Pythagorean Fuzzy Sets Research Articles

Development and Application of an Interval-Valued Pythagorean Fuzzy Set-Based Grade Evaluation Method to Foreign Fiber Content

ABSTRACT To solve the problem of the grade evaluation of foreign fiber content in cotton, this paper divided the problem into multi-criteria decision-making field and proposed an interval-valued Pythagorean fuzzy set foreign fiber content grade evaluation method. Taking into account the various properties of foreign fibers, the multi-criteria evaluation of single foreign fiber content and comprehensive foreign fiber content is carried out to improve the quality of cotton textiles. Based on the Pythagorean fuzzy set, we used AHP and TOPSIS methods to determine the relevant weight information, combined with the grade evaluation index of foreign fiber content and the interval-valued Pythagorean fuzzy weighted average or geometric operators to construct a fiber multi-criteria decision model. Then, the evaluation index function is improved to make the score function more consistent with the facts, and the digitization and intelligence methods required for foreign fiber content detection and grade evaluation are developed. Further, an example is given to verify the feasibility and effectiveness of the model. In addition, the multi-criteria decision-making method adopted has high theoretical innovation and application value for the textile industry.

RETRACTED: Multiple attribute decision making based on MAIRCA, standard deviation-based method, and Pythagorean fuzzy sets

In this paper, we propose a new multiple attribute decision making (MADM) approach based on the multi-attribute ideal-real comparative assessment (MAIRCA) method, the standard deviation-based method, and Pythagorean fuzzy sets. We also propose a weight-determining method to determine the weights of attributes using a standard deviation-based approach with Pythagorean fuzzy information. The drawbacks of the existing MADM methods in Pythagorean fuzzy environments are that they cannot distinguish the preference orders of alternatives in some situations. The proposed MADM approach can overcome the drawbacks of the existing MADM approaches in the Pythagorean fuzzy context. The main contributions of this paper include: (1) It proposes a weight-determining method to derive attributes’ weights based on the standard deviation-based method with Pythagorean fuzzy information, (2) It proposes a new MADM methodology based on the MAIRCA method, the standard deviation-based method, and PFSs for MADM in the Pythagorean fuzzy setting, and (3) The proposed MADM method can overcome the shortcomings of the existing MADM methods in the Pythagorean fuzzy context. It provides us a flexible and effective method for MADM in Pythagorean fuzzy environments.

Fine-Kinney-Based Occupational Risk Assessment using Pythagorean Fuzzy AHP-COPRAS for the Lifting Equipment in the Energy Distribution and Investment Sector

The initial risk assessment, especially when using a risk score system, is the main step in a risk assessment process that comes after determining the scope of the risks and assessment. The Fine-Kinney method, a thorough approach to quantitative assessments to help keep risks under control, is commonly used in risk assessment. A risk score (RS) is determined using the standard version of Fine-Kinney by mathematically multiplication of probability (P), exposure (E), and consequence (C) parameters. The Fine-Kinney-based risk evaluation approach has the disadvantage of not accounting for the relationships among the risk parameters' interaction and determining the risk precedence of work-related hazards. Hence, a new hazard evaluation method for occupational health and safety (OHS) is required to lessen the adverse effects of rising dangers. In this paper, a novel approach is proposed for integrating Fine–Kinney-based occupational hazard evaluation and AHP-COPRAS for the energy distribution and investment sector under the Pythagorean fuzzy environment. A lifting equipment case study is used to demonstrate practicality and efficacy of the suggested integrated approach. To verify the novel method to risk assessment, a comparative study and sensitivity analysis are also provided. As a result, using the benefit of Pythagorean fuzzy sets, which more effectively express uncertainty, the integrated approach yields more logical conclusions for assessing work-related hazards in the energy distribution and investment sector.

New similarity measure of Pythagorean fuzzy sets based on the Jaccard index with its application to clustering

