A New Decision-Making Approach Based on Fermatean Fuzzy Sets and WASPAS for Green Construction Supplier Evaluation

An identification of optimal waste disposal method for dumpsite remediation using the Fermatean fuzzy multi-criteria decision-making method

Improperly managed wastes that have been dumped in landfills over the years pose various challenges, but they also offer potential benefits. The feasibility of recycling such waste depends on the type of wastes, the condition of dumpsites, and the technology implemented for disposal. The selection of an alternative waste disposal method from the many available options for dumpsite remediation is a complex decision-making process among experts. The primary aim of this study is to assist in an extended multi-criteria decision-making (MCDM) method to reduce complexity in the proposed dumpsite remediation problem influenced by multiple criteria and to identify the optimal waste disposal method. Data uncertainties are managed with the proposed Fermatean fuzzy preference scale, and the importance of all socio-economic criteria is assessed using the full consistency method (FUCOM). The final ranking results of the weighted aggregated sum product assessment (WASPAS) method identify that the Waste-to-Energy (WtE) process could play a significant role in the disposal of land-filled unprocessed wastes, promoting sustainable waste management. Meanwhile, the methodology explores the idea that financial and logistical constraints may limit the feasibility of large-scale recycling efforts. This combination of environmental science and decision science addresses real-world challenges, helping municipal solid waste management authorities implement sustainable waste management practices.

Challenges to corporate social responsibility adoption for sustainability: A picture fuzzy approach

Corporate social responsibility (CSR) has become crucial to businesses seeking to adopt sustainable development. However, there are several challenges to CSR adoption for sustainability that the present research aims to identify and evaluate, in addition to assessing the EU's response to these challenges. To this end, a novel picture fuzzy SWARA-TOPSIS method is proposed to rank EU countries after identifying the challenges that they face through a literature review. The results indicate that out of eight identified challenges, "Leadership Mindset and Corporate Commitment" is the most significant issue to CSR adoption for sustainability. Additionally, Italy shows the best performance in adopting CSR for sustainability, while Malta shows the worst. These results are discussed, and policy implications are presented. Integr Environ Assess Manag 2023;19:1254-1275. © 2023 SETAC.

Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure

To deal with situations involving uncertainty, Fermatean fuzzy sets are more effective than Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. Applications for fuzzy similarity measures can be found in a wide range of fields, including clustering analysis, classification issues, medical diagnosis, etc. The computation of the weights of the criteria in a multi-criteria decision-making problem heavily relies on fuzzy entropy measurements. In this paper, we employ t-conorms to suggest various Fermatean fuzzy similarity measures. We have also discussed all of their interesting characteristics. Using the suggested similarity measurements, we have created some new entropy measures for Fermatean fuzzy sets. By using numerical comparison and linguistic hedging, we have established the superiority of the suggested similarity metrics and entropy measures over the existing measures in the Fermatean fuzzy environment. The usefulness of the proposed Fermatean fuzzy similarity measurements is shown by pattern analysis. Last but not least, a novel multi-attribute decision-making approach is described that tackles a significant flaw in the order preference by similarity to the ideal solution, a conventional approach to decision-making, in a Fermatean fuzzy environment.

Fermatean Fuzzy CODAS Approach with Topology and Its Application to Sustainable Supplier Selection

A Fermatean fuzzy set (FFS) is a reliable method for representing uncertainty in “multi-criteria decision-making” (MCDM). This research seeks to examine the topological properties of FFSs and to establish the notion of “Fermatean fuzzy topology” (FFT). An FFT is the generalisation of existing fuzzy topologies. Several aspects of FFT are examined and various novel concepts are proposed, which include Fermatean fuzzy α-continuity between FFTSs and Fermatean fuzzy connectedness. To deal multiple challenges in sustainable supply chain management, a Fermatean fuzzy “combinative distance-based assessment” (CODAS) method was developed. The proposed FF CODAS technique involves various key features for MCDM. Firstly, a known reputation vector or equal expert weights is determined based on the reputation, experience and qualifications of the experts. Secondly, the Fermatean fuzzy direct rating approach is used to establish the relative relevance of criteria based on the expert group’s evaluation preferences. Thirdly, the Fermatean fuzzy CODAS approach is used to construct alternative orderings based on their assessment scores. Finally, an application is developed to show the benefit of the suggested supplier selection approach. Additionally, the symmetry of an optimal decision in application is carried out by a comparison analysis of the suggested models with some existing models.

