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Single-valued neutrosophic sets (SVNSs) are efficient models to address the complexity issues potentially with three components, namely indeterminacy, truthness and falsity. Taking advantage of SVNSs, this paper introduces some new aggregation operators (AOs) for information fusion of single-valued neutrosophic numbers (SVNNs) to meet multi-criteria group decision-making (MCGDM) challenges.

Einstein operators are well-known AOs for smooth approximation, and prioritized operators are suitable to take advantage of prioritized relationships among multiple criteria. Motivated by the features of these operators, new hybrid aggregation operators are proposed named as “single-valued neutrosophic Einstein prioritized weighted average (SVNEPWA) operator” and “single-valued neutrosophic Einstein prioritized weighted geometric (SVNEPWG) operators.” These hybrid aggregation operators are more efficient and reliable for information aggregation.

A robust approach for MCGDM problems is developed to take advantage of newly developed hybrid operators. The effectiveness of the proposed MCGDM method is demonstrated by numerical examples. Moreover, a comparative analysis and authenticity analysis of the suggested MCGDM approach with existing approaches are offered to examine the practicality, validity and superiority of the proposed operators.

The study reveals that by choosing a suitable AO as per the choice of the expert, it will provide a wide range of compromise solutions for the decision-maker.

The attributes that influence the selection of applicants and the relevant crediting decisions are naturally distinguished by interactions and interdependencies. A new method of possibilistic discrimination analysis (MPDA) was developed for the second stage to address this phenomenon. The method generates positive and negative discrimination measures for each alternative applicant in relation to a particular attribute. The obtained discrimination pair reflects the interaction of attributes and represents intuitionistic fuzzy numbers (IFNs). For the aggregation of applicant's discrimination intuitionistic fuzzy assessments (with respect to attributes), new intuitionistic aggregation operators, such as AsP-IFOWA and AsP-IFOWG, are defined and studied. The new operators are certain extensions of the well-known Choquet integral and Yager OWA operators. The extensions, in contrast to the Choquet aggregation, take into account all possible interactions of the attributes by introducing associated probabilities of a fuzzy measure.

For optimal planning of investments distribution and decreasing of credit risks, it is crucial to have selected projects ranked within deeply detailed investment model. To achieve this, a new approach developed in this article involves three stages. The first stage is to reduce a possibly large number of applicants for credit, and here, the method of expertons is used. At the second stage, a model of improved decisions is built, which reduces the risks of decision making. In this model, as it is in multi-attribute decision-making (MADM) + multi-objective decision-making (MODM), expert evaluations are presented in terms of utility, gain, and more. At the third stage, the authors construct the bi-criteria discrete intuitionistic fuzzy optimization problem for making the most profitable investment portfolio with new criterion: 1) Maximization of total ranking index of selected applicants' group and classical criterion and 2) Maximization of total profit of selected applicants' group.

The example gives the Pareto fronts obtained by both new operators, the Choquet integral and Yager OWA operators also well-known TOPSIS approach, for selecting applicants and awarding credits. For a fuzzy measure, the possibility measure defined on the expert evaluations of attributes is taken.

The comparative analysis identifies the applicants who will receive the funding sequentially based on crediting resources and their requirements. It has become apparent that the use of the new criterion has given more credibility to applicants in making optimal credit decisions in the environment of extended new operators, where the phenomenon of interaction of all attributes was also taken into account.

This paper aims to carry out experimental investigations highlighting the role of melt flow index (MFI) in fused deposition modelling (FDM) process by varying the proportion of the Fe powder which is being used as a filler material. An attempt has been made to standardize MFI of Nylon6-Fe composite material to be used as hybrid FDM filament.

In this research work, it is proposed to make a suitable blend of composite material for FDM filament which can be used directly for rapid tooling applications. Three controllable parameters (namely, composition/proportion of the filler for hybrid filament, extrusion temperature and extrusion load) were studied by using Taguchi L9 orthogonal array (O.A.) MFI which is an indication of flowability has been selected as output parameter.

MFI of hybrid composite filament material has been studied, and Taguchi’s L9 O.A. was applied under both the conditions of lower the better type and larger the better type. It is observed that the contribution of the extrusion load, extrusion temperature and proportion of the filler material is almost similar, whether lower the better type situation is considered or larger the better type is considered. Further, an attempt has been made to standardize the MFI of Nylon6-Fe composite material for industrial applications, as no standard is available for composites (presently, ASTM-D-1238-95 standard is being used for plastic based materials only).

