Multiple Criteria Decision Making Methods Research Articles

Feasibility Study on using MCDM for E-Voting

An online voting system is an election system that manages the election process. This is a medium for the voters to cast their votes. It is also being used to calculate the votes collected from the voters to choose the representative for their own faculty. A typical voting system is based on a single attempt for each candidate being voted. The voting does not reflect the criteria implies to the characteristic of the candidate that going to be the student leader. To be a student leader, the student should fulfil the requirement such as good academic results, interpersonal skills with society, involving in activities of university and etc. Although the current voting system is able to maximize the participation of the voters, the voters may blindly vote the ballots casually due to they do not know the details of the candidates and the result is low quality and low public’s trust in the selected candidate. In this study, the aim is to develop an interactive online voting system that have ranking feature with MCDM method which allow online voting system to collect high-quality results from the voters. The Multiple Criteria Decision Making (MCDM) method is used in the voting system while choosing the candidate. MCDM can let the voters make decision making or selecting the candidate based on the criteria that suit the position. The study starts with the literature study on implementing MCDM for a voting system. Then, a survey will be made to get the users’ views on the with and without implementation of the MCDM method in an online voting system. The expected result of the study is to investigate the current implementation of MCDM as a tool for decision making, then identify the possibility of adopting MCDM for the online voting system while choosing the representative for faculty students’ society. As a conclusion from the survey from the users’ views, it shown that most of the users thinks that the system with the implementation with MCDM method is less time consuming and able to produce high quality result compare to the current online voting system. Most of the respondents also stated that they are more preferring to use the online voting system with MCDM method in the future.

Hesitant fuzzy partitioned Maclaurin symmetric mean aggregation operators in multi-criteria decision-making

A hesitant fuzzy set, enabling the membership of an element to be a set of various possible values, is highly helpful in describing people’s uncertainty in everyday life. Hesitant fuzzy aggregation operators are the standard mathematical tools for combining many inputs according to predefined criteria into a single result. The classic hesitant fuzzy aggregation operator-based approaches have been criticized because of the ignorance of criteria classification. In this work, we develop the conception of the hesitant fuzzy partitioned Maclaurin symmetric mean and hesitant fuzzy weighted partitioned Maclaurin symmetric mean operators spurred by the partitioned Maclaurin symmetric mean. Afterward, we analyze several features and peculiar instances of the formulated operators. A novel multiple criteria decision-making (MCDM) technique is propounded on the documented hesitant fuzzy weighted partitioned Maclaurin symmetric mean operator; the MCDM method chooses the optimal alternative from several alternatives. A case study of the best location selection for hospital construction is addressed to showcase the practicability of the presented technique. Eventually, we illustrate the devised approach is more widespread and efficacious than prevailing approaches via comparative and sensitive analyses.

The selection of renewable energy technologies using a hybrid subjective and objective multiple criteria decision making method

The use of renewable energy technologies is a key factor for sustainable development but their selection from several alternatives is a difficult task that relies on the careful assessment of relevant criteria. While Multiple Criteria Decision Making (MCDM) methods have been used successfully in various renewable energy technology selection problems, the decision process becomes more challenging when preferential judgements are made on the basis of non-homogenous and imprecise input data, and when there is uncertainty due to disparities among decision makers. This paper presents a hybrid MCDM method capable of overcoming these problems by taking into account quantitative and qualitative data under a probabilistic environment in the context of group decision making. In this method, qualitative data is fuzzified and used along with quantitative data to develop a hybrid model. A coefficient factor allows decision makers to vary the weight of each quantitative model so that the resultant criteria weights and overall alternatives’ scores consider both subjective considerations and objective information. An example is presented to showcase the usability of the method developed for ranking and evaluating renewable energy technologies in the mining industry. In addition, the impact of different coefficient factors on the final results was assessed by means of sensitivity analysis. The results indicate that the method developed is able to minimise the loss of valuable objective information, caused by the subjective bias of qualitative weights during the evaluations, by adjusting the coefficient factors of the hybrid model during the calculations.

