Risk evaluation in failure modes and effects analysis: hybrid TOPSIS and ELECTRE I solutions with Pythagorean fuzzy information

Extension of correlation coefficient based TOPSIS technique for interval-valued Pythagorean fuzzy soft set: A case study in extract, transform, and load techniques

Correlation is an essential statistical concept for analyzing two dissimilar variables' relationships. Although the correlation coefficient is a well-known indicator, it has not been applied to interval-valued Pythagorean fuzzy soft sets (IVPFSS) data. IVPFSS is a generalized form of interval-valued intuitionistic fuzzy soft sets and a refined extension of Pythagorean fuzzy soft sets. In this study, we propose the correlation coefficient (CC) and weighted correlation coefficient (WCC) for IVPFSS and examine their necessary properties. Based on the proposed correlation measures, we develop a prioritization technique for order preference by similarity to the ideal solution (TOPSIS). We use the Extract, Transform, and Load (ETL) software selection as an example to demonstrate the application of these measures and construct a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) model. The method investigates the challenge of optimizing ETL software selection for business intelligence (BI). This study offers to illuminate the significance of using correlation measures to make decisions in uncertain and complex settings. The multi-attribute decision-making (MADM) approach is a powerful instrument with many applications. This expansion is predicted to conclude in a more reliable decision-making structure. Using a sensitivity analysis, we contributed empirical studies to determine the most significant decision processes. The proposed algorithm's productivity is more consistent than prevalent models in controlling the adequate conformations of the anticipated study. Therefore, this research is expected to contribute significantly to statistics and decision-making.

A decision-making technique under interval-valued Fermatean fuzzy Hamacher interactive aggregation operators

The evolution of a novel technique to handle multi-attribute decision-making (MADM) problems under interval-valued Fermatean fuzzy numbers is the main motivation of this paper. We aim to introduce several initiative aggregation operators (AOs), including Hamacher interactive weighted averaging, Hamacher interactive ordered weighted averaging, Hamacher interactive hybrid weighted averaging operations, etc., to acquire our desired outcomes. Then, the distinguished characteristics of these AOs are investigated. Furthermore, the suggested AOs are carried out to build a technique to MADM issues using interval-valued Fermatean fuzzy information. A case study of mine emergency plan selection is then narrated to elaborate the practicality and effectiveness of the developed method. The influence of parametric values on decision-making outcomes is investigated considering the distinct values of parameter. After discussing the developed work and seeing its applications, we come across with the conclusion that the dominant privilege of adaptation of the above-mentioned AOs is situated in the fact that these operators allow a progressively complete approach on the matters to decision-makers. Hence, the method recommended in this study offers progressively wide, enhanced accuracy and actual outcomes when compared with the prevailing associated strategies. Therefore, this technique plays a vital role in actual-life MADM problems.

Failure Mode and Effects Analysis on the Air System of an Aero Turbofan Engine Using the Gaussian Model and Evidence Theory

Failure mode and effects analysis (FMEA) is a proactive risk management approach. Risk management under uncertainty with the FMEA method has attracted a lot of attention. The Dempster-Shafer (D-S) evidence theory is a popular approximate reasoning theory for addressing uncertain information and it can be adopted in FMEA for uncertain information processing because of its flexibility and superiority in coping with uncertain and subjective assessments. The assessments coming from FMEA experts may include highly conflicting evidence for information fusion in the framework of D-S evidence theory. Therefore, in this paper, we propose an improved FMEA method based on the Gaussian model and D-S evidence theory to handle the subjective assessments of FMEA experts and apply it to deal with FMEA in the air system of an aero turbofan engine. First, we define three kinds of generalized scaling by Gaussian distribution characteristics to deal with potential highly conflicting evidence in the assessments. Then, we fuse expert assessments with the Dempster combination rule. Finally, we obtain the risk priority number to rank the risk level of the FMEA items. The experimental results show that the method is effective and reasonable in dealing with risk analysis in the air system of an aero turbofan engine.