In recent past, researchers have studied and analysed the flow of the material through the nozzle of the FDM machine, but very little work has been reported on study of the flow characteristics of filament material before the composite material is fed into the machine. This research can open new avenues in the field of MFI and deals with comparison of MFI of the existing FDM feedstock material with the new composite material. The developed feedstock material is ferromagnetic in nature and can find wide variety of industrial applications.

The paper aims to introduce a novel concept to solve the bi-level multi-criteria nonlinear fractional programming (BL-MCNFP) problems. Bi-level programming problem (BLPP) is rigorously flourished and studied by several researchers, which deals with decentralized decisions by comprising a sequence of two optimization problems, namely upper and lower-level problems. However, on the other hand, many real-world decision-making problems involve multiple objectives with fraction aspects, called fractional programming problems that reflect technical and economic performance.

This paper introduces a VIKOR (“VlseKriterijumska Optimizacija I Kompromisno Resenje”) approach to solve the BL-MCNFP problem. In this approach, an aggregating function based on L_P metrics is formulated on the basis of the “closeness” scheme from the “ideal” solution. The three steps perform the solution process: First, a new concept is attempted to minimize and maximize of the numerators and denominators from their respective ideal solutions and anti-ideal values simultaneously. Second, for each level, the K-dimensional objective space of each level is converted to a one-dimensional space by an aggregating function. Third, to obtain the final solution, all levels are combined into single-level model where the decision variables of upper levels are interrelated with other levels through fuzzy strategy-based linear and nonlinear membership functions.

The effectiveness of the proposed VIKOR is demonstrated by numerical examples, where the reported results affirm that the extended VIKOR method provides superior results in comparison with the same methods in the literature, and it is a good alternative to BL-MCNFP problems.

In terms of the assistance-based right decision, a parametric analysis for the weight of the majority is provided to exhibit a wide range of compromise solutions for the decision-maker.

The purpose of this paper is to make a comprehensive analysis of 354 publications about Pythagorean fuzzy sets (PFSs) from 2013 to 2020 in order to comprehensively understand their historical progress and current situation, as well as future development trend.

First, this paper describes the fundamental information of these publications on PFSs, including their data information, annual trend and prediction and basic features. Second, the most productive and influential authors, countries/regions, institutions and the most cited documents are presented in the form of evaluation indicators. Third, with the help of VOSviewer software, the visualization analysis is conducted to show the development status of PFSs publications at the level of authors, countries/regions, institutions and keywords. Finally, the burst detection of keywords, timezone review and timeline review are exported from CiteSpace software to analyze the hotspots and development trend on PFSs.

The annual PFSs publications present a quickly increasing trend. The most productive author is Wei Guiwu (China). Wei Guiwu and Wei Cun have the strongest cooperative relationship.

The implication of this study is to provide a comprehensive perspective for the scholars who take a fancy to PFSs, and it is valuable for scholars to grasp the hotspots in this field in time.

It is the first paper that uses the bibliometric analysis to comprehensively analyze the publications on PFSs. It can help the scholars in the field of PFSs to quickly understand the development status and trend of PFSs.

The purpose of this paper is to covenant with the cost assessment of a complex repairable system, consisting of two subsystems (Subsystem 1 and Subsystem 2) connected in series configuration and being operated by a human operator. Each subsystem has two identical units in parallel configuration and has different types of failure and two types of repairs (general repair and copula repair). Through the transition diagram, the system of first-order partial differential equations is derived and solved using a supplementary variable technique, Laplace transforms. All failures are assumed to follow exponential distribution, whereas repairs follow two types of distributions that are general and Gumbel–Hougaard family copula. In this paper, explicit expressions for reliability, availability, mean time to failure (MTTF) and cost analysis functions have been obtained. In this paper, two types of repairs (copula repair and general repair) have been studied, and it has been concluded that copula repair is more reliable as compared to general repair. Some computations are taken as particular case by evaluating: reliability, availability, MTTF and cost analysis, so as to capture the effect of both failure and repair rates to reliability measures. The results have been shown in tables and graphs. The convincing part has been discussed in last section of this study.

This paper is focused on the cost assessment of a system consisting two subsystem series configuration. Each subsystem has two identical units in parallel configuration. The performance of the system has been analyzed by supplementary variable techniques and Laplace transforms. Various measures of the reliability have been discussed by evaluations. Software called Maple 13 is used for computations.

In this research paper, the authors have evaluated the operational cost and incurred profit of the system together with other reliability measures for various situations and different types of failures and two types of repairs using Gumbel–Hougaard family copula distribution.

