A Study on Hypergraph Representations of Complex Fuzzy Information

Complex spherical fuzzy Aczel Alsina aggregation operators and their application in assessment of electric cars

The multi-criteria decision-making (MCDM) tool is a robust decision-making technique utilized in several fields like networking, risk management, digital analysis, cybercrime investigation, artificial intelligence, waste management enterprises and many other selection criteria. Complex SFS (CSFS) is a new edition of the spherical fuzzy set (SFS) that offers substantial information about any item in terms of amplitude and phase terms in a wider range of real terms. Complex SFS (CSFS) can be an extension of the spherical fuzzy set (SFS). The Aczel-Alsina aggregation tools are more appropriate aggregation operators (AOs), and they are used to conquer the impact of inconsistent and uncertain data. In this paper, we reveal some new approaches based on Aczel-Alsina aggregation tools under consideration of Complex Spherical Fuzzy (CSF) information. These new approaches include the CSF Aczel-Alsina weighted average (CSFAWA) operator, and the CSF Aczel-Alsina ordered weighted average (CSFOWA) operator. In addition to this, we also introduce a list of novel techniques by making use of the theory of Aczel-Alsina aggregation tools such as CSF Aczel-Alsina weighted geometric (CSFAWG) and CSF Aczel-Alsina ordered weighted geometric (CSFOWG) operators. To demonstrate the resilience and efficacy of the approaches that have been mentioned, we will examine a few exceptional examples and remarkable properties of the methodology that we have devised. In addition, a characterization is provided for an approach to the MCDM issue using the CPF information system. We use the example of electric automobiles as a case study to illustrate the uniformity and dependability of the methodology that we have established. This example was chosen because of the high cost of fuel and the present economic challenges that are being encountered by families in the middle class. An empirical case study is also constructed to determine an electric car that is desirable based on the techniques that we have proposed. To evaluate the correctness and superiority of the established strategies, we compare the outcomes of previously used techniques with the AOs currently being provided.

On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities

In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a synchronized generalization of complex fuzzy sets and hesitant fuzzy sets in a systematic way. The novelty of the introduced notion lies in the selection of the best alternative among the available multiple favorable situations, where the possibility of its range is in the extended unit circle of the complex plane. We study the relationship between the CHFS and the complex intuitionistic fuzzy set (CIFS), along with validation of the obtained results. On the basis of the proposed notion, various properties, operations, and identities have been established with their necessary proof. The applications of CHFS in the process of filtering the signals for obtaining the reference signal using the necessary Fourier cosine transform or inverse Fourier cosine transform and identifying the maximum number of sunspots in a particular interval of solar activity have been suitably discussed with illustrative numerical examples. Some advantages of incorporating the proposed notion have also been tabulated for better understanding.

A new group decision-making framework based on 2-tuple linguistic complex q-rung picture fuzzy sets

The need for multi-attribute decision-making brings more and more complexity, and this type of decision-making extends to an ever wider range of areas of life. A recent model that captures many components of decision-making frameworks is the complex $ q $-rung picture fuzzy set (C$ q $-RPFS), a generalization of complex fuzzy sets and $ q $-rung picture fuzzy sets. From a different standpoint, linguistic terms are very useful to evaluate qualitative information without specialized knowledge. Inspired by the ease of use of the linguistic evaluations by means of 2-tuple linguistic term sets, and the broad scope of applications of C$ q $-RPFSs, in this paper we introduce the novel structure called 2-tuple linguistic complex $ q $-rung picture fuzzy sets (2TLC$ q $-RPFSs). We argue that this model prevails to represent the two-dimensional information over the boundary of C$ q $-RPFSs, thanks to the additional features of 2-tuple linguistic terms. Subsequently, some 2TLC$ q $-RPF aggregation operators are proposed. Fundamental cases include the 2TLC$ q $-RPF weighted averaging/geometric operators. Other sophisticated aggregation operators that we propose are based on the Hamacher operator. In addition, we investigate some essential properties of the new operators. These tools are the building blocks of a multi-attribute decision making strategy for problems posed in the 2TLC$ q $-RPFS setting. Furthermore, a numerical instance that selects an optimal machine is given to guarantee the applicability and effectiveness of the proposed approach. Finally, we conduct a comparison with other existing approaches.

