A Novel Approach for Evaluation of Projects Using an Interval–Valued Fuzzy Additive Ratio Assessment (ARAS) Method: A Case Study of Oil and Gas Well Drilling Projects

Decision Support in Selecting a Reliable Strategy for Sustainable Urban Transport Based on Laplacian Energy of T-Spherical Fuzzy Graphs

Sustainable transportation has a significant impact on factors related to urban development and economic development. Therefore, much research is being undertaken to select the best strategies to manage sustainable transportation. Transportation requires a carefully designed method to manage the development of mobility modes in terms of the pollution they produce or the use of renewable energy sources. However, due to numerous preferences of decision-makers and data uncertainty problems, it is challenging to select the optimal strategy. In this paper, we focus on creating a framework for determining the best strategy for sustainable transportation management. For this purpose, T-spherical fuzzy graphs will be used, which, together with the combination of Laplacian Energy, can accurately represent decision-makers’ preferences in an uncertain environment. Due to the lack of limitations of T-spherical fuzzy graphs and its numerous membership functions, decision-makers can decide which factor seems most important for selecting the optimal sustainable transportation strategy. Additionally, due to the applicability, the SFS TOPSIS approach has been used in this approach. The obtained results demonstrate the high performance of the proposed approach and the applicability of the approach in management and sustainable transport problems.

Symmetric and Asymmetric Data in Solution Models

This Special Issue covers symmetric and asymmetric data that occur in real-life problems. We invited authors to submit their theoretical or experimental research to present engineering and economic problem solution models that deal with symmetry or asymmetry of different data types. The Special Issue gained interest in the research community and received many submissions. After rigorous scientific evaluation by editors and reviewers, seventeen papers were accepted and published. The authors proposed different solution models, mainly covering uncertain data in multi-criteria decision-making problems as complex tools to balance the symmetry between goals, risks, and constraints to cope with the complicated problems in engineering or management. Therefore, we invite researchers interested in the topics to read the papers provided in the Special Issue.

An extended fuzzy decision-making framework using hesitant fuzzy sets for the drug selection to treat the mild symptoms of Coronavirus Disease 2019 (COVID-19)

The whole world is presently under threat from Coronavirus Disease 2019 (COVID-19), a new disease spread by a virus of the corona family, called a novel coronavirus. To date, the cases due to this disease are increasing exponentially, but there is no vaccine of COVID-19 available commercially. However, several antiviral therapies are used to treat the mild symptoms of COVID-19 disease. Still, it is quite complicated and uncertain decision to choose the best antiviral therapy to treat the mild symptom of COVID-19. Hesitant Fuzzy Sets (HFSs) are proven effective and valuable structures to express uncertain information in real-world issues. Therefore, here we used the hesitant fuzzy decision-making (DM) method. This study has chosen five methods or medicines to treat the mild symptom of COVID-19. These alternatives have been ranked by seven criteria for choosing an optimal method. The purpose of this study is to develop an innovative Additive Ratio Assessment (ARAS) approach to elucidate the DM problems. Next, a divergence measure based procedure is developed to assess the relative importance of the criteria rationally. To do this, a novel divergence measure is introduced for HFSs. A case study of drug selection for COVID-19 disease is considered to demonstrate the practicability and efficacy of the developed idea in real-life applications. Afterward, the outcome shows that Remdesivir is the best medicine for patients with mild symptoms of the COVID-19. Sensitivity analysis is presented to ensure the permanence of the introduced framework. Moreover, a comprehensive comparison with existing models is discussed to show the advantages of the developed framework. Finally, the results prove that the introduced ARAS approach is more effective and reliable than the existing models.

An Integrated Methodology Using Extended Swara and Dea for the Performance Analysis of Wastewater Treatment Plants: Turkey Case