A similarity measure is being widely used as a tool to create the degree of similarity between two different objects or sets. Several similarity measures between two Pythagorean fuzzy sets (PFSs) are suggested in literature. As far as our knowledge is concerned no one has considered similarity measure between two Pythagorean fuzzy sets (PFSs) based on Jaccard index (JI) so far. Therefore, in this manuscript a novel similarity measure based on JI between two PFSs is suggested. The JI is statics used to compare similarity as well as variety of simple sets. The advantages of proposed similarity based on Jaccard index includes: (i) It can be utilized to compare any two sets and it can also be applied to text data, numerical data and even categorical data. (ii) It is robust to outliers, which means that it is not significantly affected by presence of rare or unusual items exist in the data. This makes it useful in variety of applications including clustering and anomaly detection (iii) It is simple and efficient in computation which make it right choice in many applications where fast processing time is important. Then we gave several numerical examples to show the reliability of suggested similarity measures. Our proposed similarity measure between PFSs based on JI give better properties with respect to numerical results. Based on the numerical analysis, our proposed method is reliable, reasonable and better than the existing ones. Furthermore, we utilized proposed similarity measure with Pythagorean Fuzzy Technique of Order Preference by Similarity to Ideal Solution (PF-TOPSIS) in handling complex daily life issues involving multicriteria decision-making (MCDM) processes. Furthermore, similarity measure between two PFSs is also very useful in clustering. Therefore, we also apply our proposed similarity measure in an application to clustering based on Pythagorean fuzzy data set. Final results revealed that our suggested methods are well suited and reasonable in multicriteria decision-making and clustering environment.

Exponential information measures-driven Pythagorean fuzzy MADM method and its application to new energy battery supplier evaluation problem

Under the Pythagorean fuzzy environment, this paper presents a multi-attribute decision-making (MADM) model based on exponential entropy measure and exponential similarity measure to evaluate new energy battery supplier’s performance. In this method, the notion of Pythagorean fuzzy linguistic sets (PFLSs) is first introduced by combining the linguistic fuzzy sets (LFSs) and the Pythagorean fuzzy sets (PFSs). Then, the axiomatic definitions of Pythagorean fuzzy entropy and Pythagorean fuzzy similarity measure are developed to measure the degree of uncertainty and similarity between two Pythagorean fuzzy linguistic values (PFLVs). The PFLVs can be expressed by the linguistic membership degree (LMD) and linguistic non-membership degree (LNMD). In addition, we construct two new information measure formulas based on exponential function. Through a series of proofs, we verify that they satisfy the axiomatic conditions of entropy and similarity measure of Pythagorean fuzzy language respectively. On this basis, we research the relationship between the two information measures. Finally, we present a novel Pythagorean fuzzy linguistic MADM model. An example for evaluating performance of new energy battery supplier is given to explain the effectiveness of the newly-developed approach. The stability and validity of the newly-developed approach is performed by sensitivity analysis and comparative analysis.

A novel study of spherical fuzzy soft Dombi aggregation operators and their applications to multicriteria decision making

In many decision-making situations, we are not restricted to two kinds of aspects, such as membership degree or nonmembership degree, and sometimes we need to include the abstinence degree (AD). However, many fuzzy set theories fail to cover issues, such as an intuitionistic fuzzy soft set, Pythagorean fuzzy soft set and q-rung orthopair fuzzy soft set. All the above notions can only consider membership degree and a nonmembership degree in their structures. The spherical fuzzy soft set compensates for these drawbacks in its structure. Moreover, the Dombi t-norm and Dombi t-conorm are the fundamental apparatuses to generalize the basic operational laws of sum and product. Therefore, in this article, based on the dominant features of spherical fuzzy soft sets and valuable features of the Dombi t-norm and Dombi t-conorm, we initially developed the basic Dombi operational laws for spherical fuzzy soft numbers. Moreover, based on these newly developed operational laws, we introduced aggregation operators called spherical fuzzy soft Dombi average (weighted, ordered weighted, hybrid) aggregation operators. We discussed the basic properties of these aggregation operators. Additionally, we have developed a multiple criteria decision making (MCDM) approach using an explanatory example via our approach to show its effective utilization. Furthermore, a comparative study of our approach shows the superiority of our introduced notions.

Pythagorean Fuzzy Sets-based VIKOR and TOPSIS-based multi-criteria decision-making model for mitigating resource deletion attacks in WSNs