Blockchain knowledge selection under the trapezoidal fermatean fuzzy number

Blockchain knowledge signifies a useful fundamental knowledge to safeguard faith in transboundary transmittals for main banks and financial institutions. In the study of group decision-making, the most important issue is how to coordinate opinions from different blockchains to reach a compromise under uncertainty. To tackle uncertainties surrounding multi-attribute group decision-making (MAGDM) problems in real-life scenes, we introduce a trapezoidal fermatean fuzzy set which generalizes trapezoidal fuzzy sets and fermatean fuzzy sets. The trapezoidal fermatean fuzzy model enables the degrees of membership, abstention, and non-membership to be expressed by linguistic terms. We define the operational laws of trapezoidal fermatean fuzzy numbers, and Einstein aggregation operator based on the trapezoidal fermatean fuzzy number. This makes it more flexible and descriptive to model the attitudes of Blockchain knowledge in MAGDM applications. Since multi-input arguments are interconnected and Blockchain knowledge has a lot of options perception, we also define the TOPSIS technique to facilitate the fusion of trapezoidal fermatean fuzzy information. With the aid of the trapezoidal fermatean fuzzy-TOPSIS technique, the main goal of this research is to present a general MAGDM framework by integrating the step with the complex proportional assessment. A trapezoidal fermatean positive ideal solution always wants the maximum value of the benefit criteria and the minimum value of the cost criteria. On the other hand, the trapezoidal fermatean negative ideal solution always wants the maximum value of the cost criteria and the minimum value of the benefit criteria. An integrated trapezoidal fermatean fuzzy-TOPSIS framework is established. In the proposed decision framework, the trapezoidal fermatean fuzzy-TOPSIS method is utilized to identify the subjective weights of decision attributes, and the trapezoidal fermatean fuzzy-TOPSIS approach is used to rank alternatives. Lastly, a case study concerning blockchain knowledge assessment is presented to demonstrate that the suggested scheme is feasible and effective. Furthermore, sensitivity and comparison analyses are conducted to show the robustness and superiority of the proposed method.

Comparison of hospital service performances under COVID-19 pandemics for pilot regions with low vaccination rates

It is essential to measure the quality and performance of health centers and propose policies in order for health services to continue without interruption during the pandemic period and for the continuous and proper implementation of new procedures in hospitals with COVID-19.The measurement of service quality and performance in hospitals should be provided not only for the smooth flow of health services that are vital for individuals but also for the elimination of hesitations in the treatment and vaccination processes related to COVID-19. Previously, models have been proposed by introducing some criteria to measure and evaluate hospital service performance in some extraordinary conditions, but such a study has not yet been put forward under pandemic conditions. Starting from this point, we aim to fill the gap in the literature by conducting a measurement study for hospitals in the pilot region, where COVID-19 cases are common but vaccination is observed at low rates. For this aim, the evaluation criteria are gathered under basic dimensions as in SERVPERF (Service Performance), which is a widely used tool for measuring service quality and a fuzzy multi-criteria decision analysis is proposed to measure the service performance of state hospitals for a pilot region. In the proposed methodology, the integrated methods consisting of CRITIC-TOPSIS have been extended with fermatean fuzzy sets. Expert opinions are taken via questionaries to determine hospital service performances. Based on the results obtained from the hospitals in the pilot region, the policies and strategies to be adopted by the hospitals serving under pandemic conditions worldwide to increase the service quality have been put forward. Additionally, the sensitivity of the parameters in the problem is measured, and then the validity of the obtained results is also validated. According to the results, assurance is determined as the most important main service performance factor during the pandemic period. So, the managers should develop strategies to address people's concerns about vaccines and increase people's trust in hospitals.

