scholarly journals Multicriteria Decision-Making Approach for Aggregation Operators of Pythagorean Fuzzy Hypersoft Sets

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Imran Siddique ◽  
Rana Muhammad Zulqarnain ◽  
Rifaqat Ali ◽  
Fahd Jarad ◽  
Aiyared Iampan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Soft Set ◽  
Multicriteria Decision ◽  
Fundamental Properties ◽  
Operational Laws ◽  
Shift Invariance ◽  
Parameterized Family

The Pythagorean fuzzy hypersoft set (PFHSS) is the most advanced extension of the intuitionistic fuzzy hypersoft set (IFHSS) and a suitable extension of the Pythagorean fuzzy soft set. In it, we discuss the parameterized family that contracts with the multi-subattributes of the parameters. The PFHSS is used to correctly assess insufficiencies, anxiety, and hesitancy in decision-making (DM). It is the most substantial notion for relating fuzzy data in the DM procedure, which can accommodate more uncertainty compared to available techniques considering membership and nonmembership values of each subattribute of given parameters. In this paper, we will present the operational laws for Pythagorean fuzzy hypersoft numbers (PFHSNs) and also some fundamental properties such as idempotency, boundedness, shift-invariance, and homogeneity for Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators. Furthermore, a novel multicriteria decision-making (MCDM) approach has been established utilizing presented aggregation operators (AOs) to resolve decision-making complications. To validate the useability and pragmatism of the settled technique, a brief comparative analysis has been conducted with some existing approaches.

scholarly journals Multicriteria Decision-Making Approach for Pythagorean Fuzzy Hypersoft Sets’ Interaction Aggregation Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Rana Muhammad Zulqarnain ◽  
Imran Siddique ◽  
Rifaqat Ali ◽  
Fahd Jarad ◽  
Aiyared Iampan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Soft Sets ◽  
Multicriteria Decision ◽  
Fundamental Properties ◽  
Operational Laws ◽  
Fuzzy Soft Sets

In this paper, we examine the multicriteria decision-making (MCDM) difficulties for Pythagorean fuzzy hypersoft sets (PFHSSs). The PFHSSs are a suitable extension of the Pythagorean fuzzy soft sets (PFSSs) which deliberates the parametrization of multi-subattributes of considered parameters. It is a most substantial notion for describing fuzzy information in the decision-making (DM) procedure to accommodate more vagueness comparative to existing PFSSs and intuitionistic fuzzy hypersoft sets (IFHSSs). The core objective of this study is to plan some innovative operational laws considering the interaction for Pythagorean fuzzy hypersoft numbers (PFHSNs). Also, based on settled interaction operational laws, two aggregation operators (AOs) i.e., Pythagorean fuzzy hypersoft interaction weighted average (PFHSIWA) and Pythagorean fuzzy hypersoft interaction weighted geometric (PFHSIWG) operators for PFHSSs operators have been presented with their fundamental properties. Furthermore, an MCDM technique has been established using planned interaction AOs. To ensure the strength and practicality of the developed MCDM method, a mathematical illustration has been presented. The usefulness, influence, and versatility of the developed method have been demonstrated via comparative analysis with the help of some conventional studies.

scholarly journals Robust Aggregation Operators for Intuitionistic Fuzzy Hypersoft Set With Their Application to Solve MCDM Problem

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 688
Author(s):  
Rana Muhammad Zulqarnain ◽  
Imran Siddique ◽  
Rifaqat Ali ◽  
Dragan Pamucar ◽  
Dragan Marinkovic ◽  
...  
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Current Approach ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Sustainable Supply Chain ◽  
Fuzzy Soft Set ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy ◽  
Operational Laws

In this paper, we investigate the multi-criteria decision-making complications under intuitionistic fuzzy hypersoft set (IFHSS) information. The IFHSS is a proper extension of the intuitionistic fuzzy soft set (IFSS) which discusses the parametrization of multi-sub attributes of considered parameters, and accommodates more hesitation comparative to IFSS utilizing the multi sub-attributes of the considered parameters. The main objective of this research is to introduce operational laws for intuitionistic fuzzy hypersoft numbers (IFHSNs). Additionally, based on developed operational laws two aggregation operators (AOs), i.e., intuitionistic fuzzy hypersoft weighted average (IFHSWA) and intuitionistic fuzzy hypersoft weighted geometric (IFHSWG), operators have been presented with their fundamental properties. Furthermore, a decision-making approach has been established utilizing our developed aggregation operators (AOs). Through the established approach, a technique for solving decision-making (DM) complications is proposed to select sustainable suppliers in sustainable supply chain management (SSCM). Moreover, a numerical description is presented to ensure the validity and usability of the proposed technique in the DM process. The practicality, effectivity, and flexibility of the current approach are demonstrated through comparative analysis with the assistance of some prevailing studies.