In Wireless Sensor Networks (WSNs), resource depletion attacks that focusses on the compromization of routing protocol layer is identified to facilitate a major influence over the network. These resource depletion attacks drain the batter power of the sensor nodes drastically with persistent network disruption. Several protocols were established for handling the impact of Denial of Service (DoS) attack, but majority of them was not able to handle it perfectly. In specific, thwarting resource depletion attack, a specific class of DoS attack was a herculean task. At this juncture, Multicriteria Decision Making Model (MCDM) is identified as the ideal candidate for evaluating the impact introduced by each energy depletion compromised sensor nodes towards the process of cooperation into the network. In this paper, A Pythagorean Fuzzy Sets-based VIKOR and TOPSIS-based multi-criteria decision-making model (PFSVT-MCDM) is proposed for counteracting with the impacts of resource depletion attacks to improve Quality of Service (QoS) in the network. This PFSVT-MCDM used the merits of Pythagorean Fuzzy Sets information for handling uncertainty and vagueness of information exchanged in the network during the process of data routing. It utilized VIKOR and TOPSIS for exploring the trust of each sensor nodes through the exploration of possible dimensions that aids in detecting resource depletion attacks. The experimental results of PFSVT-MCDM confirmed better throughput of 21.29%, enhanced packet delivery fraction of 22.38%, minimized energy consumptions 18.92%, and reduced end-to-end delay of 21.84%, compared to the comparative resource depletion attack thwarting strategies used for evaluation.

A novel extension of Pythagorean fuzzy MULTIMOORA approach for new product development

This study explores how to enhance the decision-making processes in the phases of idea generation or alternative selection during the new product development (NPD) process. NPD is acknowledged as the central function of businesses in an increasingly competitive marketplace. In the current era, the highly uncertain and rapidly changing market environment makes the NPD extremely vague and complex. To be able to find a suitable solution to this complexity, the proposed research aims to categorize the decision points in the process of NPD regarding software development and identify the fuzziness elements affecting the process. The goal of a decision-making process is to prioritize several alternatives with respect to some required objectives and to select the best among them. Multi-Criteria Decision-Making (MCDM) may support reaching a consensus judgment with the collective assessment of Decision Makers (DMs). We introduce a novel evaluation approach for this problem. The proposed approach employs a MULTIMOORA (Multi-objective Optimization by Ratio Analysis plus the Full Multiplicative Form) MCDM technique under Pythagorean Fuzzy Sets (PFSs) objective world environment to cope with an ambiguous environment using Group Decision Making (GDM) setting to shape the decisions. The PFSs have demonstrated their advantages in dealing with vagueness and uncertainty over crisp, fuzzy, or intuitionistic fuzzy sets. Therefore, PFSs can represent the DMs’ judgments and preferences in a better structure, ensuring enhanced decision-making in a group consensus. A case study on gaming software and app development is presented to validate the functionality of the proposed method. The results are compared and assessed with the help of a sensitivity analysis. This research makes a real contribution to the literature by proposing a novel evaluation method to rate and select NPD (gaming software and apps) to deal with the inexactness and vagueness associated with the criteria and alternatives.

Pythagorean Fuzzy AHP Based Dynamic Subcontractor Management Framework

In construction projects, a significant part of construction work is done by subcontractors (SCs). Therefore, their management by main contractors (MCs) becomes an important issue as the density of SCs is created at the construction sites. In recent years, more focus on SC evaluation and selection in bidding process has been on the agenda whereas the subject of SC performance appraisal on-site during the project execution phase has been untended in the literature. Thus, this study aims to focus on the measurement and evaluation of the performance of SCs in the project execution phase, and to provide a tentative performance-based dynamic management framework that MCs will use in the management of SCs in order to take proactive measures. In line with the aim, a total number of 23 performance measurement criteria (PMC) under 7 main groups were determined as a result of a comprehensive literature review and expert evaluations. Knowing that not every criterion will have the same effect in performance measurement, pairwise comparisons of the criteria were made using the Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP) method and their importance weights were determined. The PFAHP method was obtained by integrating the Pythagorean fuzzy set into the AHP method and chosen with the aim of improving the fuzzy AHP method and obtaining more consistent results by eliminating the uncertainty since Pythagorean fuzzy sets is more capable than fuzzy sets at expressing and handling uncertainty in uncertain environments. Lastly, a framework for SC performance measurement and evaluation on project execution phase is presented. It is believed that the presented framework will allow for a proactive management style that will enable effective decisions to be made while the project is ongoing, and a dynamic way of working instead of static and conventional work.

VIKOR and TOPSIS framework with a truthful-distance measure for the (t, s)-regulated interval-valued neutrosophic soft set.

