Multiattribute decision-making under Fermatean fuzzy bipolar soft framework

Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure

To deal with situations involving uncertainty, Fermatean fuzzy sets are more effective than Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. Applications for fuzzy similarity measures can be found in a wide range of fields, including clustering analysis, classification issues, medical diagnosis, etc. The computation of the weights of the criteria in a multi-criteria decision-making problem heavily relies on fuzzy entropy measurements. In this paper, we employ t-conorms to suggest various Fermatean fuzzy similarity measures. We have also discussed all of their interesting characteristics. Using the suggested similarity measurements, we have created some new entropy measures for Fermatean fuzzy sets. By using numerical comparison and linguistic hedging, we have established the superiority of the suggested similarity metrics and entropy measures over the existing measures in the Fermatean fuzzy environment. The usefulness of the proposed Fermatean fuzzy similarity measurements is shown by pattern analysis. Last but not least, a novel multi-attribute decision-making approach is described that tackles a significant flaw in the order preference by similarity to the ideal solution, a conventional approach to decision-making, in a Fermatean fuzzy environment.

First Zagreb index of fuzzy transformation graphs

The first Zagreb index is equal to the sum of the squares of the degrees at each vertex of G. In this study, we create four distinct types of fuzzy transformation graphs and investigate the fundamental characteristics shared by them. Additionally, upper bounds on the first Zagreb index of fuzzy transformation graphs in terms of fuzzy graph G elements have been discovered.

An Innovative Hybrid Multi-Criteria Decision-Making Approach under Picture Fuzzy Information

These days, multi-criteria decision-making (MCDM) approaches play a vital role in making decisions considering multiple criteria. Among these approaches, the picture fuzzy soft set model is emerging as a powerful mathematical tool for handling various kinds of uncertainties in complex real-life MCDM situations because it is a combination of two efficient mathematical tools, namely, picture fuzzy sets and soft sets. However, the picture fuzzy soft set model is deficient; that is, it fails to tackle information symmetrically in a bipolar soft environment. To overcome this difficulty, in this paper, a model named picture fuzzy bipolar soft sets (PRFBSSs, for short) is proposed, which is a natural hybridization of two models, namely, picture fuzzy sets and bipolar soft sets. An example discussing the selection of students for a scholarship is added to illustrate the initiated model. Some novel properties of PRFBSSs such as sub-set, super-set, equality, complement, relative null and absolute PRFBSSs, extended intersection and union, and restricted intersection and union are investigated. Moreover, two fundamental operations of PRFBSSs, namely, the AND and OR operations, are studied. Thereafter, some new results (De Morgan’s law, commutativity, associativity, and distributivity) related to these proposed notions are investigated and explained through corresponding numerical examples. An algorithm is developed to deal with uncertain information in the PRFBSS environment. To show the efficacy and applicability of the initiated technique, a descriptive numerical example regarding the selection of the best graphic designer is explored under PRFBSSs. In the end, concerning both qualitative and quantitative perspectives, a detailed comparative analysis of the initiated model with certain existing models is provided.

Online Teaching Quality Evaluation of Business Statistics Course Utilizing Fermatean Fuzzy Analytical Hierarchy Process with Aggregation Operator

Due to the full-scale outbreak of COVID-19, many universities have adopted the way of online teaching to ensure the orderly development of teaching plans and teaching contents. However, whether online and offline teaching can develop homogeneously and how to ensure the teaching effect is a major challenge for colleges and universities. Therefore, it is urgent to construct a reasonable index system and evaluation approach for the quality of network teaching. Combined with the influencing factors and characteristics of online teaching, this study first puts forward a multi-index evaluation index system and then proposes a novel evaluation method for online teaching based on the analytical hierarchy process (AHP) and Dombi weighted partitioned Muirhead Mean (PMM) operator under Fermatean fuzzy (FF) environment. This presented method not only adapts to changeable evaluation information but also handles the elusive interrelationships among indexes, realizing the flexibility and comprehensiveness both in form and in the polyaddition process. The applicability and feasibility of this presented method are then discussed through the practical online teaching quality evaluation of a business statistics course case, and a group of tentative about the sensitivity analysis and comparative analysis further demonstrates the effectiveness and flexibility of the proposed method.

Resource Profiling and Performance Modeling for Distributed Scientific Computing Environments

Scientific applications often require substantial amount of computing resources for running challenging jobs potentially consisting of many tasks from hundreds of thousands to even millions. As a result, many institutions collaborate to solve large-scale problems by creating virtual organizations (VOs), and integrate hundreds of thousands of geographically distributed heterogeneous computing resources. Over the past decade, VOs have been proven to be a powerful research testbed for accessing massive amount of computing resources shared by several organizations at almost no cost. However, VOs often suffer from providing exact dynamic resource information due to their scale and autonomous resource management policies. Furthermore, shared resources are inconsistent, making it difficult to accurately forecast resource capacity. An effective VO’s resource profiling and modeling system can address these problems by forecasting resource characteristics and availability. This paper presents effective resource profiling and performance prediction models including Adaptive Filter-based Online Linear Regression (AFOLR) and Adaptive Filter-based Moving Average (AFMV) based on the linear difference equation combining past predicted values and recent profiled information, which aim to support large-scale applications in distributed scientific computing environments. We performed quantitative analysis and conducted microbenchmark experiments on a real multinational shared computing platform. Our evaluation results demonstrate that the proposed prediction schemes outperform well-known common approaches in terms of accuracy, and actually can help users in a shared resource environment to run their large-scale applications by effectively forecasting various computing resource capacity and performance.