Public and private companies make significant water infrastructure investments to meet increasing water demand. In this context, investments in wastewater treatment plants (WWTPs), which play an important role in recycling of used water, are also increasing. This study investigates determination of the efficiency scores of WWTPs considering each metropolitan municipality as a decision-making unit (DMU). In this study, a two-step methodology is established to determine efficiency scores of WWTPs. In the first step, the input and output parameters are searched by a literature review for the performance evaluation, and candidate parameters are determined. Then, to determine the most appropriate and related parameters, the importance weights of all candidate inputs and outputs are computed using the extended stepwise weight assessment ratio analysis (SWARA) method. Next, the inputs and outputs are chosen according to their importance weights. In the second step, efficiency scores of WWTPs are calculated using output-oriented data envelopment analysis (DEA) models. Based on the expert opinions, the parameters used as input variables are as follows: Daily Wastewater Amount per Person Discharged in Municipalities, WWTP Capacity, and Number of WWTPs; and the parameters used as output variables are as follows; Amount of Wastewater Treated in WWTPs and Municipal Population Served by WWTPs. The results are presented and discussed by sensitivity analysis. Results show that 14 metropolitan municipalities have total efficiency, 19 metropolitan municipalities have technical efficiency, and 21 metropolitan municipalities have scale efficiency.

An interval fuzzy number-based fuzzy collaborative forecasting approach for DRAM yield forecasting

Most existing fuzzy collaborative forecasting (FCF) methods adopt type-1 fuzzy numbers to represent fuzzy forecasts. FCF methods based on interval-valued fuzzy numbers (IFNs) are not widely used. However, the inner and outer sections of an IFN-based fuzzy forecast provide meaning information that serves different managerial purposes, which is a desirable feature for a FCF method. This study proposed an IFN-based FCF approach. Unlike existing IFN-based fuzzy association rules or fuzzy inference systems, the IFN-based FCF approach ensures that all actual values fall within the corresponding fuzzy forecasts. In addition, the IFN-based FCF approach optimizes the forecasting precision and accuracy with the outer and inner sections of the aggregation result, respectively. Based on the experimental results, the proposed FCF-II approach surpassed existing methods in forecasting the yield of a dynamic random access memory product.

Decision Making for Project Appraisal in Uncertain Environments: A Fuzzy-Possibilistic Approach of the Expanded NPV Method

The major drawback of the classic approaches for project appraisal is the lack of the possibility to handle change requests during the project’s life cycle. This fact incorporates the concept of uncertainty in the estimation of this investment’s worth. To resolve this issue, the authors use fuzzy numbers, possibilistic moments of fuzzy numbers and the hybrid (fuzzy statistic) fuzzy estimators’ method in order to introduce a fuzzy possibilistic version of the expanded net present value method (FPeNPV). This approach consists of two factors: the fuzzy possibilistic NPV and the fuzzy option premium. For the estimation of the fuzzy NPV, some basic assumptions are taken into consideration: (1) the opportunity cost of capital, used as the present value interest factor calculated through the weighted average cost of capital (WACC), (2) the equity cost, determined through the possibilistic set-up of the capital asset pricing model CAPM, and (3) the inflation factor, also included in the estimation of the NPV. The fuzzy estimators’ method is used for the computation of the fuzzy option premium. An algorithm of nine major steps leads to the computation of the FPeNPV. This gives the administration the opportunity to adapt to potential changes in the company’s internal and external environments. In this way, the symmetry between the planning and execution phase of a project can be reinstated. The results validate the statement that fuzzy and intelligent methods remain valuable tools to express uncertainty in various scientific areas. Finally, an illustrative example aims at a thorough comprehension of this new approach of the expanded NPV method.

Multi-Criteria Ranking of Green Materials According to the Goals of Sustainable Development

Modern, well-educated and experienced policy-makers support and promote the use of environmentally friendly materials and resources. The use of green resources is an exceptional and inevitable strategy to meet the needs of a rapidly growing Earth population. The growing population raises the need for new housing construction and urban infrastructure development. Such substances in construction refer to green building materials (GBMs). The environmental impact is lower if GBMs replace non-GBMs. Here, ranking among GBMs can facilitate and support the selection process. This study aimed to contribute to the body of knowledge to introduce a method for identifying and prioritizing GBMs in the construction industry to use in green building. The required data were collected using existing literature, interviews and questionnaires. Relevant Sustainable Development Goals (SDGs) are the first criteria for assessing GBM selection criteria. Critical weighted GBM selection criteria are the second criteria for prioritizing GBMs. The results show that “Natural, Plentiful and Renewable”, “Affordability from cradle to gate” and “Affordability during operation” are the top three GBM selection criteria. The real case study helped select “Stramit Strawboard”, “Aluminium Composite Panels (ACPs)” and “Solar Roof Tiles” as the most suitable GBMs for use in the context of the study. The model and results presented in this study will help actors of the construction industry to select and use GBMs more quickly and thus achieve a better level of construction sustainability, as well as environmental friendliness, than before.