Interaction aggregation operators to solve multi criteria decision making problem under pythagorean fuzzy soft environment

2021 ◽  
pp. 1-21
Author(s):  
Rana Muhammad Zulqarnain ◽  
Xiao Long Xin ◽  
Harish Garg ◽  
Rifaqat Ali
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Soft Set ◽  
Multi Criteria Decision Making ◽  
Fuzzy Soft Set ◽  
Pythagorean Fuzzy Set ◽  
Operational Laws ◽  
Decision Making Problem ◽  
Soft Interaction

In this article, we investigate the multi-criteria decision-making complications under Pythagorean fuzzy soft information. The Pythagorean fuzzy soft set (PFSS) is a proper extension of the Pythagorean fuzzy set (PFS) which discusses the parametrization of the attributes of alternatives. It is also a generalization of the intuitionistic fuzzy soft set (IFSS). The PFSS is used to precisely evaluate the deficiencies, anxiety, and hesitation in decision-making (DM). The most essential determination of the current study is to advance some operational laws along with aggregation operators (AOs) within the Pythagorean fuzzy soft environs such as Pythagorean fuzzy soft interaction weighted average (PFSIWA) and Pythagorean fuzzy soft interaction weighted geometric (PFSIWG) operators with their desirable features. Furthermore, a DM technique has been established based on the developed operators to solve multi-criteria decision-making (MCDM) problems. Moreover, an application of the projected method is presented for the selection of an effective hand sanitizer during the COVID-19 pandemic. A comparative analysis with the merits, effectivity, tractability, along with some available research deduces the effectiveness of this approach.

scholarly journals A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1489
Author(s):  
Shahzad Faizi ◽  
Wojciech Sałabun ◽  
Nisbha Shaheen ◽  
Atiq ur Rehman ◽  
Jarosław Wątróbski
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Geometric Bonferroni Mean ◽  
The Individual ◽  
Heronian Mean

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.

Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bushra Batool ◽  
Saleem Abdullah ◽  
Shahzaib Ashraf ◽  
Mumtaz Ahmad
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Content Type ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Emergency Decision Making ◽  
Emergency Decision ◽  
Established Technique

PurposeThis is mainly because the restrictive condition of intuitionistic hesitant fuzzy number (IHFN) is relaxed by the membership functions of Pythagorean probabilistic hesitant fuzzy number (PyPHFN), so the range of domain value of PyPHFN is greatly expanded. The paper aims to develop a novel decision-making technique based on aggregation operators under PyPHFNs. For this, the authors propose Algebraic operational laws using algebraic norm for PyPHFNs. Furthermore, a list of aggregation operators, namely Pythagorean probabilistic hesitant fuzzy weighted average (PyPHFWA) operator, Pythagorean probabilistic hesitant fuzzy weighted geometric (PyPHFWG) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted average (PyPHFOWA) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted geometric (PyPHFOWG) operator, Pythagorean probabilistic hesitant fuzzy hybrid weighted average (PyPHFHWA) operator and Pythagorean probabilistic hesitant fuzzy hybrid weighted geometric (PyPHFHWG) operator, are proposed based on the defined algebraic operational laws. Also, interesting properties of these aggregation operators are discussed in detail.Design/methodology/approachPyPHFN is not only a generalization of the traditional IHFN, but also a more effective tool to deal with uncertain multi-attribute decision-making problems.FindingsIn addition, the authors design the algorithm to handle the uncertainty in emergency decision-making issues. At last, a numerical case study of coronavirus disease 2019 (COVID-19) as an emergency decision-making is introduced to show the implementation and validity of the established technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.Originality/valuePaper is original and not submitted elsewhere.

ORDERINGS FOR CLASSES OF AGGREGATION OPERATORS

1996 ◽  
Vol 04 (02) ◽  
pp. 145-156 ◽  
Author(s):  
L. BASILE ◽  
L. D’APUZZO
Keyword(s):  
Decision Making ◽  
Weighting Function ◽  
Multicriteria Decision Making ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Monotonic Function ◽  
Weighting Functions ◽  
Multicriteria Decision ◽  
Monotonic Functions

Some procedures for synthesizing values of judgements in multicriteria decision making have been provided by several authors. The functionals of synthesis they consider are frequently means. The most general form of these operators involves both a weighting function w and a continuous and strictly monotonic function φ. Our aim is to analyze the behaviour of the aggregation operator Fωφ depending on w and φ. To this purpose we introduce a pre-ordering relation on the set W of weighting functions and on the set Φ of continuous and strictly monotonic functions, which allows us to compare the synthesizing functionals.

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