How to choose the right influencer for a marketing strategy

This paper attempts to build a new model for deciding which social media influencers (SMIs) are suitable for the marketing strategies of businesses. How to choose social media influencers is an unanswered question in the literature, and this study attempts to fill this gap. The study employs a Multiple-Criteria Decision-Making (MCDM) method, the fuzzy decision-making trial and evaluation laboratory model (DEMATEL), to determine the relevance of criteria constructed. It observed SMIs on Instagram and reviewed insights from the literature. Five criteria are proposed for selecting the correct influencers: 1) positioning; 2) target; 3) budget; 4) past campaigns; and 5) the number of followers. Businesses were asked to evaluate these criteria according to their experience with using SMIs. The results suggest that the most important criterion is ‘target’, whereas ‘past campaigns’ is the least influential.

Developing a Harvest Plan by Considering the Effects of Skidding Techniques on Forest Soil Using a Hybrid TOPSIS-Entropy Method

Abstract The aim of this study was to evaluate skidding techniques, which result in minimal damage to the soil, depending on the slope and stand type. Thus, three skidding techniques with tractor for harvesting (suspended skidding [SS], using a skidding cone [SC], and cable-pulling [CP]) were used in six different study sites and the variations in soil properties were examined at three different slopes (0%–20%, 20%–33%, >33%), 2 different stand types (A, B), and 2 different soil depths (0–5 cm, 5–10 cm). Soil bulk density, soil organic matter, soil compaction, organic carbon (C), and total nitrogen (N) were determined. The Entropy and TOPSIS methods were used among the multiple-criteria decision-making methods for six different coniferous stands. With the combination of the Entropy and TOPSIS methods, we found that slope was an important factor in determining the preferred skidding technique. Suspended skidding was seen as the preferred method of skidding technique in the 0–20% slope group. For the 20%–33% slope group, the usability of the three methods varied depending on stand type and soil depth, whereas the technique using a skidding cone was found to be the preferred skidding technique in the > 33% slope group.

Assessment of Maize Drought Risk in Midwestern Jilin Province: A Comparative Analysis of TOPSIS and VIKOR Models

Drought is a major natural disaster that causes a reduction in rain-fed maize yield. Agricultural drought risk assessment is conducive to improving regional disaster management ability, thereby reducing food security risks and economic losses. Considering the complexity of risk assessment research, an increasing number of researchers are focusing on the multiple-criteria decision-making (MCDM) method. However, the applicability of the MCDM method to agro-meteorological disaster risk assessments is not clear. Therefore, this study comprehensively evaluated hazard, exposure, vulnerability, and emergency response and recovery capability using the TOPSIS and VIKOR models to generate a maize drought risk map in mid-western Jilin Province and ranked the drought risk of each county. The results showed that: (1) maize drought risk in the middle and west of Jilin province showed an increasing trend. Spatially, the risk diminished from west to east. The drought risks faced by Tongyu, Changchun, and Dehui were more severe; (2) the evaluation results of the two models were verified using the yield reduction rate. The VIKOR model was found to be more suitable for agrometeorological drought risk assessments; (3) according to the damage degree of drought disaster to maize, the cluster analysis method was used to divide the study area into three sub-regions: safe, moderate drought, and severe drought. Combined with the characteristics of different regions, suggestions on disaster prevention and mitigation are proposed. The results of this study can provide a basis for formulating strategies to alleviate drought, reduce losses, and ensure the sustainable development of agriculture.

Selection of Optimum Hybrid Composite Material for Structural Applications Through TOPSIS Technique

Currently Aluminum alloys and polymer based fibre composites are being used for various structural applications. It is always an advantageous to have light weight high strength materials. In this context, hybrid nanocomposites are fabricated and tested for their mechanical properties to meet various applications. Due to the conflicting nature of the mechanical properties, a multi criteria decision model employing AHP (Analytic Hierarchy Process), Entropy, and TOPSIS techniques were developed with the goal of selecting an appropriate material to meet the objective out of various material combinations. A framework has been developed to assist composite structure designers in selecting the best fibre types for a given application. The purpose of this paper is to first investigate the impact of weighting methods in multiple criteria decision making (MCDM), and then to develop a systematic framework for optimum fibre selection among all fibre reinforced polymer (FRP) composites.

