A Novel Decision-Making Approach under Complex Pythagorean Fuzzy Environment

Multi-attribute decision-making method based on complex T-spherical fuzzy frank prioritized aggregation operators

This article aims to introduce new aggregation operators (AOs) by assigning the positive real values known as priority degree among the strict priority levels. To Develop the complex T-spherical fuzzy (TSF) frank prioritized (CTSFFP) AOs, using the frank t-norm (FTN) and frank t-conorm (FTCN) operational laws, also explain sum, product, and power operations under complex TSF information. The TSF set framework has a superior structure for uncertain data handling than an existing intuitionistic fuzzy set (FS), Pythagorean FS (PyFS), q-rung orthopair FS (q-ROFS), picture FS (PFS), and spherical FS (SFS). Because the structure of the TSF set has the most generalized form of IFS, PyFS, q-ROFS, PFS, and SFS, it provides greater freedom to decision experts for handling information where these discussed sets fail to aggregate ambiguous details. Utilizing the idea of priority degree, proposed new AOs called CTSFFP weighted averaging (CTSFFPWA), CTSFFP ordered weighted averaging (CTSFFPOWA), CTSFFP hybrid weighted averaging (CTSFFPHWA), CTSFFP weighted geometric (CTSFFPWG), CTSFFP ordered weighted geometric (CTSFFPOWG), CTSFFP hybrid weighted geometric (CTSFFPHWG) operators. Some desirable properties of AOs, such as idempotency, monotonicity, and boundedness, are also discussed. To show the importance of proposed AOs, the real-life problem of multi-attribute decision-making (MADM) is solved with the help of developed CTSFFPWA and CTSFFPWG operators. To enhance the proposed AOs' superiority, compare the diagnosed theory with existing AOs and give conclusions.

New optimization technique for group decision analysis with complex pythagorean fuzzy sets

The striking theory of ELECTRE III approach, being a marvelous strategy to deal with pseudo criterion, prevails over the traditional variants of ELECTRE method and other decision-making approaches for veracious decision-making. The noticeable efficiency and broader space of complex Pythagorean fuzzy model make it more significant and dominant for modeling two dimensional imprecise knowledge. The remarkable contribution of this study is to present a high aptitude variant of ELECTRE method by taking the advantage of the flexible structure of complex Pythagorean fuzzy sets closely following the outranking principles of ELECTRE III method. The proposed complex Pythagorean fuzzy ELECTRE III method is accredited to employ the theory of ELECTRE III technique to excellently deal with pseudo criterion as well as the two dimensional imprecise data for authentic decision-making. The proposed methodology uses three different threshold values, including preference, indifference and veto threshold values, to check the preference relation between alternatives. The presented strategy is applied to a case study for material selection to get the befitting decision. The comparative study with Pythagorean fuzzy ELECTRE III method is also included in this article to verify its decision-making aptitude.

Power Bonferroni mean operators under complex pythagorean fuzzy settings and their applications in decision-making problems

Bonferroni means (BM) operator is the extended form of the arithmetic mean operator, used for simplifying non-dominant and non-feasible problems diagnosed in genuine life scenarios. A lot of aggregation operators are the specific parts of the BM operators under the consideration of different values of parameters which are the main parts of the BM operators. In the presence of the BM operator and a very well-known conception in the scenario of fuzzy set, called complex Pythagorean fuzzy (CPF) setting, the objective of this scenario is to diagnose the CPF power BM (CPFPBM) operator and utilize their beneficial results with important properties. Moreover, a multi-attribute decision-making (MADM) technique is evaluated in the presence of invented operators for CPF settings. In the last of this study, we diagnosed the superiority and efficiency of the invented works with the help of sensitive analysis and graphical illustrations to enhance the gap of the research works.

Mathematical calculation of COVID-19 disease in Pakistan by emergency response modeling based on complex Pythagorean fuzzy information

The new emerged infectious disease that is known the coronavirus disease (COVID-19), which is a high contagious viral infection that started in December 2019 in China city Wuhan and spread very fast to the rest of the world. This infection caused millions of infected cases globally and still poses an alarming situation for human lives. Pakistan in Asian countries is considered the third country with higher number of cases of coronavirus with more than 649824. Recently, some mathematical models have been constructed for better understanding the coronavirus infection. Mostly, these models are based on classical integer-order derivative using real numbers which cannot capture the fading memory. So at the current position it is a challenge for the world to understand and control the spreading of COVID-19. Therefore, the aim of our paper is to develop some novel techniques, namely complex Pythagorean fuzzy weighted averaging (abbreviated as CPFWA) operator, complex Pythagorean fuzzy ordered weighted averaging (abbreviated as CPFOWA) operator, complex Pythagorean fuzzy hybrid averaging (abbreviated as CPFHA) operator, induced complex Pythagorean fuzzy ordered weighted averaging (abbreviated as I-CPFOWA) operator and induced complex Pythagorean fuzzy hybrid averaging (abbreviated as I-CPFHA) operator to analysis the spreading of COVID-19. At the end of the paper, an illustrative the emergency situation of COVID-19 is given for demonstrating the effectiveness of the suggested approach along with a sensitivity analysis, showing the feasibility and reliability of its results.