This article introduces the structure of the -regulated interval-valued neutrosophic soft set (abbr. -INSS). The structure of -INSS is shown to be capable of handling the sheer heterogeneity and complexity of real-life situations, i.e. multiple inputs with various natures (hence neutrosophic), uncertainties over the input strength (hence interval-valued), the existence of different opinions (hence soft), and the perception at different strictness levels (hence -regulated). Besides, a novel distance measure for the -INSS model is proposed, which is truthful to the nature of each of the three membership (truth, indeterminacy, falsity) values present in a neutrosophic system. Finally, a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and a Viekriterijumsko Kompromisno Rangiranje (VIKOR) algorithm that works on the -INSS are introduced. The design of the proposed algorithms consists of TOPSIS and VIKOR frameworks that deploy a novel distance measure truthful to its intuitive meaning. The conventional method of TOPSIS and VIKOR will be generalized for the structure of -INSS. The parameters and in the -INSS model take the role of strictness in accepting a collection of data subject to the amount of mutually contradicting information present in that collection of data. The proposed algorithm will then be subjected to rigorous testing to justify its consistency with human intuition, using numerous examples which are specifically made to tally with the various human intuitions. Both the proposed algorithms are shown to be consistent with human intuitions through all the tests that were conducted. In comparison, all other works in the previous literature failed to comply with all the tests for consistency with human intuition. The -INSS model is designed to be a conclusive generalization of Pythagorean fuzzy sets, interval neutrosophic sets, and fuzzy soft sets. This combines the advantages of all the three previously established structures, as well as having user-customizable parameters and , thereby enabling the -INSS model to handle data of an unprecedentedly heterogeneous nature. The distance measure is a significant improvement over the current disputable distance measures, which handles the three types of membership values in a neutrosophic system as independent components, as if from a Euclidean vector. Lastly, the proposed algorithms were applied to data relevant to the ongoing COVID-19 pandemic which proves indispensable for the practical implementation of artificial intelligence.

Expanding Pythagorean fuzzy sets with distinctive radii: disc Pythagorean fuzzy sets

AbstractThis article presents the circular Pythagorean fuzzy set (C-PFS) model, a generalization of the circular intuitionistic fuzzy set model that improves its performance thanks to the acclaimed extension of intuitionistic fuzzy sets to Pythagorean fuzzy sets. Then, we generalize C-PFSs to produce the novel disc Pythagorean fuzzy sets (D-PFSs). The constituent elements of both C-PFSs and D-PFSs are circular Pythagorean fuzzy values, either with a common or a distinctive radius. We lay out some fundamental algebraic and arithmetic operations on D-PFSs (hence on C-PFSs), namely union, intersection, addition, multiplication, and scalar multiplication, and we explore the main features of these operations. We propose and investigate the properties of the novel circular Pythagorean fuzzy weighted average/geometric aggregation operators. The “COmbinative Distance based ASsesment" approach, which is based on the Hamming and Euclidean distances, is expanded to the D-PFS framework. To justify its implementability, we apply the new methodology to a case study (selection of the best supermarkets to buy fresh fruit for a hotel) and then we compare it to related solutions.

A New Algorithm on Pythagorean Fuzzy-Based Multi-Criteria Decision-Making and Its Application

The rapid growth in information technology (IT) and the implementation of IT tools has aided hospitals in delivering healthcare at an unprecedented pace. However, without the proper knowledge and understanding of software tools, healthcare establishments may find it difficult to select the best hospital management system software solution for their business. In this paper, a problem based on multi-criteria decision-making (MCDM) is modelled to identify the best hospital management software on the basis of a thorough analysis of every aspect of the healthcare needs and required software competencies, so that hospitals can select a robust hospital management software system. This article presents an extended MCDM method for estimating and selecting robust hospital management system alternatives using the Pythagorean fuzzy method based on the removal effects of criteria (MEREC) and stepwise weight assessment ratio analysis (SWARA). To do this, the objective weights and subjective weights are assessed by the MEREC and SWARA models, and the measurement alternatives and ranking according to compromise solution (MARCOS) method determines the order of preference of the alternatives on the basis of the Pythagorean fuzzy set. Moreover, after in-depth analysis of every aspect of healthcare needs and required software competencies in India, the proposed method is designed to identify the best hospital management software tool, so that the hospital can choose a robust hospital management system. Comparative discussion is presented to exhibit the rationality and sustainability of the established approach to prioritize hospital management software options.