A novel GIS-based MCDM approach to identify the potential eco-tourism sites in the Eastern Dooars region (Himalayan foothill) of West Bengal, India

The present study was designed to assess the capability of the novel Multiple-criteria decision-making (MCDM) method such as Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) along with Analytical Hierarchy Process (AHP) in identifying the potential site of ecotourism in the Eastern Dooars region of West Bengal, India. Two popular objective weighting methods such as Entropy and Criteria Importance through Interaction Correlation (CRITIC), were used to minimize the subjectivity of AHP methods. The suitability map obtained from these applied methods showed that the northern and north-eastern parts, namely Kalchini and Kumargram blocks, were identified as the highly suitable zone for ecotourism development. Finally, the obtained suitability map was validated using receiver operating characteristic (ROC) and Area Under Curve (AUC) analysis. The AUC value of ROC was more than 0.80 for all the applied methods, indicating the reliability of all the applied models.

Evaluation of Sustainable Digital Currency Exchange Platforms Using Analytic Models

This study presents an analytic model to support the general public in evaluating digital currency exchange platforms. Advances in technologies have offered profitable opportunities, but the general public has difficulty accessing appropriate information on digital currency exchange platforms to facilitate their investments and trading. This study aims to provide a decision support system using analytic models that will guide the public in deciding the appropriate digital currency exchange platform for trading and investment. The overarching objective is to support the public in embracing the new era of a dependable, trustworthy, and sustainable digital society. Particularly, this study offers an analytics model that compares numerous well-known digital currency exchange platforms based on the opinions of 34 human expert members on six main criteria to identify the most suitable platform. In this study, the analytic hierarchy process approach, which is a multiple-criteria decision-making method, and Expert Choice software were used for decision support. Using pairwise comparisons of exchanges with respect to the criteria in the software, the weight of each exchange was determined, and these weights became the basis for prioritizing the exchange platform. This study provides valuable insight into how an analytics-driven expert system can support the public in selecting their digital currency exchange platform. This work is an integral part of an effort to help disruptive digital technology become widely accepted by the general public.

Identifying Key Financial, Environmental, Social, Governance (ESG), Bond, and COVID-19 Factors Affecting Global Shipping Companies—A Hybrid Multiple-Criteria Decision-Making Method

The international shipping industry is the largest transportation system in the world. However, shipping stock prices were highly volatile during the 2020–2021 COVID-19 pandemic. The purpose of this study is to identify the causal relationships of the four dimensions (financial performance, bond financing, environmental, social, governance, and COVID-19) and 20 criteria affecting the sustainability of global shipping companies. The research scope includes a sample of nine listed international shipping companies accounting for 49% of the global market share with data collected from 2010 to 2020. Survey responses from 15 investment experts were also obtained. We applied a hybrid multiple criteria decision-making (MCDM) method integrating the Decision-Making Trial and Evaluation Laboratory (DEMATEL), analytic network process, and modified VlseKriterijumska Optimizacija I Kompromisno techniques to be the DANP-mV model to identify the causal relationships among the dimensions and criteria, providing ways of narrowing the performance gaps of shipping companies. The results indicate that financial performance is the main cause affecting COVID-19 and ESG practices. The ESG practices influence bond financing. The largest performance gaps across shipping companies include earnings per share (EPS), yield to maturity, corporate social responsibility (CSR), and timely delivery. The findings of this study suggest that shipping companies may focus on gross profit margin to improve EPS, term to maturity to enhance yield to maturity, social distancing policy to meet timely delivery, and the board size to enhance corporate social responsibility (CSR). The outcome of this study aids shipping companies in prioritizing their resources and investors in selecting shipping company stocks in response to COVID-19.

A Comparative Study of Using MCDM Methods Integrated with Entropy Weight Method for Evaluating Facility Location Problem

The location selection of facilities became a major interest for the organizations to establish their planned business for a long period of time. The choice of the best location among a set of candidate locations is a complex process. Although the multiple criteria decision making (MCDM) methods are applicable for location selection problems, different solutions can be obtained using different MCDM methods. Thus, a comparative study between four different MCDM methods was applied within numerical example to show the deviations in ranking of the alternatives that occurs when different methods are used. The weights of attributes are assigned using objective method namely Entropy weight method. The rank disagreements are expressed using spearman`s correlation coefficients.

