scholarly journals q-Rung Orthopair Fuzzy Hypergraphs with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 260 ◽  
Author(s):  
Anam Luqman ◽  
Muhammad Akram ◽  
Ahmad N. Al-Kenani
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Research Study ◽  
Uncertain Data ◽  
Intuitionistic Fuzzy Sets ◽  
Uncertain Information ◽  
Pythagorean Fuzzy Sets ◽  
Proposed Model ◽  
Fuzzy Hypergraphs ◽  
New Framework

The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the q th power of the truth-membership and the q th power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter q, q ≥ 1 . In this research study, we design a new framework for handling uncertain data by means of the combinative theory of q-rung orthopair fuzzy sets and hypergraphs. We define q-rung orthopair fuzzy hypergraphs to achieve the advantages of both theories. Further, we propose certain novel concepts, including adjacent levels of q-rung orthopair fuzzy hypergraphs, ( α , β ) -level hypergraphs, transversals, and minimal transversals of q-rung orthopair fuzzy hypergraphs. We present a brief comparison of our proposed model with other existing theories. Moreover, we implement some interesting concepts of q-rung orthopair fuzzy hypergraphs for decision-making to prove the effectiveness of our proposed model.

scholarly journals Generalized orthopair fuzzy sets based on Hamacher T-norm and T-conorm

2021 ◽  
Vol 5 (1) ◽  
pp. 44-64
Author(s):  
I. Silambarasan ◽  
Keyword(s):  
Fuzzy Sets ◽  
Uncertain Data ◽  
Intuitionistic Fuzzy Sets ◽  
Scalar Multiplication ◽  
Uncertain Information ◽  
Pythagorean Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Algebraic Properties

The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the \(q^{th}\) power of the truth-membership and the \(q^{th}\) power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter \(q, ~q\geq 1\). In this paper, we define the Hamacher operations of q-rung orthopair fuzzy sets and proved some desirable properties of these operations, such as commutativity, idempotency, and monotonicity. Further, we proved De Morgan's laws for these operations over complement. Furthermore, we defined the Hamacher scalar multiplication \(({n._{h}}A)\) and Hamacher exponentiation \((A^{\wedge_{h}n})\) operations on q-rung orthopair fuzzy sets and investigated their algebraic properties. Finally, we defined the necessity and possibility operators based on q-rung orthopair fuzzy sets and some properties of Hamacher operations that are considered.

scholarly journals The n-Pythagorean Fuzzy Sets

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1772
Author(s):  
Anna Bryniarska
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Quadratic Function ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Functions ◽  
Power Functions ◽  
Pythagorean Fuzzy Sets ◽  
Conceptual Apparatus ◽  
Intuitionistic Fuzzy ◽  
Classic Theory

The following paper presents deductive theories of n-Pythagorean fuzzy sets (n-PFS). N-PFS objects are a generalization of the intuitionistic fuzzy sets (IFSs) and the Yager Pythagorean fuzzy sets (PFSs). Until now, the values of membership and non-membership functions have been described on a one-to-one scale and a quadratic function scale. There is a symmetry between the values of this membership and non-membership functions. The scales of any power functions are used here in order to increase the scope of the decision-making problems. The theory of n-PFS introduces a conceptual apparatus analogous to the classic theory of Zadeh fuzzy sets, consistently striving to correctly define the n-PFS algebra.

scholarly journals Energy of Pythagorean Fuzzy Graphs with Applications

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 136 ◽  
Author(s):  
Muhammad Akram ◽  
Sumera Naz
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Satellite Communication ◽  
Research Study ◽  
Upper Bounds ◽  
Intuitionistic Fuzzy Sets ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Duality Property

Pythagorean fuzzy sets (PFSs), an extension of intuitionistic fuzzy sets (IFSs), inherit the duality property of IFSs and have a more powerful ability than IFSs to model the obscurity in practical decision-making problems. In this research study, we compute the energy and Laplacian energy of Pythagorean fuzzy graphs (PFGs) and Pythagorean fuzzy digraphs (PFDGs). Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of PFGs. Finally, we present numerical examples, including the design of a satellite communication system and the evaluation of the schemes of reservoir operation to illustrate the applications of our proposed concepts in decision making.

scholarly journals Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huimin Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Score Function ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Linguistic Intuitionistic Fuzzy Sets