A developed gained and lost dominance score method for risk prioritization in FMEA with Fermatean fuzzy information

Failure mode and effect analysis (FMEA) is one of the most effective means for potential systematic risk assessment in a real work environment. Nevertheless, the traditional FMEA approach has been extensively criticized for many deficiencies in coping with risk evaluation and prioritization problems under inter-uncertain environments. To overcome the limitations, in this paper, a synthesized risk priority calculation framework is proposed for FMEA by combining the gained and lost dominance score (GLDS) method, the combination ordered weighted averaging (C-OWA) operator, and Fermatean fuzzy set (FFS). Firstly, we use FFS to express the experts’ uncertain risk evaluation information which can depict the fuzziness and ambiguity of the information. Secondly, the C-OWA operator combined with FFS is introduced to build the group risk matrix which can provide a more reasonable risk analysis result. Then, the developed GLDS method with FFS is presented to calculate the risk priority of each failure mode which takes both individual and group risk attitudes into consideration. Finally, a medical device risk analysis case is introduced to demonstrate the proposed FMEA framework. We also perform comparison analyses to confirm the effectiveness and rationality of the hybrid risk prioritization framework for FMEA under a complex and uncertain situation.

Multi-attribute decision-making for electronic waste recycling using interval-valued Fermatean fuzzy Hamacher aggregation operators

The utilization of electrical and electronics equipments in waste recycling has become a paramount for various countries. The waste electrical and electronics equipment (WEEE) recyclers own a crucial position in the environmental growth of a country as they help to minimize the carbon emissions during the recycling of WEEE in the most eco-friendly way. Therefore, the selection and assessment of an appropriate WEEE recycling partner has become a most important part of DM (decision-making) applications. The collusion of numerous quantitative and qualitative factors makes the recycling partner selection problem, a multifaced and significant decision for the managerial experts. The main objective of this work is to propose MADM (multi-attribute decision-making) techniques to evaluate the WEEE recycling partners under interval-valued Fermatean fuzzy (IVFF) information. In this regard, certain Hamacher AOs (aggregation operators) are proposed to develop the required DM method. These AOs include Hamacher weighted averaging, ordered weighted averaging, weighted geometric, ordered weighted geometric, generalized Einstein weighted averaging, generalized Einstein ordered weighted averaging, generalized Einstein weighted geometric, etc. Then, these averaging operators are utilized to come up with a MADM techniques under IVFF environment. Furthermore, the constructed technique is applied to a case study in China to incorporate with the e-waste recycling partner selection problem. Moreover, a brief comparison of the proposed with is presented with various existing techniques to manifest the productivity and coherence of the proposed model. Finally, the accuracy and consistency of results shows that the proposed technique is fully compatible and applicable to handle any MADM problem.

Evaluation of product conceptual design based on Pythagorean fuzzy set under big data environment

The concept design evaluation phase of the new product launch is extremely important. However, current evaluation information relies mainly on the a priori knowledge of decision makers and is subjective and ambiguous. For this reason, a conceptual design solution decision model based on Pythagorean fuzzy sets in a big data environment is proposed. Firstly, we use the ability of big data to mine and analyze information to construct a new standard for product concept design evaluation in the big data environment. Secondly, the Pythagorean fuzzy set (PFS), Analytic Hierarchy Process (AHP), and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are integrated into a decision model. AHP, extended by the Pythagorean fuzzy set, is used to determine the weights of new conceptual design criteria in a big data environment. The Pythagorean fuzzy TOPSIS is used to prioritize alternative conceptual design solutions. The feasibility of the approach is proven with a practical case, the generalizability of the method is confirmed with two descriptive digital cases, and the reliability, validity, and superiority of the process are demonstrated with sensitivity analysis, comparative analysis, and computational complexity analysis.

q-Rung Orthopair Probabilistic Hesitant Fuzzy Rough Aggregation Information and Their Application in Decision Making

The core contribution of this study is to develop a novel generalized idea of q-rung orthopair probabilistic hesitant fuzzy rough set (q-ROPHFRS) which is hybrid structure of the q-rung orthopair fuzzy set, probabilistic hesitant fuzzy set, and rough set. The q-ROPHFRS covers the positive and negative membership grades in the form of probabilistic hesitant fuzzy rough information to address the uncertainties in real-world decision-making problems. This paper proposes a list of novel q-rung orthopair probabilistic hesitant fuzzy rough averaging/geometric aggregation operators to handle the uncertainty effectively and reliably to aggregate the uncertain information under q-ROPHFRSs. Several interesting elementary properties have been investigated. Furthermore, a novel multi-attribute decision-making approach based on the proposed aggregation information is presented. Finally, a numerical application regarding selecting a medical oxygen supplier to the hospital is presented to illustrate the consistency of the developed decision-making technique. The comparison of the proposed technique with q-rung orthopair probabilistic hesitant fuzzy rough TOPSIS shows that the proposed multi-criteria decision-making methodology is reliable and effective in addressing the uncertainty in real-world decision-making problems.