$\inf$-Hesitant and $(\sup, \inf)$-Hesitant fuzzy ideals of ternary semigroups

The notions of an $\inf$-hesitant fuzzy right (left, lateral) ideal, an $\inf$-hesitant fuzzy ideal, a $(\sup, \inf)$-hesitant fuzzy right (left, lateral) ideal, and a $(\sup, \inf)$-hesitant fuzzy ideal, which are generalizations of an interval-valued fuzzy ideal of a ternary semigroup, are introduced and their properties are investigated. Conditions for a hesitant fuzzy set to be an $\inf$-hesitant fuzzy right (left, lateral) ideal, an $\inf$-hesitant fuzzy ideal, a $(\sup, \inf)$-hesitant fuzzy right (left, lateral) ideal, and a $(\sup, \inf)$-hesitant fuzzy ideal of a ternary semigroup are provided in terms of sets, fuzzy sets, Pythagorean fuzzy sets, interval-valued fuzzy sets, and hesitant fuzzy sets. Furthermore, characterizations of an ideal of a ternary semigroup are studied via a generalization of the characteristic hesitant and the characteristic interval-valued fuzzy set.

A new definition for quartic fuzzy sets with hesitation grade applied to multi-criteria decision-making problems under uncertainty

Pythagorean fuzzy sets and Fermatean fuzzy sets are used to enhance the flexibility of intuitionistic fuzzy sets for decision-making under uncertainty in fuzzy environments. This study presents and compares a new definition of quartic fuzzy sets with intuitionistic, Pythagorean, and Fermatean fuzzy sets. In addition, we study set operations, score function, and accuracy function of the quartic fuzzy sets. Euclidean distance and similarity measures for quartic fuzzy sets are proposed, which will help solve many real-life problems under uncertainty. We then develop an algorithm to tackle the problem of multiple criteria decision-making. A comparison of the novel quartic fuzzy sets with the existing intuitionistic, Pythagorean, and Fermatean fuzzy sets is provided to demonstrate the advantages of the proposed quartic fuzzy sets. Finally, a practical example is presented to demonstrate the applicability and efficacy of the proposed fuzzy sets. The results of the study indicate that new definition of quartic fuzzy sets produce the most consistent and reliable ranking for handling uncertain and indeterminate information.

Development of type-2 Pythagorean fuzzy set with its application to sustainable transport system selection

In resolving multicriteria decision-making (MCDM) problems, it is observed that the solution process is frequently affected by the available vague information together with intra-personal uncertainties associated with expert’s opinion. In most of the time fuzzy set or its existing variants fail to capture such uncertainties for making reasonable balance in decision making processes. To reduce the effects of uncertainties, this paper introduces a new variant of fuzzy set, viz., type-2 Pythagorean fuzzy set (T2PFS). The main advantage of using T2PFS in MCDM is that the membership and non-membership values of each argument are presented by Pythagorean fuzzy numbers rather than using fuzzy number or intuitionistic fuzzy number. In model formulation process, at first, T2PFS is explicitly formulated and some basic operations are defined. Subsequently, four aggregation operators are constructed to aggregate the arguments, and their properties are verified. Afterwards, two information measures and a score function are defined. Moreover, two MCDM algorithms based on the developed aggregation operators and TOPSIS are framed. To show the application potentiality of the proposed method, a case study relating to the selection of sustainable transport system in India is considered and solved. In the case study five different fuel-based vehicles, mostly used in India in recent times, are evaluated by the experts as transport alternatives with the consideration of thirteen sustainability related criteria. From the achieved result it is found that in future electric cars would become the most sustainable vehicle in India. Sensitivity analysis of the developed models and comparative study with existing fuzzy and non-fuzzy MCDM methods establish effectiveness of the developed models. This study may facilitate transport authority to select appropriate transport system in connection with sustainable development of a region.

On Similarity Measures Between Pythagorean Fuzzy Sets Derived from Overlap and Grouping Functions

On Similarity Measures Between Pythagorean Fuzzy Sets Derived from Overlap and Grouping Functions

Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection

BackgroundThe concept of Pythagorean fuzzy sets (PFSs) is an utmost valuable mathematical framework, which handles the ambiguity generally arising in decision-making problems. Three parameters, namely membership degree, non-membership degree, and indeterminate (hesitancy) degree, characterize a PFS, where the sum of the square of each of the parameters equals one. PFSs have the unique ability to handle indeterminate or inconsistent information at ease, and which demonstrates its wider scope of applicability over intuitionistic fuzzy sets.ResultsIn the present article, we opt to define two nonlinear distances, namely generalized chordal distance and non-Archimedean chordal distance for PFSs. Most of the established measures possess linearity, and we cannot incorporate them to approximate the nonlinear nature of information as it might lead to counter-intuitive results. Moreover, the concept of non-Archimedean normed space theory plays a significant role in numerous research domains. The proficiency of our proposed measures to overcome the impediments of the existing measures is demonstrated utilizing twelve different sets of fuzzy numbers, supported by a diligent comparative analysis. Numerical examples of pattern recognition and medical diagnosis have been considered where we depict the validity and applicability of our newly constructed distances. In addition, we also demonstrate a problem of suitable medicine selection for COVID-19 so that the transmission rate of the prevailing viral pandemic could be minimized and more lives could be saved.ConclusionsAlthough the issues concerning the COVID-19 pandemic are very much challenging, yet it is the current need of the hour to save the human race. Furthermore, the justifiable structure of our proposed distances and also their feasible nature suggest that their applications are not only limited to some specific research domains, but decision-makers from other spheres as well shall hugely benefit from them and possibly come up with some further extensions of the ideas.

Three-way conflict analysis and resolution based on q-rung orthopair fuzzy information

In solving some complex conflict problems, compared with intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs), q-rung orthopair fuzzy sets (q-ROFSs) can better express and model imprecise information. In addition, three-way decisions (TWDs), an emerging theory of simulating human decision-making behavior, play an increasingly important role in the study of conflict problems. In order to solve conflict problems under q-rung orthopair fuzzy information (q-ROFI), we propose a three-way conflict analysis and resolution model based on TWDs and decision-theoretic rough sets (DTRSs) theory, which provides another answer for Deja's fundamental questions about Pawlak's conflict model, namely, “what are the inherent causes of conflict?” and “how can a viable strategy be found?” different from the existing ones. To be specific, firstly, we define new conflict distances and conflict function for q-ROFI system using aggregation functions and weight determination method, and prove some of their properties. On this basis, the concepts of three-level of contention set and agent set, a trisection of conflict set under individual contention and contention set, and maximum doughty coalition of q-ROFI are introduced. Secondly, after introducing the rough approximation threshold calculation method on the basis of standard evaluation set, to find the optimal viable strategy under the given q-ROFI, we calculate and sort the score function by the upper and lower approximation operators in the proposed q-rung orthopair fuzzy decision-theoretic rough sets (q-ROFDTRSs) model. Thirdly, we use the proposed model to study a land-use conflict case in a metropolitan area to verify the feasibility. Finally, from sensitivity and comparative analysis, we verify the stability and validity of the q-ROFDTRSs model.

Development of the ELECTRE Method Under Pythagorean Fuzzy Sets Based on Existing Correlation Coefficients for Cotton Fabric Selection

ABSTRACT Cotton fabric selection is a challenging task in the garment product design and development process, and the selection of optimal alternative under the presence of multiple decision criteria becomes complex, and hence it is considered as a multi-criteria decision-making (MCDM) problem. In addition, the selection process involves fuzziness and uncertainty. In this study, Pythagorean fuzzy sets (PFSs) are introduced to handle uncertain information. Elimination and choice translating reality (ELECTRE) is a well-known outranking method for solving MCDM problems. Therefore, we extend the ELECTRE method under the PFS environment, and a correlation-based closeness coefficient is proposed to compare Pythagorean fuzzy numbers (PFNs). This paper applies the proposed PF-ELECTRE approach in solving a practical case involving the ranking cotton fabrics. To exhibit the superiority and robustness of the suggested method, sensitivity analysis is performed to examine the impacts of weights variation, as well as a comparative analysis is carried out between the PF-ELECTRE with several existing MCDM methods. The research contributes to the advancement and development of outranking MCDM methods through a novel PF-ELECTRE approach that utilizes the weighted correlation coefficient. Moreover, the developed method can obtain reliable results and can be used to other textile domains.

Multi-Criteria Decision-Making with Novel Pythagorean Fuzzy Aggregation Operators

Unpredictability and fuzziness coexist in decision-making analysis due to the complexity of the decision-making environment. “Pythagorean fuzzy numbers” (PFNs) outperform “intuitionistic fuzzy numbers” (IFNs) when dealing with unclear data. The “Pythagorean fuzzy set” (PFS) is a useful tool because it removes the restriction that the sum of membership degrees be less than or equal to one by substituting the square sum for the sum of membership degrees. This study proposes two aggregating operators (AOs). The recommended operators outperform the already specified PFN operators. The proposed operator is utilised in the multicriteria decision-making process to identify the best candidate for instruction (MCDM).