Use of DELPHI-AHP Method to Identify annd Analyze Risks in Seaport Dry Port System

The dry port concept has recently gained rising consideration in the multimodal transport context from the point of view both of researchers and stakeholders related to the benefits of the seaport dry port system. Given the relevance of the topic, the present paper aims to identify the potential risk factors of the three major parts that constitute the seaport dry port system and present a conceptual framework to facilitate risk factors analysis. Based on a three-step approach, starting with a systematic literature review, which resulted in 204 collected and examined papers, which allowed identifying 181 potential risk factors with an average of 60 risk factors in each major part of the studied system. In addition, we used a survey based on the Delphi technique to ensure a good extraction of data from 12 selected experts related to the seaport dry port system; then, we used the MCDM (Multiple-Criteria Decision-Making) method AHP (Analytic Hierarchy Process) in order to: 1) present a hierarchy that simplifies the complexity of the studied system in an organized structure; 2) analyze and assess risk factors based on the identified criteria. A case study involving the Moroccan seaport dry port system of Casablanca illustrates that the seaport part is critical and any major risk factor in this part can even paralyze the operations of the whole system, especially if that risk factor belongs to the human factors category or economic risk category, which is also considered in the study as a critical category.

A Novel Multi-Criteria Assessment Approach for Post-COVID-19 Production Strategies in Vietnam Manufacturing Industry: OPA–Fuzzy EDAS Model

The global manufacturing supply chain has been disrupted by the negative impacts of the pandemic. In Southeast Asia, Vietnam’s manufacturing industry is one of the most strongly integrated with global and regional supply chains. The production strategies in the “new normal” are the key solution to the survival and sustainable development of manufacturers. This study aims to develop a two-stage framework to investigate the impacts of COVID-19 and the post-COVID-19 production strategies for Vietnam’s manufacturing industry. As a theoretical contribution, this study proposes a novel and robust integration approach, which combines the Ordinal Priority Approach (OPA) and Fuzzy Evaluation Based on Distance from Average Solution (Fuzzy EDAS), for the first time. The negative impacts of the pandemic were identified and weighted by the OPA method. Then, production strategies were comprehensively evaluated using the Fuzzy EDAS method. Findings indicate that digitization and on-site renewable energy are the most essential recovery strategies for manufacturing in Vietnam. These findings are validated by comparisons with the results of recent multiple criteria decision-making (MCDM) methods. Furthermore, weight sensitivity analysis reveals different suitability of strategies for short-term and long-term negative impacts. As a managerial implication, the multi-scenario ranking results help managers to make resource-allocation decisions for the implementation of post-COVID-19 production strategies.

A Qualitative-Quantitative Fuzzy Evaluation Model for Selecting an International Ocean Freight Logistics Provider

To ensure the best possible integrated logistics service performance, how to select an international ocean freight logistics provider (IOFLP) suitable for shippers is an important issue. The main purpose of this paper is to construct a qualitative-quantitative fuzzy multiple criteria decision-making (MCDM) evaluation model to empirically select an optimal IOFLP. After reviewing the literature and gathering experts' opinions, 23 criteria in five assessment aspects suitable for the selection of an IOFLP were obtained. The study then constructed a fuzzy MCDM selection model based on quantitative-qualitative criteria, and conducted a questionnaire survey of import/export shippers in Taiwan in order to interpret the operating processes of the proposed model. The empirical results indicated that company P was the IOFLP considered optimal by the shippers in Taiwan. Moreover, the proposed qualitative-quantitative fuzzy MCDM method and research methodology in this study can be employed as a practical tool for business applications in the future.

Circular supplier selection in the construction industry: A sustainability perspective for the emerging economies

Supplier selection is one of the most important multi-criteria problems in supply chain management (SCM). Most of the existing decision-making frameworks for selecting suppliers in the construction industry have given priority to criteria such as cost, delivery, and quality. However, due to the current emphasis on achieving sustainability and reducing environmental impact, organizations are increasingly embracing circular economy (CE) principles. In this study, thereby, we proposed an integrated multiple-criteria decision-making (MCDM) framework, which is comprised of a fuzzy analytical hierarchy process (FAHP) and a preference ranking organization method for enrichment of evaluations II (PROMETHEE II) for circular supplier selection in the construction industry from the perspective of countries with emerging economies. In the proposed framework, FAHP was used to first identify the weight of each criterion and sub-criteria, and PROMETHEE II was used to rank the suppliers from best to worst. Results showed that on-time delivery, conformance to specifications, and rejection rate are the top three criteria for supplier selection. Additionally, the top three circular supplier selection criteria included pollution control initiatives, green packaging, and responses toward environmental regulations and standards. The result of this approach has been compared with another MCDM method, namely the weighted aggregated sum product assessment (WASPAS) method, which validated the accuracy and efficiency of the proposed approach. Through the implementation of circular supplier selection, the proposed research is expected to reinforce the circular supply chain model, which can help managers in the construction sector to improve the sustainability of their overall business.