Alternative Water Resources Selection to Supply Drinking Water in Flood Disasters by Multicriteria Decision-Making Techniques (DANP and VIKOR)

Background

Emergency is generally caused by natural disaster and infectious disease outbreaks, or it is man-made. Floods are natural phenomena that generally appear in multiple parts of the world. Flooding is one of the most destructive naturally occurring environmental hazards and can cause public, infrastructural, and environmental damage. The purpose of this study is to select alternative water resources for supplying Bandar Abbas in flood disasters by multicriteria decision-making techniques.

Methods

Information required includes possible water resources alternative for flood, quantitative and qualitative characteristics of the water resources, climatic circumstances, and demographic information used in organizations data and previous studies. After selecting and proposing water resources alternative for Bandar Abbas in flood, the subcriteria were weighed applying DANP (DEMATEL-ANP) techniques and water resources were prioritized with the VIKOR technique. According to the network structure and internal and external dependence of the criteria and subcriteria, the advantages of DANP in calculating weights have been used to adapt to more real-world problems. The VIKOR technique was developed for multicriteria optimization of complex systems.

Results

After reviewing and extracting the criteria from various studies, 9 main criteria and 44 subcriteria were defined to select water resources in disasters and emergencies. According to field studies and related organizations' information, the proposed water resources for Bandar Abbas to use in flood disasters include humidity, sea (Persian Gulf), Sarkhoon plain, and wastewater treatment plant of Bandar Abbas.

Conclusion

Results showed that the optimal water resources for Bandar Abbas in flood disasters are the sea and wastewater treatment plant effluent (after advanced treatment). The study proposed appropriate model to select optimal water resources for various natural disasters in different geographical areas. This model can help officials and decision-makers to plan for drinking water supply from disaster-prone areas before disasters occur.

Modified WASPAS method based on the pythagorean fuzzy frank interaction aggregation operators and its application in cloud computing product selection

Frank operations are more robust and flexible than other algebraic operations, and interaction operational laws consider interrelationship between membership functions in Pythagorean fuzzy number. Combining the strengths of both, we define some Frank interaction operational laws of Pythagorean fuzzy numbers for the first time in this article. Based on this, the Pythagorean fuzzy Frank interaction weighted averaging and geometric operators are developed. Meanwhile, we discuss their basic properties and related special cases. Furthermore, a novel multiple attribute decision-making framework is established based on the modified WASPAS method in Pythagorean fuzzy environment. The proposed method is implemented in a real-case study of cloud computing product selection to test the proposed methodology’s plausibility. A sensitivity analysis is conducted to verify our method’s reliability, and the effectiveness and superiority are illustrated by comparative study.

Models for MAGDM with dual hesitant q-rung orthopair fuzzy 2-tuple linguistic MSM operators and their application to COVID-19 pandemic

In this article, we introduce dual hesitantq -rung orthopair fuzzy 2-tuple linguistic set (DHq-ROFTLS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into dual hesitantq -rung orthopair fuzzy set (DHq-ROFS). DHq-ROFTLS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the DHq-ROFTL weighted averaging (DHq-ROFTLWA) operator and the DHq-ROFTL weighted geometric (DHq-ROFTLWG) operator are presented to fuse the DHq-ROFTL numbers (DHq-ROFTLNs). As Maclaurin symmetric mean (MSM) aggregation operator is a useful tool to model the interrelationship between multi-input arguments, we generalize the traditional MSM to aggregate DHq-ROFTL information. Firstly, the DHq-ROFTL Maclaurin symmetric mean (DHq-ROFTLMSM) and the DHq-ROFTL weighted Maclaurin symmetric mean (DHq-ROFTLWMSM) operators are proposed along with some of their desirable properties and some special cases. Further, the DHq-ROFTL dual Maclaurin symmetric mean (DHq-ROFTLDMSM) and weighted dual Maclaurin symmetric mean (DHq-ROFTLWDMSM) operators with some properties and cases are presented. Moreover, the assessment and prioritizing of the most important aspects in multiple attribute group decision-making (MAGDM) problems is analysed by an extended novel approach based on the proposed aggregation operators under DHq-ROFTL framework. At long last, a numerical model is provided for the selection of adequate medication to control COVID-19 outbreaks to demonstrate the use of the generated technique and exhibit its adequacy. Finally, to analyse the advantages of the proposed method, a comparison analysis is conducted and the superiorities are illustrated.