Locating a disinfection facility for hazardous healthcare waste in the COVID-19 era: a novel approach based on Fermatean fuzzy ITARA-MARCOS and random forest recursive feature elimination algorithm

Hazardous healthcare waste (HCW) management system is one of the most critical urban systems affected by the COVID-19 pandemic due to the increase in waste generation rate in hospitals and medical centers dealing with infected patients as well as the degree of hazardousness of generated waste due to exposure to the virus. In this regard, waste network flow would face severe problems without taking care of hazardous waste through disinfection facilities. For this purpose, this study aims to develop an advanced decision support system based on a multi-stage model that was combined with the random forest recursive feature elimination (RF-RFE) algorithm, the indifference threshold-based attribute ratio analysis (ITARA), and measurement of alternatives and ranking according to compromise solution (MARCOS) methods into a unique framework under the Fermatean fuzzy environment. In the first stage, the innovative Fermatean fuzzy RF-RFE algorithm extracts core criteria from a finite set of initial criteria. In the second stage, the novel Fermatean fuzzy ITARA determines the semi-objective importance of the core criteria. In the third stage, the new Fermatean fuzzy MARCOS method ranks alternatives. A real-life case study in Istanbul, Turkey, illustrates the applicability of the introduced methodology. Our empirical findings indicate that "Pendik" is the best among five candidate locations for sitting a new disinfection facility for hazardous HCW in Istanbul. The sensitivity and comparative analyses confirmed that our approach is highly robust and reliable. This approach could be used to tackle other critical multi-dimensional problems related to COVID-19 and support sustainability and circular economy.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10479-022-04822-0.

An enhanced VIKOR method for multi-criteria group decision-making with complex Fermatean fuzzy sets

This paper aims to propose a new decision-making approach retaining the fascinating traits of the conventional VIKOR method in the context of the enrich multidimensional complex Fermatean fuzzy $ N $-soft set. The VIKOR technique is contemplated as the most reliable decision-making approach among others which employs a strategy to identify the compromise solution with advantageous distance from the positive ideal solution possesses maximum majority utility and minimum individual regret. At the same time, the paramount characteristic of the complex Fermatean fuzzy $ N $-soft set considers the proclivity to capture two-dimensional uncertain and imprecise information along with the multi-valued parameters. This article expands the literature to handle the multi-attribute group decision-making strategy by introducing a technique, namely, the complex Fermatean fuzzy $ N $-soft VIKOR method that amalgamates the unconventional traits of complex Fermatean fuzzy $ N $-soft with the capability of the VIKOR method. The proposed technique permits the assignment of the $ N $-soft grades to the decision-makers, alternatives, and attributes based on their performances. Firstly, we unify these individual opinions of all decision-makers about the alternatives by employing the complex Fermatean fuzzy $ N $-soft weighted average operator. After that, all entities of the aggregated decision matrix are converted into crisp data by utilizing the score function. Furthermore, we calculate the ranking measures of the group utility and the individual regret by assigning the weight of strategy belongs to the interval $ [0, 1]. $ To find the compromise solution, we arrange the ranking measures in ascending order, and the alternative that possesses the conditions of compromise solution is selected. We demonstrate the presented multi-attribute group decision-making technique by selecting the best location for a nuclear power plant. We conduct the comparative analysis of the presented technique with Fermatean fuzzy TOPSIS to endorse the veracity and accuracy of our method. Finally, we explain the merits and limitations of our strategy and give some concluding remarks.

Fermatean fuzzy copula aggregation operators and similarity measures-based complex proportional assessment approach for renewable energy source selection

Selecting the optimal renewable energy source (RES) is a complex multi-criteria decision-making (MCDM) problem due to the association of diverse conflicting criteria with uncertain information. The utilization of Fermatean fuzzy numbers is successfully treated with the qualitative data and uncertain information that often occur in realistic MCDM problems. In this paper, an extended complex proportional assessment (COPRAS) approach is developed to treat the decision-making problems in a Fermatean fuzzy set (FFS) context. First, to aggregate the Fermatean fuzzy information, a new Fermatean fuzzy Archimedean copula-based Maclaurin symmetric mean operator is introduced with its desirable characteristics. This proposed operator not only considers the interrelationships between multiple numbers of criteria, but also associates more than one marginal distribution, thus avoiding information loss in the process of aggregation. Second, new similarity measures are developed to quantify the degree of similarity between Fermatean fuzzy perspectives more effectively and are further utilized to compute the weights of the criteria. Third, an integrated Fermatean fuzzy-COPRAS approach using the Archimedean copula-based Maclaurin symmetric mean operator and similarity measure has been developed to assess and rank the alternatives under the FFS perspective. Furthermore, a case study of RES selection is presented to validate the feasibility and practicality of the developed model. Comparative and sensitivity analyses are used to check the reliability and strength of the proposed method.

