Micromobility is an innovative urban transport solution that can effectively tackle greenhouse gases and reduce the use of private vehicles, especially for short-distance travel options. As a type of shared micromobility service, the electric scooter (e-scooter) is designed to provide convenient and quick rides for short distances. The constantly growing adoption of these emerging transportation technologies brings many factors to be considered. In this paper, we evaluate the available e-scooters and identify the most appropriate choice with respect to several factors. To this aim, we propose a decision support tool with the combination of modified symmetry point of criterion (SPC), the pivot pairwise relative criteria importance assessment (PIPRECIA), and the weighted aggregated sum product assessment (WASPAS) approaches under the setting of q-rung orthopair fuzzy (q-ROF) sets. First, the developed method calculates the significance values of decision experts through a new q-ROF-score function. Next, the criteria weights are determined using an incorporated objective-subjective weighting model. It comprises a q-ROF-modified SPC tool for objective weighting and a q-ROF-PIPRECIA tool for subjective weighting. Subsequently, we present the stepwise mathematical algorithm of a q-ROF-WASPAS approach using q-ROF aggregation operators and criteria weighting tools. To verify the compatibility and effectiveness of the introduced model, it is applied to evaluate and prioritize the e-scooters under the q-ROF environment. Sensitivity analysis is made to examine the impact of varying values of weighting and utility parameters. The efficiency of the introduced approach is confirmed by different comparative investigations.

The emergence of blockchain technology (BT) has indicated a new era for the supply chain and logistics industries wherein uncertainty significantly affects the establishment of suitable blockchain platforms for logistics firms. Moreover, uncertainty widely occurs in such realistic situations. This study develops a hybrid picture fuzzy information-based framework for assessing and ranking the blockchain platforms in the logistics firm. The experts' significance values are obtained using a distance measure and a rank sum model-based process under the picture fuzzy set (PFS) context. A novel distance measure is offered for PFSs, and its effectiveness over previously developed measures is demonstrated. To estimate the criteria weights, an integrated weighting model is utilized, which is based on the criteria importance through inter-criteria correlation (CRITIC) method for objective weights and the ranking comparison (RANCOM) approach for subjective weights. Moreover, the picture fuzzy compromise ranking of alternatives from distance to ideal solution (CRADIS) approach is utilized to rank the alternatives. To illustrate the superiority and practicality of the model, it is applied to a case study of blockchain platform selection including six alternatives and thirteen criteria to assess and rank the BTs options based on PFSs. The findings demonstrate that “Microsoft (1.0)” emerges as the best choice with the highest compromise measure among a set of six blockchain platforms in the logistics firm. Finally, sensitivity and comparative analyses are conducted to test the robustness and superiority of the developed method.

Digital transformation (DT) has become vital for companies trying to remain competitive in the recent ever-changing technological environment. DT is the integration of digital technologies into all disciplines of business from regular activities to strategic decision making. Risk management planning requires projects to assess possible risks that may negatively or positively affect a DT project. The purpose of the study is to introduce a hybridized decision support system (DSS) by combining the distance measure, ranking comparison (RANCOM) model and additive ratio assessment (ARAS) approach in the context of a picture fuzzy set (PFS). In this framework, the decision experts’ significance values are computed using a picture fuzzy score function-based formula. With the combination of objective weight using distance measure and subjective weight through the RANCOM model, a combined weight-determining approach is developed to determine the significance values of considered DT risks under picture fuzzy environment, while a hybrid ARAS model is developed to evaluate and rank DT projects from the risks perspective. To exhibit the feasibility of the introduced framework, a case study of a DT projects assessment problem is discussed in the context of picture fuzzy sets. A sensitivity study is also discussed over different values of the strategy coefficient, which confirms the strength of the proposed model. Further, a comparison with the existing picture fuzzy information-based methods is presented to prove the robustness of the developed decision-making framework.