A PROBABILISTIC LINGUISTIC VIKOR METHOD TO SOLVE MCDM PROBLEMS WITH INCONSISTENT CRITERIA FOR DIFFERENT ALTERNATIVES

VIKOR is a well-defined multiple criteria decision-making (MCDM) method since it reflects different risk attitudes of decision-makers by measuring the overall performance of an alternative under all criteria as “group value” and the worst performance of the alternative under all criteria as “individual regret”, but it cannot deal with MCDM problems where the criteria of different alternatives are inconsistent (different) and the decision information is uncertain. To address these problems, we present a probabilistic linguistic VIKOR method by combining with probabilistic linguistic term sets which portrays uncertain information such as individual hesitancy and incomplete belief flexibly. In addition, we introduce the aspired and tolerable values of criteria as reference points to measure the closeness degrees of alternatives to the ideal solution. To compare group values and individual regrets of different alternatives, we develop a vector normalization method that considers the number of criteria. The robustness of the aggregation results of group values and individual regrets is improved based on the extended Borda rule, which takes into account both values and ranks of alternatives in the aggregation. A case study of personnel evaluation demonstrates the effectiveness of the proposed method for solving MCDM problems with inconsistent criteria and uncertain decision information.

A Study on the Optimization of In-Process Inspection Procedure for Active Pharmaceutical Ingredients Manufacturing Process

The in-process inspection procedure is one of the critical operations in the active pharmaceutical ingredients manufacturing process. This study aims to improve the performance of the IPI service system in terms of three main criteria, namely service level, cycle time, and maximum tardy time. In solving this multiple-criteria decision-making problem, the proposed study seeks to redesign three process control factors, namely the service configuration, the dispatching rule, and the scheduling rule. The problem is solved using the Taguchi robust design methodology. Since the Taguchi method handles parameter design problems with only one criterion, Technique for Order Preference by Similarity to an Ideal Solution, a multiple-criteria decision-making method, is used to provide a surrogate response to the Taguchi method. The numerical results show that the redesigned IPI system improves the service level by 28.75%, the cycle time by 18.32%, and the maximum tardy time by 22.22%.

Application of a Robust Decision-Making Rule for Comprehensive Assessment of Laser Cutting Conditions and Performance

Laser cutting parameters synergistically affect, although in different quantitative and qualitative manners, multiple process performances, such as the resulting cut quality characteristics, material removal rate, cutting time, and costs, and the determination of the most appropriate laser cutting conditions for a given application is of prime importance. Given the existence of multiple mutually opposite performances, assessment and laser cutting conditions and performance can be considered a multiple-criteria decision-making (MCDM) problem. In order to overcome the possible inconsistency of rankings determined by different MCDM methods while solving the same decision-making problem, the present study promotes a novel methodology for the assessment and selection of laser cutting conditions by developing a robust decision-making rule (RDMR) that combines different decision-making rules from six MCDM methods and Taguchi’s principles of robust design. In order to illustrate the application of the proposed methodology, CO2 laser cutting in a stainless-steel experiment, based on the use of the Box–Behnken design, was conducted. On the basis of the experimental results, a comprehensive laser cutting MCDM model was developed with seven criteria related to cut quality (i.e., kerf geometry and cut surface), productivity, variable costs, and environmental aspects. It was observed that there was no laser cutting condition that could be considered as the best regime with respect to the different laser cutting process performances. Kendall’s and Spearman’s rank correlation coefficients indicated a certain level of disagreement among the resulting rankings of the laser cutting conditions produced by the considered MCDM methods, whereas the application of the proposed RDMR ensured the highest level of ranking consistency. Some possibilities for modeling of RDMR and its further use for the assessment of arbitrarily chosen laser cutting conditions and the use of the derived model to perform sensitivity analysis for determining the most influential laser cutting parameters are also discussed and addressed. It was observed that laser cutting parameters in different laser cutting conditions may have a variable effect on the resulting overall process performances. The comparison of the obtained results and the results determined by classical desirability-based multi-objective optimization revealed that there exists substantial agreement between the most preferable and least preferable laser cutting conditions, thus justifying the applied methodology.