A Distinctive Symmetric Analyzation of Improving Air Quality Using Multi-Criteria Decision Making Method under Uncertainty Conditions

This world has a wide range of technologies and possibilities that are available to control air pollution. Still, finding the best solution to control the contamination of the air without having any impact on humans is a complicated task. This proposal helps to improve the air quality using the multi-criteria decision making method. The decision to improve air quality is a challenging problem with today’s technology and environmental development level. The multi-criteria decision making method is quite often faced with conditions of uncertainty, which can be tackled by employing fuzzy set theory. In this paper, based on an objective weighting method (CCSD), we explore the improved fuzzy MULTIMOORA approach. We use the classical Interval-Valued Triangular Fuzzy Numbers (IVTFNs), viz. the symmetric lower and upper triangular numbers, as the basis. The triangular fuzzy number is identified by the triplets; the lowest, the most promising, and the highest possible values, symmetric with respect to the most promising value. When the lower and upper membership functions are equated to one, we get the normalized interval-valued triangular fuzzy numbers, which consist of symmetric intervals. We evaluate five alternatives among the four criteria using an improved MULTIMOORA method and select the best method for improving air quality in Tamil Nadu, India. Finally, a numerical example is illustrated to show the efficiency of the proposed method.

Picture Fuzzy ARAS Method for Freight Distribution Concept Selection

Companies can perform their freight distribution in three different ways. The first concept, the in-house concept, represents the use of a company’s own resources and knowledge to organize transportation from the production to retailers or from the warehouse to customers. The opposite concept is to outsource distribution activities by hiring third-party logistics providers. The third concept represents a combination of the previous two. Although the arguments in favor of outsourcing can be found in the literature, an appropriate selection of a freight distribution concept is specific for each company and depends on many evaluation criteria and their symmetrical roles. This paper presents a methodology that can be used by companies that need to choose their freight distribution concept. An advanced extension of the Additive Ratio ASsessment (ARAS) method is developed to solve the freight distribution concept selection problem. To illustrate the implementation of the proposed methodology, a tire manufacturing company from the Czech Republic is taken as a case study. However, the proposed picture fuzzy ARAS method is general and can be used by any other company. To validate the novel picture fuzzy ARAS method, a comparative analysis with the nine existing state-of-the-art picture fuzzy multi-criteria decision-making methods is provided.

Modeling an Uncertain Productivity Learning Process Using an Interval Fuzzy Methodology

Existing methods for forecasting the productivity of a factory are subject to a major drawback—the lower and upper bounds of productivity are usually determined by a few extreme cases, which unacceptably widens the productivity range. To address this drawback, an interval fuzzy number (IFN)-based mixed binary quadratic programming (MBQP)–ordered weighted average (OWA) approach is proposed in this study for modeling an uncertain productivity learning process. In the proposed methodology, the productivity range is divided into the inner and outer sections, which correspond to the lower and upper membership functions of an IFN-based fuzzy productivity forecast, respectively. In this manner, all actual values are included in the outer section, whereas most of the values are included within the inner section to fulfill different managerial purposes. According to the percentages of outlier cases, a suitable forecasting strategy can be selected. To derive the values of parameters in the IFN-based fuzzy productivity learning model, an MBQP model is proposed and optimized. Subsequently, according to the selected forecasting strategy, the OWA method is applied to defuzzify a fuzzy productivity forecast. The proposed methodology has been applied to the real case of a dynamic random access memory factory to evaluate its effectiveness. The experimental results indicate that the proposed methodology was superior to several existing methods, especially in terms of mean absolute error, mean absolute percentage error, and root mean square error in evaluating the forecasting accuracy. The forecasting precision achieved using the proposed methodology was also satisfactory.