As the importance of environmental and social responsibility gains momentum, the financial sector is ever more aware of its dynamic role in assisting the evolution to a low-carbon economy and a sustainable future. Digital Transformation (DT) is the application of technologies for building innovative models, procedures and systems that generates more profitable revenue, greater competitive advantage and better productivity. However, the DT in sustainable financial services is slower than the other sectors. In this regard, very few articles have been presented in the literature. This paper aims to assess the sustainable financial services based on the indicators of DT using a decision support system. In this framework, the classical Alternative Ranking Order Method Accounting for Two-Step Normalization (AROMAN) is extended from q-rung orthopair fuzzy rough information (q-ROFRI) and combined with the decision-making experts (DMEs) and criteria weight-determination models. In this method, firstly the DMEs’ weights are calculated using standard deviation-based tool. Second, the DMEs’ opinions are aggregated through novel Sugeno-Weber weighted averaging operator. In this regard, Sugeno-Weber operators are proposed for q-ROFRI. Third, an integrated criteria weighting formula is determined in which the objective weights are calculated using a distance measure-based model, while the subjective weights are derived via relative closeness coefficient-based model with q-ROFRI. For this purpose, a novel distance measure is proposed for q-ROFRI. Combining all these steps, a hybrid q-rung orthopair fuzzy rough AROMAN method is introduced in which the weighted normalized ratings are computed through a new score function. Further, an empirical study is presented to prioritize the sustainable financial services with respect to DT indicators’ assessment, which also shows the practicality and feasibility of presented method. The findings of this work show that the option “green banking” is the most optimal choice among a set of five sustainable financial services with the overall evaluation grade of 0.384, while the ranking order of options is green banking (0.384) > values-based banking (0.3745) > ESG finance (0.3714) > climate finance (0.356) > social banking (0.3384). To prove the stability of obtained results, sensitivity assessment is conducted on the basis of different values of considered parameters. At last, comparison with extant methods is made to exemplify the robustness of proposed framework under the context of q-ROFRI.

The household waste (HW) disposal and recycling have become a significant challenge due to increasing quantities of generated household wastes and increased levels of urbanization. Selecting locations/sites for building new HW recycling plant comprises numerous sustainability dimensions, thus, this work aims to develop new decision-making model for evaluating and prioritizing the HW recycling plant locations. This paper is categorized into three phases. First, we propose new improved score function to compare the Fermatean fuzzy numbers. Moreover, an example is presented to validate the effectiveness of proposed score function over the extant ones. Second, we introduce new distance measure to estimate the discrimination degree between Fermatean fuzzy sets (FFSs) and further discuss its advantages over the prior developed Fermatean fuzzy distance measures. Third, we introduce an integrated methodology by combining the method with the removal effects of criteria (MEREC), the stepwise weight assessment ratio analysis (SWARA) and the measurement alternatives and the ranking according to compromise solution (MARCOS) approaches with Fermatean fuzzy (FF) information, and named as the “FF-MEREC-SWARA-MARCOS” framework. In this method, the FF-distance measure is used to find the weights of involved decision-making experts. Moreover, an integrated criteria weighting method is presented with the combination of MEREC and SWARA models under the context of FFSs, while the combined FF-MEREC-SWARA-MARCOS model is applied to evaluate and prioritize the locations for HW recycling plant development, which illustrates its feasibility of the developed framework. Comparative study and sensitivity assessment are conducted to validate the obtained outcomes. This work provides a hybrid decision analysis approach, which marks a significant impact to the HW recycling plant location selection process with uncertain information.

In the theory of interval-valued intuitionistic fuzzy set (IVIFS), the rating/grade of an element is the subset of the closed interval [0, 1], therefore the IVIFS doctrine is more useful for the decision expert to present their judgments in terms of intervals rather than the crisp values. The present work develops an integrated decision-making methodology for evaluating sustainable wastewater treatment technologies within the context of IVIFS. The proposed decision-making framework is divided into three stages. First, some Yager weighted aggregation operators and their axioms are developed to combine the interval-valued intuitionistic fuzzy information. These operators can offer us a flexible way to solve the realistic multi-criteria decision-making problems under IVIFS context. Second, an extension of Symmetry Point of Criterion model is introduced to determine the criteria weights under IVIFS environment. Third, an integrated alternative ranking order model accounting for two-step normalization (AROMAN) approach is proposed from IVIF information perspective. Next, the practicability and efficacy of the developed model is proven by implementing it on a case study of sustainable wastewater treatment technologies evaluation problem with multiple criteria and decision experts. Finally, comparative analysis is discussed to illustrate the consistency and robustness of the obtained outcomes.

This article examines the academic research conducted by universities in Small Island Developing States (SIDS) and aims to identify and comprehend its distinctive features, as well as its significance to the respective host countries. An analysis of the 327 narrow Scopus fields of the 167,080 journal articles published by 38 SIDS between 2010 and 2019 found that they focus more on sustainability related research about ecology, public health, infectious diseases, and species diversity, but less on industrially relevant research. Only four states had a main publication field reflecting a core economic activity. Thus, while academic research on sustainability is welcome, the lack of evidence of research support for national economic activities is concerning. The patterns found may be due to historical education policies and the path-dependent model of development adopted by many SIDS. The study suggests that research policies in these nations may need to reassess their support for industrially relevant research.