To better deal with imprecise and uncertain information in decision making, the definition of linguistic intuitionistic fuzzy sets (LIFSs) is introduced, which is characterized by a linguistic membership degree and a linguistic nonmembership degree, respectively. To compare any two linguistic intuitionistic fuzzy values (LIFVs), the score function and accuracy function are defined. Then, based ont-norm andt-conorm, several aggregation operators are proposed to aggregate linguistic intuitionistic fuzzy information, which avoid the limitations in exiting linguistic operation. In addition, the desired properties of these linguistic intuitionistic fuzzy aggregation operators are discussed. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in multiple attribute group decision making (MAGDM).

scholarly journals Intuitionistic Fuzzy Sets in Multi-Criteria Group Decision Making Problems Using the Characteristic Objects Method

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1382 ◽  
Author(s):  
Shahzad Faizi ◽  
Wojciech Sałabun ◽  
Tabasam Rashid ◽  
Sohail Zafar ◽  
Jarosław Wątróbski
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Uncertain Data ◽  
Research Area ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy

Over the past few decades, several researchers and professionals have focused on the development and application of multi-criteria group decision making (MCGDM) methods under a fuzzy environment in different areas and disciplines. This complex research area has become one of the more popular topics, and it seems that this trend will be increasing. In this paper, we propose a new MCGDM approach combining intuitionistic fuzzy sets (IFSs) and the Characteristic Object Method (COMET) for solving the group decision making (GDM) problems. The COMET method is resistant to the rank reversal phenomenon, and at the same time it remains relatively simple and intuitive in practical problems. This method can be used for both symmetric and asymmetric information. The Triangular Intuitionistic Fuzzy Numbers (TIFNs) have been used to handle uncertain data. This concept can ensure the preference information about an alternative under specific criteria more comprehensively and allows for easy modelling of symmetrical or asymmetrical linguistic values. Each expert provides the membership and non-membership degree values of intuitionistic fuzzy numbers (IFNs). So this approach deals with a different kind of uncertainty than with hesitant fuzzy sets (HFSs). The proposed combination of COMET and IFSs required an adaptation of the matrix of expert judgment (MEJ) and allowed to capture the behaviour aspects of the decision makers (DMs). Therefore, we get more reliable solutions while solving MCGDM problems. Finally, the proposed method is presented in a simple academic example.

An interval type-2 hesitant fuzzy best-worst method

2021 ◽  
pp. 1-28
Author(s):  
Ashraf Norouzi ◽  
Hossein Razavi hajiagha
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Fuzzy Ahp ◽  
Uncertain Data ◽  
Interval Type ◽  
Best Worst Method

Multi criteria decision-making problems are usually encounter implicit, vague and uncertain data. Interval type-2 fuzzy sets (IT2FS) are widely used to develop various MCDM techniques especially for cases with uncertain linguistic approximation. However, there are few researches that extend IT2FS-based MCDM techniques into qualitative and group decision-making environment. The present study aims to adopt a combination of hesitant and interval type-2 fuzzy sets to develop an extension of Best-Worst method (BWM). The proposed approach provides a flexible and convenient way to depict the experts’ hesitant opinions especially in group decision-making context through a straightforward procedure. The proposed approach is called IT2HF-BWM. Some numerical case studies from literature have been used to provide illustrations about the feasibility and effectiveness of our proposed approach. Besides, a comparative analysis with an interval type-2 fuzzy AHP is carried out to evaluate the results of our proposed approach. In each case, the consistency ratio was calculated to determine the reliability of results. The findings imply that the proposed approach not only provides acceptable results but also outperforms the traditional BWM and its type-1 fuzzy extension.

scholarly journals Towards Better Concordance among Contextualized Evaluations in FAST-GDM Problems

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 93
Author(s):  
Marcelo Loor ◽  
Ana Tapia-Rosero ◽  
Guy De Tré
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Heterogeneous Group ◽  
Intuitionistic Fuzzy ◽  
High Level ◽  
Consensus Reaching ◽  
Novel Algorithm

A flexible attribute-set group decision-making (FAST-GDM) problem consists in finding the most suitable option(s) out of the options under consideration, with a general agreement among a heterogeneous group of experts who can focus on different attributes to evaluate those options. An open challenge in FAST-GDM problems is to design consensus reaching processes (CRPs) by which the participants can perform evaluations with a high level of consensus. To address this challenge, a novel algorithm for reaching consensus is proposed in this paper. By means of the algorithm, called FAST-CR-XMIS, a participant can reconsider his/her evaluations after studying the most influential samples that have been shared by others through contextualized evaluations. Since exchanging those samples may make participants’ understandings more like each other, an increase of the level of consensus is expected. A simulation of a CRP where contextualized evaluations of newswire stories are characterized as augmented intuitionistic fuzzy sets (AIFS) shows how FAST-CR-XMIS can increase the level of consensus among the participants during the CRP.

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