The present research focuses on the series and parallel configured complex systems that is used everywhere in industry and other sectors. The authors main aim is to claim that repair through the joint probability distribution copula is far better than general repair. Copula repair for a completely failed system is more beneficial for industrial system operations that will increase profit to the industrial sector.

The authors have observed that when repair follows general distribution the values of reliability obtained of the system are less compared to the those obtained when the authors apply copula repair, a joint probability distribution. It is a clear implication for industrial sector and organization to use the policy for a better generate revenue.

According to the best of authors’ knowledge, there is no social implication as this study is meant for reliability section. The study in management and case study matters is considered to have social implication.

This research is the original work of authors. Nothing has been copied from any paper or book. The references are cited according to the relevance of study.

The purpose of this paper is to present a technique for analyzing the behavior of an industrial system utilizing vague, imprecise, and uncertain data. The synthesis unit of a urea plant situated in northern part of India has been considered to demonstrate the proposed approach. Sensitivity analysis of system's behaviour has also been done in it.

In the proposed approach, traditional Lambda‐Tau technique is used to analyze the behavior of a complex repairable synthesis unit of a fertilizer industry up to a desired degree of accuracy. This technique has been demonstrated by computing eight well‐known reliability indices which are used for behaviour analysis of the considered system in a more promising way.

The study of analysis of reliability, availability, maintainability etc can help in increasing the production and quality of synthesis. To ensure the system performance throughout its service life, it is necessary to set up proper maintenance, planning and control which can be done after studying the variation of reliability, availability with respect to time. Thus, it may be a more useful analysis tool to access the current system condition and involved uncertainties. The present paper suggested an approach to improve the system's performance.

The paper suggests a technique for analyzing the stochastic behavior of an industrial subsystem by computing eight well‐known reliability indices in the form of fuzzy membership function. The benefits for the methodology include the ability to model and deal with highly complex system as fuzzy sets can deal easily with approximations and it helps in improving and handling the uncertainties and possibilities.

This study deals with the reliability analysis of a hybrid series–parallel system consisting of two subsystems A and B with two human operators. Subsystem A has two units in active parallel while subsystem B consists of two-out-of-four units. Both units have exponential failure and repair time. The system under consideration has two states: partial failure state and complete failure state. The mathematical equations associated with the transition diagram have been formulated using regenerative point techniques. The system is analysed using Laplace transforms to solve the mathematical equations. Some important measures of reliability such as availability of system, reliability of the system, mean time to failure (MTTF), sensitivity for MTTF and cost analysis have been discussed. Some particular cases have also been derived and examined to see the practical effect of the model. The computed results are demonstrated by tables and graphs. Furthermore, the results of the designed model are beneficial for system engineers and designers, reliability and maintenance managers.

This paper considered a hybrid series–parallel system consisting of two subsystems A and B with two human operators. The performance of the system is studied using the supplementary variable technique and Laplace transforms. The various measures of reliability such as availability, reliability, mean time to system failure (MTSF), sensitivity for MTTF and cost analysis have been computed for various values of failure and repair rates. Maple 13 software has been used for computations.

In this research paper, the authors have computed various measures of reliability such as availability, reliability, MTSF, sensitivity for MTTF and cost analysis for various values of failure and repair rates and find that failure due to human operators are more responsible for successful operation of the system and also regular repair should be invoked to improve system performance.

This research paper is the original work of authors. The references are well cited based on the importance of study. Nothing has been detached from any research paper or books.

The purpose of this paper is to develop the Pythagorean fuzzy extension of CODAS method.

Supplier selection is a critical issue for manufacturing companies since it is a multidimensional problem including several conflicting criteria. A suitable multi criteria decision making (MCDM) method that could consider vagueness and impreciseness in the assessments should be used for this kind of problems. Pythagorean fuzzy sets (PFSs) are characterized by a membership degree and a non-membership degree satisfying the condition that their square sum is equal to or less than 1. PFSs extend the concept of intuitionistic fuzzy sets (IFSs). COmbinative Distance-based Assessment (CODAS) method is relatively a new MCDM technique introduced by Keshavarz Ghorabaee et al. (2016).

Pythagorean fuzzy CODAS gives better results than ordinary fuzzy CODAS since it considers the hesitancy of decision makers and presents a larger space for membership and non-membership definition.

The value of this paper is the proposal of a new method to use for the solutions of MCDM problems under vagueness and impreciseness. To show validity and effectiveness of the proposed method, an application to the supplier selection problem is given.