Improper management of healthcare wastes can lead to severe health hazard and environmental pollution such as water, air and soil. Selection of the suitable disposal technique requires consideration of multiple alternatives and evaluation criteria. Multi-criteria decision-making frameworks can be appropriate to handle the decision-making problem of healthcare waste disposal techniques assessment. However, uncertainty is inherently appeared in the assessment of such types of real-life applications. To this aim, the present work develops a hybrid picture fuzzy group decision-making framework and applies to assess healthcare waste disposal techniques based on various criteria and uncertainty perspective. In this regard, we introduce a new distance measure for picture fuzzy sets and further use to find the decision experts’ weights. The proposed measure can overwhelm the shortcomings of some of the previously introduced picture fuzzy distance measures. Based on the proposed measure, we further present an improved maximizing deviation model to derive the weight of criteria in the picture fuzzy environment. Further, we introduce a hybrid gained and lost dominance score method by incorporating the proposed distance measure-based weighting model for experts' weights and maximizing deviation method-based criteria weights. The developed framework considers the dominance relations between options and provides more efficient outcomes in the assessment of group decision-making problems. Finally, the developed method is applied to an empirical study of healthcare waste disposal techniques assessment problem, which illustrates the usefulness of introduced framework. Sensitivity analysis is performed to test different scenarios related to the proposed approach, which demonstrates the robustness of determined outcomes. Comparison with existing studies is discussed to show the robustness of the developed group decision-making framework. The present work contributes to the field of decision support through which the policymakers can take responsible decisions in the healthcare industry.

The development opportunities and high-performance capacity of offshore wind energy project depends on the selection of the suitable offshore wind power station (OWPS) location. The present study aims to introduce a decision-making model for assessing the locations for OWPS from multiple criteria and uncertainty perspectives. In this regard, the concept of interval-valued intuitionistic fuzzy set (IVIFS) is utilized to express uncertain information. To quantify the degree of difference between IVIFSs, an improved distance measure is proposed and further utilized for deriving the objective weights of criteria. Numerical examples are discussed to illustrate the usefulness of introduced IVIF-distance measure. The RANking COMparison (RANCOM) based on interval-valued intuitionistic fuzzy information is presented to determine the subjective weights of criteria. With the combination of objective and subjective weights of criteria, an integrated weighting tool is presented to find the numeric weights of criteria under IVIFS environment. Further, a hybrid interval-valued intuitionistic fuzzy Weighted integrated Sum Product (WISP) approach is developed to prioritize the OWPS locations from multiple criteria and uncertainty perspectives. This approach combines the benefits of two normalization tools and four utility measures, which approves the effect of beneficial and non-beneficial criteria by means of weighted sum and weighted product measures. Further, the developed approach is applied to the OWPS location selection problem of Gujarat, India. Sensitivity and comparative analyses are presented to confirm the robustness and stability of the present WISP approach. This study provides an innovative decision analysis framework, which makes a significant contribution to the OWPS locations assessment problem under uncertain environment.

The use of trade credit finance is becoming more widely acknowledged as a crucial approach to improving inventory system profitability. We review an inventory model with depending on permitted payment delays for which, if the retailer place an orders higher than or equal to a predefined quantity , then the supplier will provide a fully pay in later facility of periods (i.e., there will be no charge of interest until ). On the other hand the retailer need to pay a partial amount of payment to the supplier if the order quantity is less than , and the remaining amount may be deferred for up to periods. Main objective of this study is to investigate the inventory model with different situations under delayed payment facility. In addition, determining the product's demand also involves taking into account the item's greenness and selling price. We have also considered the fact that the cost of buying is influenced by the product's degree of greenness. We employ the meta heuristic algorithm Grey Wolf Optimizar (GWO) to assist us in solving the problem, and we compare the outcomes with the aid of a few other algorithms (Whale optimization algorithm (WOA) and Artificial electric field algorithm (AEFA)). In the end, we resolve several numerical cases to support the model. The concavity of the desired function is graphically displayed using MATLAB software.