Hypergraph and Uncertain Hypergraph Representation Learning Theory and Methods

With the advent of big data and the information age, the data magnitude of various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have the ability to describe and characterize higher order relationships, which have attracted extensive attention from academia and industry in recent years. Firstly, this paper described the development process, the application areas, and the existing review research of hypergraphs; secondly, introduced the theory of hypergraphs briefly; then, compared the learning methods of ordinary graphs and hypergraphs from three aspects: matrix decomposition, random walk, and deep learning; next, introduced the structural optimization of hypergraphs from three perspectives: dynamic hypergraphs, hyperedge weight optimization, and multimodal hypergraph generation; after that, the applicability of three uncertain hypergraph models were analyzed based on three uncertainty theories: probability theory, fuzzy set, and rough set; finally, the future research directions of hypergraphs and uncertain hypergraphs were prospected.

Bipolar interval-valued fuzzy set in graph and hypergraph settings

Graphs and hypergraphs are popular models for data structured representation. For example, traffic data, weather data, and animal skeleton data are all described by graph structures. Interval-valued fuzzy sets change the membership function of general fuzzy sets from single value functions to interval-valued functions, and thus describe the fuzzy attributes of things in terms of fuzzy intervals, which is more in line with the characteristics of fuzzy objectives. This paper aims to define the bipolar interval-valued fuzzy hypergraph to reveal the inner relationship of fuzzy data, and give some characterizations of it. The characteristics of bipolar interval-valued intuitionistic fuzzy hypergraph and bipolar interval-valued Pythagorean fuzzy hypergraph are studied. In addition, we discuss the characteristics of the bipolar interval-valued fuzzy threshold graph. Finally, some instances are presented as the applications of bipolar interval-valued fuzzy hypergraphs.

Uncertain Hypergraphs: A Conceptual Framework and Some Topological Characteristics Indexes

In practical applications of hypergraph theory, we are usually surrounded by the state of indeterminacy. This paper employs uncertainty theory to address indeterministic information. We initially put forward the idea of an uncertain hypergraph by combining hypergraph theory with uncertainty theory in order to provide a useful tool to deal with a variety of uncertain complex systems and to create a new interdisciplinary research field. The main focus of this paper is to propose a conceptual framework of uncertain hypergraphs and to study the operations of uncertain hypergraphs. Moreover, some topological indexes are proposed to describe the characteristics of the structures of uncertain hypergraph. Additionally, some further research directions are discussed.

A new outranking method for multicriteria decision making with complex Pythagorean fuzzy information

This article contributes to the advancement and evolution of outranking decision-making methodologies, with a novel essay on the ELimination and Choice Translating REality (ELECTRE) family of methods. Its primary target is to unfold the constituents and expound the implementation of the ELECTRE II method for group decision making in complex Pythagorean fuzzy framework. This results in the complex Pythagorean fuzzy ELECTRE II method. By inception, it is intrinsically superior to models using one-dimensional data. It is designed to perform the pairwise comparisons of the alternatives using the core notions of concordance, discordance and indifferent sets, which is then followed by the construction of complex Pythagorean fuzzy concordance and discordance matrices. Further, the strong and weak outranking relations are developed by the comparison of concordance and discordance indices with the concordance and discordance levels. Later, the forward, reverse and average rankings of the alternatives are computed by the dint of strong and weak outranking graphs. This methodology is supported by a case study for the selection of wastewater treatment process, and by a numerical example for the selection of the best cloud solution for a big data project. Its consistency is confirmed by an effectiveness test and comparison analysis with the Pythagorean fuzzy ELECTRE II and complex Pythagorean fuzzy ELECTRE I methods.