Multi-criteria decision-making for coronavirus disease 2019 applications: a theoretical analysis review.

The influence of the ongoing COVID-19 pandemic that is being felt in all spheres of our lives and has a remarkable effect on global health care delivery occurs amongst the ongoing global health crisis of patients and the required services. From the time of the first detection of infection amongst the public, researchers investigated various applications in the fight against the COVID-19 outbreak and outlined the crucial roles of different research areas in this unprecedented battle. In the context of existing studies in the literature surrounding COVID-19, related to medical treatment decisions, the dimensions of context addressed in previous multidisciplinary studies reveal the lack of appropriate decision mechanisms during the COVID-19 outbreak. Multiple criteria decision making (MCDM) has been applied widely in our daily lives in various ways with numerous successful stories to help analyse complex decisions and provide an accurate decision process. The rise of MCDM in combating COVID-19 from a theoretical perspective view needs further investigation to meet the important characteristic points that match integrating MCDM and COVID-19. To this end, a comprehensive review and an analysis of these multidisciplinary fields, carried out by different MCDM theories concerning COVID19 in complex case studies, are provided. Research directions on exploring the potentials of MCDM and enhancing its capabilities and power through two directions (i.e. development and evaluation) in COVID-19 are thoroughly discussed. In addition, Bibliometrics has been analysed, visualization and interpretation based on the evaluation and development category using R-tool involves; annual scientific production, country scientific production, Wordcloud, factor analysis in bibliographic, and country collaboration map. Furthermore, 8 characteristic points that go through the analysis based on new tables of information are highlighted and discussed to cover several important facts and percentages associated with standardising the evaluation criteria, MCDM theory in ranking alternatives and weighting criteria, operators used with the MCDM methods, normalisation types for the data used, MCDM theory contexts, selected experts ways, validation scheme for effective MCDM theory and the challenges of MCDM theory used in COVID-19 studies. Accordingly, a recommended MCDM theory solution is presented through three distinct phases as a future direction in COVID19 studies. Key phases of this methodology include the Fuzzy Delphi method for unifying criteria and establishing importance level, Fuzzy weighted Zero Inconsistency for weighting to mitigate the shortcomings of the previous weighting techniques and the MCDM approach by the name Fuzzy Decision by Opinion Score method for prioritising alternatives and providing a unique ranking solution. This study will provide MCDM researchers and the wider community an overview of the current status of MCDM evaluation and development methods and motivate researchers in harnessing MCDM potentials in tackling an accurate decision for different fields against COVID-19.

A Novel Integration of IF-DEMATEL and TOPSIS for the Classifier Selection Problem in Assistive Technology Adoption for People with Dementia.

The classifier selection problem in Assistive Technology Adoption refers to selecting the classification algorithms that have the best performance in predicting the adoption of technology, and is often addressed through measuring different single performance indicators. Satisfactory classifier selection can help in reducing time and costs involved in the technology adoption process. As there are multiple criteria from different domains and several candidate classification algorithms, the classifier selection process is now a problem that can be addressed using Multiple-Criteria Decision-Making (MCDM) methods. This paper proposes a novel approach to address the classifier selection problem by integrating Intuitionistic Fuzzy Sets (IFS), Decision Making Trial and Evaluation Laboratory (DEMATEL), and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The step-by-step procedure behind this application is as follows. First, IF-DEMATEL was used for estimating the criteria and sub-criteria weights considering uncertainty. This method was also employed to evaluate the interrelations among classifier selection criteria. Finally, a modified TOPSIS was applied to generate an overall suitability index per classifier so that the most effective ones can be selected. The proposed approach was validated using a real-world case study concerning the adoption of a mobile-based reminding solution by People with Dementia (PwD). The outputs allow public health managers to accurately identify whether PwD can adopt an assistive technology which results in (i) reduced cost overruns due to wrong classification, (ii) improved quality of life of adopters, and (iii) rapid deployment of intervention alternatives for non-adopters.