This paper deals with the microgrid's bidding strategy (MGBS) problem in a day-ahead (DA) electricity market. To this end, the DA electricity prices, demand, and renewable energy uncertainties are modeled by different scenarios via generating several representative daily curves. However, the real-time (RT) electricity prices are modeled using robust optimization (RO) via predicting appropriate intervals. The existing paradigm to predict the RT intervals is to minimize the statistical errors, while this accuracy-oriented method may not necessarily yield the best MGBS plan against the actual realization of RT prices. The novelty of this research is to present a smart predict-and-optimize (SPO) methodology in which a cost-oriented prediction model replaces the existing accuracy-oriented methods. Trilevel mathematical programming is established to construct a cost-oriented model where the first level maximizes/minimizes the actual profit/cost by adjusting the predicted interval bounds of the RT prices. Knowing these trained interval bounds, the second level runs a scenario-based DA-MGBS. Then, a rescheduling problem is solved at the third level based on the actual realization of uncertainties. To solve this trilevel problem, a reformulation-and-decomposition (R&D) algorithm is utilized. The numerical experiment illustrates the advantages of the SPO method in terms of the microgrid (MG) cost.

Uncertainty refers to a lack of precise knowledge or information about a particular event, situation, or outcome. It is an inherent characteristic of many real-world phenomena and is often associated with the presence of risk or ambiguity. Uncertainty can arise due to various factors, such as incomplete information, unpredictability, complexity, or variability of a system or process. In many cases, uncertainty can lead to difficulties in decision-making and pose challenges in planning, forecasting, and managing risks. There are different types of uncertainty, including epistemic uncertainty, which arises from the inherent randomness or variability of a system or process. This study encompasses the inclusion of all inventory parameters as uncertainty parameters, which are expressed in the form of intervals. Furthermore, demand for the product is taken into account in interval form. The conversion of the differential equation into an interval differential equation is carried out in order to account for the variability in demand within a certain interval. The utilisation of the centre-radius technique leads to the derivation of the related optimisation problem under a ‘buy now, pay later’ (BNPL) payment scheme. In order to demonstrate the concept, a numerical case is selected and solved with the MATHEMATICA software and interval order relations. In the end, a comprehensive sensitivity analysis has been conducted to derive insightful conclusions pertaining to this study.

In this paper, we study the marginal distribution of concomitants of k-record (KR) values from generalized Farlie–Gumbel–Morgenstern (GFGM) of bivariate distributions. In addition, the joint distribution of concomitants of KR for this family is obtained. Furthermore, some useful recurrence relations between moments of concomitants are derived. In addition, the hazard rate, the reversed hazard rate, and mean residual life functions of concomitants for this family are obtained. Some recent new measures of information, such as weighted extropy, weighted cumulative past extropy, and weighted cumulative residual extropy, are investigated for the concomitant of KR under the GFGM family. A non-parametric estimator of the proposed measure is provided by combining the empirical method with the concurrent use of KR in the GFGM family. Finally, we analyzed real-world data to examine our findings.

Nowadays, consumers show more interest towards eco-friendly products. To meet this demand, however, manufacturing processes often generate a lot of hazardous waste, which creates challenges for companies. To tackle these issues, this work develops an optimization model to help companies with managing production, reduce waste, and maintain green product standards. To navigate solution of the profit maximization problem became apparent in the model, a new meta-heuristics called Artificial Hummingbird Algorithm is employed and compared with a wide range of other optimization techniques. The results demonstrate that this algorithm outperforms others on the majority of case studies. Sensitivity analyses are also performed to help managers make informed decisions.

This study introduces a ground-breaking approach to analyzing dihedral groups through the lens of fuzzy graph theory, significantly enhancing computational efficiency in group theory. By extending the fuzzy topological indices to polynomial forms, this research drastically reduces the calculation time for these indices from hours to mere seconds. A notable feature of this work is the innovative use of polynomial regression, a machine learning technique, to generate polynomials for adjacency and degree matrices within the fuzzy conjugate graph of a dihedral group. This method not only simplifies calculations but also incorporates an error analysis component, ensuring accuracy and reliability. The integration of fuzzy graph theory with polynomial regression in this context is a pioneering step, offering valuable insights into the structural attributes of dihedral groups. This research goes beyond traditional methods, highlighting the effectiveness of machine learning in deciphering complex patterns in group theory. The findings and techniques presented hold great promise for future applications in graph theory and group theory, offering a novel perspective for understanding and analyzing intricate graph structures. This study stands as a significant contribution to the field, potentially revolutionizing the way complex mathematical problems are approached and solved.