A wind power plant site selection algorithm based on q-rung orthopair hesitant fuzzy rough Einstein aggregation information

Wind power is often recognized as one of the best clean energy solutions due to its widespread availability, low environmental impact, and great cost-effectiveness. The successful design of optimal wind power sites to create power is one of the most vital concerns in the exploitation of wind farms. Wind energy site selection is determined by the rules and standards of environmentally sustainable development, leading to a low, renewable energy source that is cost effective and contributes to global advancement. The major contribution of this research is a comprehensive analysis of information for the multi-attribute decision-making (MADM) approach and evaluation of ideal site selection for wind power plants employing q-rung orthopair hesitant fuzzy rough Einstein aggregation operators. A MADM technique is then developed using q-rung orthopair hesitant fuzzy rough aggregation operators. For further validation of the potential of the suggested method, a real case study on wind power plant site has been given. A comparison analysis based on the unique extended TOPSIS approach is presented to illustrate the offered method’s capability. The results show that this method has a larger space for presenting information, is more flexible in its use, and produces more consistent evaluation results. This research is a comprehensive collection of information that should be considered when choosing the optimum site for wind projects.

Waste Clothing Recycling Channel Selection Using a CoCoSo-D Method Based on Sine Trigonometric Interaction Operational Laws with Pythagorean Fuzzy Information

Under the influence of circular economy theory, waste clothing recycling has been widely studied in the resource sector, and the waste clothing recycling channel (WCRC) is the vital link that affects the recycling efficiency of waste clothing. How to select the optimal WCRC is considered a typical multiple attribute group decision-making (MAGDM) problem. In this article, we develop sine trigonometric interaction operational laws (IOLs) (STIOLs) using Pythagorean fuzzy information. The sine trigonometric interaction Pythagorean fuzzy weighted averaging (STI-PyFWA) and sine trigonometric interaction Pythagorean fuzzy weighted geometric (STI-PyFWG) operators are advanced, and their several desirable properties are discussed. Further, we build a MAGDM framework based on the modified Pythagorean fuzzy CoCoSo (Combined Compromise Solution) method to solve the WCRC selection problem. The combined weight of attributes is determined, and the proposed aggregation operators (AOs) are applied to the CoCoSo method. A Pythagorean fuzzy distance measure is used to achieve the defuzzification of aggregation strategies. Finally, we deal with the WCRC selection problem for a sustainable environment by implementing the proposed method and performing sensitivity analysis and comparative study to validate its effectiveness and superiority.

A New Entropy Measurement for the Analysis of Uncertain Data in MCDA Problems Using Intuitionistic Fuzzy Sets and COPRAS Method

In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance. The Complex Proportional Assessment (COPRAS) method identifies the preferences and ranking of decisional variants. It also allows for a more comprehensive analysis of complex decision-making problems, where many opposite criteria are observed. This approach allows us to minimize cost and maximize profit in the finally chosen decision (alternative). This paper presents a new entropy measurement for fuzzy intuitionistic sets and an application example using the IFS COPRAS method. The new entropy method was used in the decision-making process to calculate the objective weights. In addition, other entropy methods determining objective weights were also compared with the proposed approach. The presented results allow us to conclude that the new entropy measure can be applied to decision problems in uncertain data environments since the proposed entropy measure is stable and unambiguous.

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.

Degree based models of granular computing under fuzzy indiscernibility relations

The aim of this research work is to put forward fuzzy models of granular computing based on fuzzy relation and fuzzy indiscernibility relation. Thanks to fuzzy information granulation to provide multi-level visualization of problems that include uncertain information. In such a granulation, fuzzy sets and fuzzy graphs help us to represent relationships among granules, groups or clusters. We consider the fuzzy indiscernibility relation of a fuzzy knowledge representation system (I). We describe the granular structures of I, including discernibility, core, reduct and essentiality of I. Then we examine the contribution of these structures to granular computing. Moreover, we introduce certain granular structures using fuzzy graph models and discuss degree based model of fuzzy granular structures. Granulation of network models based on fuzzy information effectively handles real life data which possesses uncertainty and vagueness. Finally, certain algorithms of proposed models are developed and implemented to solve real life problems involving uncertain granularities. We also present a concise comparison of the models developed in our work with other existing methodologies.