Rough fermatean fuzzy ideals in semigroups

In multiple criteria decision making (MCDM) problem, the decision maker deal with a situation where the sum of membership and non-membership grade of an attributes does not belongs to [0, 1]. To avoid such a situation, we proposed a new type of fuzzy system known as fermatean fuzzy system. More precisely, we presented the notion of fermatean fuzzy ideal theory and rough fermatean fuzzy sets in semigroups. The idea of lower and upper approximation in fermatean fuzzy sets has been initiated. The study has been further extended to rough fermatean fuzzy left(resp. right, interior) ideals in semigroup. Several results related to this notion are determined.

A new extension of fuzzy decision by opinion score method based on Fermatean fuzzy: A benchmarking COVID-19 machine learning methods

To date, for the purpose of solving the complex problems in the area of expert system, Multi criteria decision making is the best technique to offer the suitable solution. In the academic literature, the MCDM methods suffered from many challenges. The most important challenges are uncertainty and vagueness. One of the latest MCDM method, called the fuzzy decision by opinion score method (FDOSM). However, there are still some vagueness issues around these methods (mention some of them). According to the advantage of the Fermatean fuzzy set in solving these issues, in this research extends FDOSM into Fermatean-FDOSM so as to effectively benchmark the real-life problem. In this study, we present our methodology in two phases. The first phase presents the mathematical model of Fermatean-FDOSM which is composed of three stages of FDOSM. The second phase applied the new extension to benchmark the COVID-19 machine learning methods. The finding of Fermatean-FDOSM after comparing the result with the basic FDSOM and TOPSIS, is more logical and undergoing a systematic ranking. In the validation process, objective validation is applied to validate the final result of Fermatean-FDOSM. The result of Fermatean-FDOSM is valid, and more logical and in line with decision makers’ opinions.

Adapting Urban Transport Planning to the COVID-19 Pandemic: An Integrated Fermatean Fuzzy Model

The critical worldwide problem of adapting urban transport planning to COVID-19 is for the first time comprehensively addressed and solved in this study. It primarily aims to help transport planners increase the resilience of transport systems. Firstly, a multi-level decision-making hierarchy structure based on four main criteria and 17 sub-criteria is introduced for relevant stakeholders to provide a practical framework for assessing existing transport plans. Then, a three-stage integrated Fermatean fuzzy model for adapting urban transport planning to the pandemic is presented. The model hybridizes the method based on the removal effects of criteria (MEREC) and combined compromise solution (CoCoSo) method into a unique methodological framework under the Fermatean fuzzy environment. A case study provides decision-making guidelines on how to adapt transport plans to COVID-19 in the real-world context of Belgrade, Serbia. The research findings show that the pandemic significantly changed the priorities of transport planning strategies and measures. "Non-motorized travel" is now the best alternative since its numerous short-term measures lead to better transport service. The major advantages of the introduced model are higher flexibility and a more precise fusion of experts' preference information. The integrated Fermatean fuzzy model could be used for adapting other emerging problems to COVID-19.

An extended MABAC method based on prospect theory with unknown weight information under Fermatean fuzzy environment for risk investment assessment in B&R

The assessment of investment risk for the countries along the route in Belt and Road (B&R) can be deemed as a multiple criteria group decision making (MCGDM) issue since multiple investment options based on diverse criterions are assessment by experts. Pondering that the complexity and uncertainty of the assessment setting and the cognition fuzziness and psychological behavior of experts bring challenges to risk assessment, this paper designed an integrated MCGDM risk investment evaluation framework by synthesizing MABAC method and prospect theory under Fermatean fuzzy setting. Firstly, a Fermatean fuzzy interactive distance measure is presented to ascertain the weight of evaluation experts and criterions. Next, some Fermatean fuzzy Frank aggregation operators based upon the proposed Frank operations are developed to fuse Fermatean fuzzy information efficiently. In addition, an innovative evaluation framework for risk investment is designed based on improved prospect theory MABAC and CRITIC approaches. Conclusively, an empirical concerning risk investment issues in B&R is employed to confirm the applicability and feasibility of the constructed evaluation framework, involving the simulation experiments on sensitivity analysis and contrast studies. The assessment information provided by investors using the linguistic assessment terms based upon their cognition ability of them. These outcomes obtained by the propounded method and comparison analysis further emphasize the validity and salient merits of the propounded framework and provide several auxiliary suggestions for investors.

