Son ◽  
Jin Han Park ◽  
Ka Hyun Ko
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
New Approach ◽  
Multiple Attribute

As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.

scholarly journals Decision-Making Based on q-Rung Orthopair Fuzzy Soft Rough Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Yinyu Wang ◽  
Azmat Hussain ◽  
Tahir Mahmood ◽  
Muhammad Irfan Ali ◽  
Hecheng Wu ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Significant Feature ◽  
Pythagorean Fuzzy Set ◽  
Hybrid Concept ◽  
Significant Generalization

Recently, Yager presented the new concept of q-rung orthopair fuzzy (q-ROF) set (q-ROFS) which emerged as the most significant generalization of Pythagorean fuzzy set (PFS). From the analysis of q-ROFS, it is clear that the rung q is the most significant feature of this notion. When the rung q increases, the orthopair adjusts in the boundary range which is needed. Thus, the input range of q-ROFS is more flexible, resilient, and suitable than the intuitionistic fuzzy set (IFS) and PFS. The aim of this manuscript is to investigate the hybrid concept of soft set ( S t S) and rough set with the notion of q-ROFS to obtain the new notion of q-ROF soft rough (q-ROF S t R) set (q-ROF S t RS). In addition, some averaging aggregation operators such as q-ROF S t R weighted averaging (q-ROF S t RWA), q-ROF S t R ordered weighted averaging (q-ROF S t ROWA), and q-ROF S t R hybrid averaging (q-ROF S t RHA) operators are presented. Then, the basic desirable properties of these investigated averaging operators are discussed in detail. Moreover, we investigated the geometric aggregation operators, such as q-ROF S t R weighted geometric (q-ROF S t RWG), q-ROF S t R ordered weighted geometric (q-ROF S t ROWG), and q-ROF S t R hybrid geometric (q-ROF S t RHG) operators, and proposed the basic desirable characteristics of the investigated geometric operators. The technique for multicriteria decision-making (MCDM) and the stepwise algorithm for decision-making by utilizing the proposed approaches are demonstrated clearly. Finally, a numerical example for the developed approach is presented and a comparative study of the investigated models with some existing methods is brought to light in detail which shows that the initiated models are more effective and useful than the existing methodologies.

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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