Bipolar Complex Fuzzy Hamacher Aggregation Operators and Their Applications in Multi-Attribute Decision Making

On the basis of Hamacher operations, in this manuscript, we interpret bipolar complex fuzzy Hamacher weighted average (BCFHWA) operator, bipolar complex fuzzy Hamacher ordered weighted average (BCFHOWA) operator, bipolar complex fuzzy Hamacher hybrid average (BCFHHA) operator, bipolar complex fuzzy Hamacher weighted geometric (BCFHWG) operator, bipolar complex fuzzy Hamacher ordered weighted geometric (BCFHOWG) operator, and bipolar complex fuzzy Hamacher hybrid geometric (BCFHHG) operator. We present the features and particular cases of the above-mentioned operators. Subsequently, we use these operators for methods that can resolve bipolar complex fuzzy multiple attribute decision making (MADM) issues. We provide a numerical example to authenticate the interpreted methods. In the end, we compare our approach with existing methods in order to show its effectiveness and practicality.

Multi-criteria Optimization Technique with Complex Pythagorean Fuzzy N-soft Information

The main objective of this article is to lay the foundations of a novel multi-criteria optimization technique, namely, the complex Pythagorean fuzzy N-soft VIKOR (CPFNS-VIKOR) method that is highly proficient to express a great deal of linguistic imprecision and vagueness inherent in human assessments. This strategy provides a versatile decision-making tool for the ranking-based fuzzy modeling of two-dimensional parameterized data. The CPFNS-VIKOR method integrates the ground-breaking specialities of the VIKOR method with the outstanding parametric structure of the complex Pythagorean fuzzy N-soft model. It is exclusively designed for the specification of a compromise optimal solution having maximum group utility and minimum individual regret of the opponent by analyzing their weighted proximity from ideal solutions. The developed strategy factually permits specific linguistic terms to demystify the individual perspectives of the decision-making experts regarding the efficacy of the alternatives and the priorities of the applicable criteria. We comprehensively assemble these independent appraisals of all the experts using the complex Pythagorean fuzzy N-soft weighted averaging operator. Moreover, we calibrate the ranking measure by utilizing group utility measure and regret measure in order to specify the hierarchical outranking of the feasible alternatives. We demonstrate the systematic methodology and framework of the proposed method with the assistance of an explicative flow chart. We skilfully investigate an empirical analysis related to selection of constructive industrial robots for the modernization of a manufacturing industry which really justifies the remarkable accountability of the proposed strategy. Furthermore, we validate this technique by a comparative study with the existing complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method, complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method and Pythagorean fuzzy TOPSIS (PF-TOPSIS) method. The comparative study is exemplified with an illustrative bar chart that visually endorses the rationality of the proposed methodology by interpreting highly compatible and accurate final outcomes. Finally, we holistically analyze the functionality of the developed strategy to enlighten its merits and prominence over other available competent approaches.

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

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.

Extension of competition graphs under complex fuzzy environment

A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

Hypergraphs Based on Pythagorean Fuzzy Soft Model

A Pythagorean fuzzy soft set (PFSS) model is an extension of an intuitionistic fuzzy soft set (IFSS) model to deal with vague knowledge according to different parameters. The PFSS model is a more powerful tool for expressing uncertain information when making decisions and it relaxes the constraint of IFSS. Hypergraphs are helpful to handle the complex relationships among objects. Here, we apply the concept of PFSSs to hypergraphs, and present the notion of Pythagorean fuzzy soft hypergraphs (PFSHs). Further, we illustrate some operations on PFSHs. Moreover, we describe the regular PFSHs, perfectly regular PFSHs and perfectly irregular PFSHs. Finally, we consider the application of PFSHs for the selection of a team of workers for business and got the appropriate result by using score function.