Safety Assessment of Casting Workshop by Cloud Model and Cause and Effect-LOPA to Protect Employee Health

Safety assessment of a casting workshop will provide a clearer understanding of the important safety level required for a foundry. The main purpose of this study was to construct a composite safety assessment method to protect employee health using the cloud model and cause and effect–Layer of Protection Analysis (LOPA). In this study, the weights of evaluation indicators were determined using the subjective analytic hierarchy process and objective entropy weight method respectively. Then, to obtain the preference coefficient of the integrated weight more precisely, a new algorithm was proposed based on the least square method. Next, the safety level of the casting workshop was presented based on the qualitative and quantitative analysis of the cloud model, which realized the uncertainty conversion between qualitative concepts and their corresponding quantitative values, as well as taking the fuzziness and randomness into account; the validity of cloud model evaluation was validated by grey relational analysis. In addition, cause and effect was used to proactively identify factors that may lead to accidents. LOPA was used to correlate corresponding safety measures to the identified risk factors. 6 causes and 19 sub-causes that may contribute to accidents were identified, and 18 potential remedies, or independent protection layers (IPLs), were described as ways to protect employee health in foundry operations. A mechanical manufacturing business in Hunan, China was considered as a case study to demonstrate the applicability and benefits of the proposed safety assessment approach.

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

An Improved Multi-Source Data Fusion Method Based on the Belief Entropy and Divergence Measure

Dempster–Shafer (DS) evidence theory is widely applied in multi-source data fusion technology. However, classical DS combination rule fails to deal with the situation when evidence is highly in conflict. To address this problem, a novel multi-source data fusion method is proposed in this paper. The main steps of the proposed method are presented as follows. Firstly, the credibility weight of each piece of evidence is obtained after transforming the belief Jenson–Shannon divergence into belief similarities. Next, the belief entropy of each piece of evidence is calculated and the information volume weights of evidence are generated. Then, both credibility weights and information volume weights of evidence are unified to generate the final weight of each piece of evidence before the weighted average evidence is calculated. Then, the classical DS combination rule is used multiple times on the modified evidence to generate the fusing results. A numerical example compares the fusing result of the proposed method with that of other existing combination rules. Further, a practical application of fault diagnosis is presented to illustrate the plausibility and efficiency of the proposed method. The experimental result shows that the targeted type of fault is recognized most accurately by the proposed method in comparing with other combination rules.

Civil Engineering and Symmetry

A topic of utmost importance in civil engineering is finding optimal solutions throughout the life cycle of buildings and infrastructural objects, including their design, manufacturing, use, and maintenance. Operational research, management science, and optimisation methods provide a consistent and applicable groundwork for engineering decision-making. These topics have received the interest of researchers, and, after a rigorous peer-review process, eight papers have been published in the current special issue. The articles in this issue demonstrate how solutions in civil engineering, which bring economic, social and environmental benefits, are obtained through a variety of methodologies and tools. Usually, decision-makers need to take into account not just a single criterion, but several different criteria and, therefore, multi-criteria decision-making (MCDM) approaches have been suggested for application in five of the published papers; the rest of the papers apply other research methods. The methods and application case studies are shortly described further in the editorial.

Solution Models based on Symmetric and Asymmetric Information

This Special Issue covers symmetry and asymmetry phenomena occurring in real-life problems. We invited authors to submit their theoretical or experimental research presenting engineering and economic problem solution models dealing with the symmetry or asymmetry of different types of information. The issue gained interest in the research community and received many submissions. After rigorous scientific evaluation by editors and reviewers, nine papers were accepted and published. The authors proposed different solution models as integrated tools to find a balance between the components of sustainable global development, i.e., to find a symmetry axis concerning goals, risks, and constraints to cope with the complicated problems. We hope that a summary of the Special Issue as provided in this editorial will encourage a detailed analysis of the papers.

Time Series Data Fusion Based on Evidence Theory and OWA Operator

Time series data fusion is important in real applications such as target recognition based on sensors' information. The existing credibility decay model (CDM) is not efficient in the situation when the time interval between data from sensors is too long. To address this issue, a new method based on the ordered weighted aggregation operator (OWA) is presented in this paper. With the improvement to use the Q function in the OWA, the effect of time interval on the final fusion result is decreased. The application in target recognition based on time series data fusion illustrates the efficiency of the new method. The proposed method has promising aspects in time series data fusion.