Complex Interval-Valued q-Rung Orthopair Fuzzy Hamy Mean Operators and Their Application in Decision-Making Strategy

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. Multi-attribute decision-making (MADM) technique is a very effective and well-known tool to investigate fuzzy information more effectively. However, the selection of houses cannot be carried out by utilizing symmetry information, because enterprises does not have complete information, so asymmetric information should be used when selecting enterprises. Hamy mean (HM) operator is a feasible tool to handle strategic decision-making problems because it can capture the order between the finite input terms. Additionally, the complex interval-valued q-rung orthopair fuzzy (CIVq-ROF) setting is a broadly flexible and massively dominant technique to operate problematic and awkward data in actual life problems. The major contribution of this analysis is how to aggregate the collection of alternatives into a singleton set, for this we analyzed the technique of CIVq-ROF Hamy mean (CIVq-ROFHM) operator and CIVq-ROF weighted Hamy mean (Cq-ROFWHM) operator and some well-known results are deliberated. Keeping the advantages of the parameters in HM operators, we discussed the specific cases of the invented operators. To investigate the decision-making problems based on CIVq-ROF information, we suggested the following multi-attribute decision-making (MADM) technique to determine the beneficial term from the finite group of alternatives with the help of evaluating several examples. This manuscript showed how to make decisions when there is asymmetric information about enterprises. Finally, based on the evaluating examples, we try to discover the sensitive analysis and supremacy of the invented operators to find the flexibility and dominancy of the diagnosed approaches.

Confidence levels under complex q-rung orthopair fuzzy aggregation operators and their applications

The major contribution of this analysis is to analyze the confidence complex q-rung orthopair fuzzy weighted averaging (CCQROFWA) operator, confidence complex q-rung orthopair fuzzy ordered weighted averaging (CCQROFOWA) operator, confidence complex q-rung orthopair fuzzy weighted geometric (CCQROFWG) operator, and confidence complex q-rung orthopair fuzzy ordered weighted geometric (CCQROFOWG) operator and invented their feasible properties and related results. Future more, under the invented operators, we diagnosed the best crystalline solid from the family of crystalline solids with the help of the opinion of different experts in the environment of decision-making strategy. Finally, to demonstrate the feasibility and flexibility of the invented works, we explored the sensitivity analysis and graphically shown of the initiated works.

Complex pythagorean fuzzy aggregation operators based on confidence levels and their applications

The most important influence of this assessment is to analyze some new operational laws based on confidential levels (CLs) for complex Pythagorean fuzzy (CPF) settings. Moreover, to demonstrate the closeness between finite numbers of alternatives, the conception of confidence CPF weighted averaging (CCPFWA), confidence CPF ordered weighted averaging (CCPFOWA), confidence CPF weighted geometric (CCPFWG), and confidence CPF ordered weighted geometric (CCPFOWG) operators are invented. Several significant features of the invented works are also diagnosed. Moreover, to investigate the beneficial optimal from a large number of alternatives, a multi-attribute decision-making (MADM) analysis is analyzed based on CPF data. A lot of examples are demonstrated based on invented works to evaluate the supremacy and ability of the initiated works. For massive convenience, the sensitivity analysis and merits of the identified works are also explored with the help of comparative analysis and they're graphical shown.

A Multi-MOORA decision making method based on Muirhead mean operators and complex spherical fuzzy uncertain linguistic setting

The Muirhead mean (MM) operators offer a flexible arrangement with its modifiable factors because of Muirhead’s general structure. On the other hand, MM aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. In this manuscript, the complex spherical fuzzy uncertain linguistic set (CSFULS), covering the grade of truth, abstinence, falsity, and their uncertain linguistic terms is proposed to accomplish with awkward and intricate data in actual life dilemmas. Furthermore, by using the MM aggregation operators with the CSFULS, the complex spherical fuzzy uncertain linguistic MM (CSFULMM), complex spherical fuzzy uncertain linguistic weighted MM (CSFULWMM), complex spherical fuzzy uncertain linguistic dual MM (CSFULDMM), complex spherical fuzzy uncertain linguistic dual weighted MM (CSFULDWMM) operators, and their important results are also elaborated with the help of some remarkable cases. Additionally, multi-attribute decision-making (MADM) based on the Multi-MOORA (Multi-Objective Optimization Based on a Ratio Analysis plus full multiplicative form), and proposed operators are developed. To determine the rationality and reliability of the elaborated approach, some numerical examples are illustrated. Finally, the supremacy and comparative analysis of the elaborated approaches with the help of graphical expressions are also developed.

Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making

In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved.

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.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

Geometric-arithmetic energy and atom bond connectivity energy of dual hesitant q-rung orthopair fuzzy graphs

 q-Rung orthopair fuzzy sets (q-ROFSs), originally proposed by Yager, can powerfully modify the range of indication of decision information by changing a parameter q based on the different hesitation degree, and the dual hesitant q-rung orthopair fuzzy set (DHq-ROFS), a new technique to consider human’s hesitance, can be more substantial of dealing with real multi-attribute decision making (MADM) problems. Inspired by DHq-ROFSs, in this article, we extend the concept of q-rung orthopair fuzzy graphs to dual hesitant q-rung orthopair fuzzy context and introduce the innovative concept of a dual hesitant q-rung orthopair fuzzy graphs based on Hamacher operator called dual hesitant q-rung orthopair fuzzy Hamacher graphs (DHq-ROFHGs). We propose the new concepts of geometric-arithmetic energy and atom bond connectivity energy of a DHq-ROFHG and determine its upper and lower bounds. Moreover, on the basis of the proposed concept of DHq-ROFHGs, we introduce a new approach to solve the MADM problems with dual hesitant q-rung orthopair fuzzy information. At the end, we give a numerical model related to the selection of most significant defensive factor to illustrate the applicability of the developed approach, and exhibit its viability. Comparative analysis is conducted and the superiorities are illustrated.

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.

Prioritized weighted aggregation operators under complex pythagorean fuzzy information

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.

Maximal Product of Graphs under Vague Environment

Graph models are found everywhere in natural and human made structures, including process dynamics in physical, biological and social systems. The product of graphs are appropriately used in several combinatorial applications and in the formation of different structural models. In this paper, we present a new product of graphs, namely, maximal product of two vague graphs. Then we describe certain concepts, including strongly, completely, regularity and connectedness on a maximal product of vague graphs. Further, we consider some results of edge regular and totally edge regular in a maximal product of vague graphs. Finally, we present an application for optimization of the biomass based on a maximal product of vague graphs.

Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making

In this manuscript, the notions of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets (CFSs) are combined is to propose the complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental laws. The Cq-ROFSs are an important way to express uncertain information, and they are superior to the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the real part (similarly for imaginary part) of complex-valued membership degree and the qth power of the real part (similarly for imaginary part) of complex-valued non‐membership degree is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we develop the score function, accuracy function and comparison method for two Cq-ROFNs. Based on Cq-ROFSs, some new aggregation operators are called complex q-rung orthopair fuzzy weighted averaging (Cq-ROFWA) and complex q-rung orthopair fuzzy weighted geometric (Cq-ROFWG) operators are investigated, and their properties are described. Further, based on proposed operators, we present a new method to deal with the multi‐attribute group decision making (MAGDM) problems under the environment of fuzzy set theory. Finally, we use some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

A Study on Hypergraph Representations of Complex Fuzzy Information

The paradigm shift prompted by Zadeh’s fuzzy sets in 1965 did not end with the fuzzy model and logic. Extensions in various lines have produced e.g., intuitionistic fuzzy sets in 1983, complex fuzzy sets in 2002, or hesitant fuzzy sets in 2010. The researcher can avail himself of graphs of various types in order to represent concepts like networks with imprecise information, whether it is fuzzy, intuitionistic, or has more general characteristics. When the relationships in the network are symmetrical, and each member can be linked with groups of members, the natural concept for a representation is a hypergraph. In this paper we develop novel generalized hypergraphs in a wide fuzzy context, namely, complex intuitionistic fuzzy hypergraphs, complex Pythagorean fuzzy hypergraphs, and complex q-rung orthopair fuzzy hypergraphs. Further, we consider the transversals and minimal transversals of complex q-rung orthopair fuzzy hypergraphs. We present some algorithms to construct the minimal transversals and certain related concepts. As an application, we describe a collaboration network model through a complex q-rung orthopair fuzzy hypergraph. We use it to find the author having the most outstanding collaboration skills using score and choice values.

Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment

With the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SNHFS) is an efficient tool to process the vague information and contains the ideas of a single-valued neutrosophic hesitant fuzzy set (SVNHFS) and an interval neutrosophic hesitant fuzzy set (INHFS). In this paper, we propose a decision-making approach based on the maximizing deviation method and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) to solve the MADM problems, in which the attribute weight information is incomplete, and the decision information is expressed in simplified neutrosophic hesitant fuzzy elements. Firstly, we inaugurate an optimization model on the basis of maximizing deviation method, which is useful to determine the attribute weights. Secondly, using the idea of the TOPSIS, we determine the relative closeness coefficient of each alternative and based on which we rank the considered alternatives to select the optimal one(s). Finally, we use a numerical example to show the detailed implementation procedure and effectiveness of our method in solving MADM problems under simplified neutrosophic hesitant fuzzy environment.