Two-stage adaptive robust optimization (RO) has been widely used to formulate the transmission expansion planning (TEP) problem. The goal is to acquire an optimal least-cost expansion plan that is robust against any future realization of the uncertain parameters. The existing models are constructed based on a tri-level min-max-min optimization problem solved using a decomposition-based column-and-constraint generation (CCG) algorithm. These approaches assume that the peak load and generation capacity lie in a prespecified uncertainty set by fixing minimum (lower) and maximum (upper) amounts. However, the minimum and maximum values fixed in these models are assumed to be fully known, while they are uncertain with unknown probability density functions (PDFs), if any. This paper aims to fill this gap by establishing an RO-based model using four-level (min-max-max-min) programming rather than tri-level programming. The presented tri-stage methodological framework is solved by a nested CCG (NCCG). The first stage determines the optimal investment decision, while the second stage specifies the worst-case scenario over an uncertainty set of lower and upper bounds. Then, the third stage identifies the worst-case operation cost over an uncertainty set of peak load and generation capacity. Simulation results indicate the effectiveness of the developed method.

Numerous studies have explored pricing and lot-sizing strategies for various payment methods, but most have focused primarily on the buyer’s perspective. This study, however, approaches these strategies from a different perspective, incorporating key and relevant factors often overlooked. The volume of sales increases when a seller accepts a buyer’s credit. However, it reduces sales volume when a seller requests a buyer make a payment in advance. To boost sales and profitability, a vendor occasionally provides a price reduction in exchange for a down payment. Demanding a down payment from a customer earns interest and carries without any risk of default. When a vendor offers customers the option to pay with credit, a higher delay payment period facility plan may boost sales volume, but it also increases the risk of default. To maximize profit per unit of time, the vendor aims to simultaneously determine the optimal selling price, replenishment schedule, and payment method. This is achieved by comparing and calculating the vendor’s profit per time unit for credit, cash, and advance payment options. This is done by comparing and calculating the seller’s profit for each piece of time for credit, cash, and advance payments. The following managerial impacts are highlighted by means of numerical analyses: (1) A particular payment type, among the three available options, yields the seller’s highest profit under certain conditions. (2) It is vitally crucial for a vendor to provide a price reduction if an advance payment is required. (3) Advance payment results in higher profit than delayed payment if sales volume does not significantly fall while switching from credit to advance payments, or vice versa. To solve the optimization problem, a popular metaheuristic algorithm (viz., Grey Wolf Optimizer) is used and finally performed a post optimality analysis for making a fruitful conclusion.

Wearable sensors (WS) played a vital role in health assistance to improve the patient monitoring process. However, the existing data collection process faces difficulties in error corrections, rehabilitation, and training validations. Therefore, the fuzzy data analysis requires additional effort to reduce the overall problems in sports rehabilitation. The research difficulties are overcome by applying the spatial correlation with a support vector machine (SDC-SVM). The algorithm uses the hyperplane function that recognizes the sports person activities and improves overall activity recognition efficiency. The sensor data is analyzed according to the input margin, and the classification process is performed. In addition, feature correlation and input size are considered to maximize the overall classification procedure of WS data correlation using the size and margin of the input and previously stored data. In both the differentiation and classification instances, the data’s spatiotemporal features are extracted and analyzed using support vectors. This proposed method can improve the accuracy of recognition, F1 score, and computing time for the varying WS inputs, classifications, and subjects.

The present work proposes a new decision support tool for assessing the sustainable suppliers in the healthcare supply chain. For this purpose, the classical Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) model is integrated with the Sugeno-Weber weighted averaging operators, modified symmetry point of criterion (SPC) model, rank sum (RS) tool and Fermatean fuzzy sets (FFSs), and named as the 'FF-SPC-RS-MARCOS' framework. The developed model firstly determines the decision experts' weights through RS model. Second, novel Sugeno-Weber weighted operators are introduced to combine the experts' opinions. Third, a unified weighting procedure is presented based on the combination of modified SPC approach for objective weight and RS method for subjective weight of attributes. To this aim, a novel distance measure is introduced for FFSs and further applied to compute the distance between aggregated Fermatean fuzzy numbers and symmetry point value of an attribute in the modified SPC approach. Further, a hybrid FF-SPC-RS-MARCOS approach is proposed to tackle the decision-making problems on FFSs setting. To elucidate the efficacy of the developed method, it is applied to a case study of sustainable supplier selection problem in the healthcare supply chain. The paper further conducts sensitivity investigation and comparison with existent approaches to test the stability and robustness of the ranking outcomes. This study shows how the proposed MARCOS method in combination with SPC and RS models can be used to prioritize the alternative suppliers in the healthcare supply chain. The introduced work provides a new methodology, which can help the practitioners and academics to evaluate suppliers with uncertain information and can also be employed to other areas facing similar types of decision-making problems.