Evaluation of employee green behavior ability based on a fuzzy BWM-VIKOR approach

As a core resource of the company, employees play a major role to implement green management related behaviors in enterprises. Management department is also working hard to improve the ability of employees to perform these green behaviors for the company’s sustainable development capabilities. This study is the first effort that evaluation of effect factors of employee green behavior ability (EGBA) by intuitionistic fuzzy number-best worst method (IFN-BWM). To reach the study objective, a total of four criteria and twenty-seven sub-criteria for evaluation of EGBA are collected from the existing literatures. Subsequently, the PFN-VIKOR methodology (Pythagorean Fuzzy Number-Visekriterijumska Optimizacija I Kom-promisno Resenje) is proposed to rank EGBA levels. The results of this study show that employee self-efficacy and employee initiative in learning relevant green knowledge are important factors to enhance EGBA. Moreover, findings confirm that extended fuzzy semantic values and novel algorithm can accurately measure the decision makers’ mind and improve the accuracy of evaluation. This study also provides a framework for managers to evaluate their employee’ green behavior ability.

Multicriteria decision-making based on distance measures and knowledge measures of Fermatean fuzzy sets

Fermatean fuzzy sets are more powerful than fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets in handling various problems involving uncertainty. The distance measures in the fuzzy and non-standard fuzzy frameworks have got their applicability in various areas such as pattern analysis, clustering, medical diagnosis, etc. Also, the fuzzy and non-standard fuzzy knowledge measures have played a vital role in computing the criteria weights in the multicriteria decision-making problems. As there is no study concerning the distance and knowledge measures of Fermatean fuzzy sets, so in this paper, we propose some novel distance measures for Fermatean fuzzy sets using t-conorms. We also discuss their various desirable properties. With the help of suggested distance measures, we introduce some knowledge measures for Fermatean fuzzy sets. Through numerical comparison and linguistic hedges, we establish the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean/Fermatean fuzzy setting. At last, we demonstrate the application of the suggested measures in pattern analyis and multicriteria decision-making.

Selection of a Wheat Harvester according to Qualitative and Quantitative Criteria

With the development of technology and the expansion of agricultural machinery diversity, the need for an appropriate group decision-making system has arisen. The increasing number of criteria and alternatives complicates the decision-making process. Moreover, the uncertainty in the data leads to more complexity in the decision. To select a wheat combine, multiple quantitative criteria were considered, such as the grain tank, rated horsepower, speed draining, and cleaning, along with qualitative criteria, including the level of harvest or harvest losses, fuel consumption, comfort and safety, the ability to harvest wet and lying, and price. To rank seven alternatives through the MULTIMOORA (multi-objective optimization on the basis of ratio analysis) method, a group decision making model applied for qualitative criteria and the Simos method was used for weighting as a subsidiary of mental groups. The performance of the hybrid model was confirmed by experts in agricultural machinery. The consensus model, when used in the process of group decision making, reduces the conflict level of decision-makers regarding criteria, alternatives and the decision matrix. The results of this research will be beneficial for industrial agriculture, especially wheat combine buyers. The proposed explainable consensus model can be used to construct decision support systems and can be applied to various decision-making problems owing to operability and easiness.

Group decision-making with Fermatean fuzzy soft expert knowledge

With the rapid growth of population, the global impact of solar technology is increasing by the day due to its advantages over other power production technologies. Demand for solar panel systems is soaring, thus provoking the arrival of many new manufacturers. Sale dealers or suppliers face an uncertain problem to choose the most adequate technological solution. To effectively address such kind of issues, in this paper we propose the Fermatean fuzzy soft expert set model by combining Fermatean fuzzy sets and soft expert sets. We describe this hybrid model with numerical examples. From a theoretical standpoint, we demonstrate some essential properties and define operations for this setting. They comprise the definitions of complement, union and intersection, the OR operation and the AND operation. Concerning practice in this new environment, we provide an algorithm for multi-criteria group decision making whose productiveness and authenticity is dutifully tested. We explore a practical application of this approach (that is, the selection of a suitable brand of solar panel system). Lastly, we give a comparison of our model with certain related mathematical tools, including fuzzy and intuitionistic fuzzy soft expert set models.

A Novel MADM Framework under q-Rung Orthopair Fuzzy Bipolar Soft Sets

In many real-life problems, decision-making is reckoned as a powerful tool to manipulate the data involving imprecise and vague information. To fix the mathematical problems containing more generalized datasets, an emerging model called q-rung orthopair fuzzy soft sets offers a comprehensive framework for a number of multi-attribute decision-making (MADM) situations but this model is not capable to deal effectively with situations having bipolar soft data. In this research study, a novel hybrid model under the name of q-rung orthopair fuzzy bipolar soft set (q-ROFBSS, henceforth), an efficient bipolar soft generalization of q-rung orthopair fuzzy set model, is introduced and illustrated by an example. The proposed model is successfully tested for several significant operations like subset, complement, extended union and intersection, restricted union and intersection, the ‘AND’ operation and the ‘OR’ operation. The De Morgan’s laws are also verified for q-ROFBSSs regarding above-mentioned operations. Ultimately, two applications are investigated by using the proposed framework. In first real-life application, the selection of land for cropping the carrots and the lettuces is studied, while in second practical application, the selection of an eligible student for a scholarship is discussed. At last, a comparison of the initiated model with certain existing models, including Pythagorean and Fermatean fuzzy bipolar soft set models is provided.