An algorithm to compute the strength of competing interactions in the Bering Sea based on pythagorean fuzzy hypergraphs

The networks of various problems have competing constituents, and there is a concern to compute the strength of competition among these entities. Competition hypergraphs capture all groups of predators that are competing in a community through their hyperedges. This paper reintroduces competition hypergraphs in the context of Pythagorean fuzzy set theory, thereby producing Pythagorean fuzzy competition hypergraphs. The data of real-world ecological systems posses uncertainty, and the proposed hypergraphs can efficiently deal with such information to model wide range of competing interactions. We suggest several extensions of Pythagorean fuzzy competition hypergraphs, including Pythagorean fuzzy economic competition hypergraphs, Pythagorean fuzzy row as well as column hypergraphs, Pythagorean fuzzy k-competition hypergraphs, m-step Pythagorean fuzzy competition hypergraphs and Pythagorean fuzzy neighborhood hypergraphs. The proposed graphical structures are good tools to measure the strength of direct and indirect competing and non-competing interactions. Their aptness is illustrated through examples, and results support their intrinsic interest. We propose algorithms that help to compose some of the presented graphical structures. We consider predator-prey interactions among organisms of the Bering Sea as an application: Pythagorean fuzzy competition hypergraphs encapsulate the competing relationships among its inhabitants. Specifically, the algorithm which constructs the Pythagorean fuzzy competition hypergraphs can also compute the strength of competing and non-competing relations of this scenario.

Approach-oriented and avoidance-oriented measures under complex Pythagorean fuzzy information and an area-based model to multiple criteria decision-aiding systems

The purpose of this paper is to evolve a novel area-based Pythagorean fuzzy decision model via an approach-oriented measure and an avoidance-oriented measure in support of multiple criteria decision analysis involving intricate uncertainty of Pythagorean fuzziness. Pythagorean membership grades embedded in a Pythagorean fuzzy set is featured by tensible functions of membership, non-membership, indeterminacy, strength, and direction, which delivers flexibility and adaptability in manipulating higher-order uncertainties. However, a well-defined ordered structure is never popular in real-life issues, seldom seen in Pythagorean fuzzy circumstances. Consider that point operators can make a systematic allocation of the indeterminacy composition contained in Pythagorean fuzzy information. This paper exploits the codomains of the point operations (i.e., the quantities that express the extents of point operators) to launch new measurements of approach orientation and avoidance orientation for performance ratings. This paper employs such measurements to develop an area-based performance index and an area-based comprehensive index for conducting a decision analysis. The applications and comparative analyses of the advanced area-based approach to some decision-making problems concerning sustainable recycling partner selection, company investment decisions, stock investment decisions, and working capital financing decisions give support to methodological advantages and practical effectiveness.

Multiple attribute group decision-making based on cubic linguistic Pythagorean fuzzy sets and power Hamy mean

The linguistic Pythagorean fuzzy sets (LPFSs), which employ linguistic terms to express membership and non-membership degrees, can effectively deal with decision makers’ complicated evaluation values in the process of multiple attribute group decision-making (MAGDM). To improve the ability of LPFSs in depicting fuzzy information, this paper generalized LPFSs to cubic LPFSs (CLPFSs) and studied CLPFSs-based MAGDM method. First, the definition, operational rules, comparison method and distance measure of CLPFSs are investigated. The CLPFSs fully adsorb the advantages of LPFSs and cubic fuzzy sets and hence they are suitable and flexible to depict attribute values in fuzzy and complicated decision-making environments. Second, based on the extension of power Hamy mean operator in CLPFSs, the cubic linguistic Pythagorean fuzzy power average operator, the cubic linguistic Pythagorean fuzzy power Hamy mean operator as well as their weighted forms were introduced. These aggregation operators can effectively and comprehensively aggregate attribute values in MAGDM problems. Besides, some important properties of these operators were studied. Finally, we presented a new MAGDM method based on CLPFSs and their aggregation operators. Illustrative examples and comparative analysis are provided to show the effectiveness and advantages of our proposed decision-making method.