Sustainable Development Goals Indicators: A Methodological Proposal for a Multidimensional Fuzzy Index in the Mediterranean Area

This paper describes a methodology for the construction of a multidimensional index for sustainability assessment in the context of the Sustainable Development Goals (SDGs) of the UN 2030 Agenda. The methodology is designed to properly capture the multidimensional nature of sustainable development and the SDG framework, introducing an innovative Fuzzy Multidimensional Index to measure the performance of Mediterranean countries. The focus is on agro-food sustainability, in-line with the aims of the Partnership for Research and Innovation in the Mediterranean Area (PRIMA). Drawing on fuzzy set theory, a step-by-step procedure was developed: the underlying dimensions of a set of selected indicators for the SDGs are identified by exploratory factor analysis; an innovative weighting method is applied to aggregate the indicators and calculate the country scores for each dimension and the Fuzzy Multidimensional Index. The PRIMA program will be a first step towards the implementation of innovative solutions, by funding international cooperation projects between countries on both sides of the Mediterranean for a decade: the Fuzzy Multidimensional Index will be the primary source of data for evaluating such projects and policies implemented from them; the Index will therefore be able to close a gap in the availability of appropriate data.

The Pentagonal Fuzzy Number:Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problems

In this paper, different measures of interval-valued pentagonal fuzzy numbers (IVPFN) associated with assorted membership functions (MF) were explored, considering significant exposure of multifarious interval-valued fuzzy numbers in neoteric studies.Also, the idea of MF is generalized somewhat to nonlinear membership functions for viewing the symmetries and asymmetries of the pentagonal fuzzy structures. Accordingly,the construction of level sets, for each case of linear and nonlinear MF was also carried out. Besides, defuzzification was undertaken using three methods and a ranking method, which were also the main features of this framework.The developed intellects were implemented in a game problem by taking the parameters as PFNs, ultimately resulting in a new direction for modeling real world problems and to comprehend the uncertainty of the parameters more precisely in the evaluation process.

Fuzzy Attribute Expansion Method for Multiple Attribute Decision-Making with Partial Attribute Values and Weights Unknown and Its Applications

In the real world, there commonly exists types of multiple attribute decision-making (MADM) problems with partial attribute values and weights totally unknown. Symmetry among some attribute information that is already known and unknown, and symmetry between the pure attribute set and fuzzy attribute membership set can be a considerable way to solve this type of MADM problem. In this paper, a fuzzy attribute expansion method is proposed to solve this type of problem based on two key techniques: the spline interpolation technique and the attribute weight reconfiguration technique, which are respectively used for the determination of attribute values and the reconfiguration of attribute weights. The spline interpolation technique to expand attribute values can enhance the performance of some regression methods and clustering methods by the comparisons between the results of these methods dealing with practical cases with and without the application of the technique, which further illustrates the effectiveness of this technique. For MADM problems with partial attribute values and weights totally unknown, compared with traditional fuzzy comprehensive evaluation (FCE), FCE with the application of fuzzy attribute expansion method can obtain results more similar with the ones when all attribute values and weights are known, which is proved by the practical power quality evaluation example.

Renewable Energy Technology Selection Problem Using Integrated H-SWARA-MULTIMOORA Approach

Due to the adaptation of recent pollution mitigation and justification policies there has been a growing trend for electricity generation from various renewable resources. The selection of the optimal renewable energy technology could be measured as a complex problem due to the complication of forthcoming circumstances in any country. Consequently, the proposed similar complex assessment problem can be tackled with the support of Multiple Attribute Decision Making (MADM) methods. The current research study investigates a technology selection problem by proposing a hybrid MADM approach based on the Step-Wise Weight Assessment Ratio Analysis (SWARA) approach with a hierarchical arrangement combined with the Multi-Objective Optimization on the basis of Ratio Analysis plus the full MULTIplicative form (MULTIMOORA). Ultimately, a conceptual case study regarding the selection of the optimal renewable energy technology based on a conceptual development project in Iran has been examined by the proposed combinative MADM methodology.

Interval Fuzzy Segments

In this paper, we bring together two concepts related to uncertainty and vagueness: fuzzy numbers and intervals. With them, we build a new structure whose elements we call interval fuzzy segments. We have undertaken this based on the conviction that the fuzzy numbers are a correct representation of the real numbers under situations of indeterminacy. We also believe that if it makes sense to consider the set of real numbers between two real bounds, then it also makes sense to consider the set of all the fuzzy numbers between two fuzzy number bounds. In this way, we extend the concept of real interval to the concept of interval fuzzy segment defined by two fuzzy bounds and a transition mapping that leads from the lower fuzzy bound to the upper fuzzy bound and this transition mapping generates the set of all the fuzzy numbers comprised between those fuzzy bounds. At the same time, this transition mapping brings the concept of interval fuzzy segment closer to the concept of line segment.