Multicriteria decision-making based on distance measures and knowledge measures of Fermatean fuzzy sets

Fermatean fuzzy sets are more powerful than fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets in handling various problems involving uncertainty. The distance measures in the fuzzy and non-standard fuzzy frameworks have got their applicability in various areas such as pattern analysis, clustering, medical diagnosis, etc. Also, the fuzzy and non-standard fuzzy knowledge measures have played a vital role in computing the criteria weights in the multicriteria decision-making problems. As there is no study concerning the distance and knowledge measures of Fermatean fuzzy sets, so in this paper, we propose some novel distance measures for Fermatean fuzzy sets using t-conorms. We also discuss their various desirable properties. With the help of suggested distance measures, we introduce some knowledge measures for Fermatean fuzzy sets. Through numerical comparison and linguistic hedges, we establish the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean/Fermatean fuzzy setting. At last, we demonstrate the application of the suggested measures in pattern analyis and multicriteria decision-making.

Interval-valued fermatean fuzzy sets with multi-criteria weighted aggregated sum product assessment-based decision analysis framework

Fermatean fuzzy set, a generalization of the fuzzy set, is a significant way to tackle the complex uncertain information that arises in decision-analysis procedure and thus can be employed on a wider range of applications. Due to the inadequacy in accessible data, it is hard for decision experts to exactly define the belongingness grade (BG) and non-belongingness grade (NG) by crisp values. In such a situation, interval BG and interval NG are good selections. Thus, the aim of the study is to develop the doctrine of interval-valued Fermatean fuzzy sets (IVFFSs) and their fundamental operations. Next, the score and accuracy functions are proposed for interval-valued Fermatean fuzzy numbers (IVFFNs). Two aggregation operators (AOs) are developed for aggregating the IVFFSs information and discussed some axioms. Further, a weighted aggregated sum product assessment method for IVFFSs using developed AOs is introduced to handle the uncertain multi-criteria decision analysis problems. A case study of e-waste recycling partner selection is also considered to elucidate the feasibility and efficacy of the introduced framework. Finally, sensitivity and comparative analyses are given to elucidate the reliability and robustness of the obtained results.

Group decision-making with Fermatean fuzzy soft expert knowledge

With the rapid growth of population, the global impact of solar technology is increasing by the day due to its advantages over other power production technologies. Demand for solar panel systems is soaring, thus provoking the arrival of many new manufacturers. Sale dealers or suppliers face an uncertain problem to choose the most adequate technological solution. To effectively address such kind of issues, in this paper we propose the Fermatean fuzzy soft expert set model by combining Fermatean fuzzy sets and soft expert sets. We describe this hybrid model with numerical examples. From a theoretical standpoint, we demonstrate some essential properties and define operations for this setting. They comprise the definitions of complement, union and intersection, the OR operation and the AND operation. Concerning practice in this new environment, we provide an algorithm for multi-criteria group decision making whose productiveness and authenticity is dutifully tested. We explore a practical application of this approach (that is, the selection of a suitable brand of solar panel system). Lastly, we give a comparison of our model with certain related mathematical tools, including fuzzy and intuitionistic fuzzy soft expert set models.

A New Integrated FUCOM–CODAS Framework with Fermatean Fuzzy Information for Multi-Criteria Group Decision-Making

Smartphones have become an inevitable part of every facet of modern society. The selection of a particular smartphone brand from multiple options that are available is a complex and dynamic decision-making problem, involving multiple conflicting criteria that are associated with imprecise asymmetric information imposed by the uncertainty of the consumers. In this paper, we propose a novel hybrid full consistency method (FUCOM) and a combinative distance based assessment (CODAS) based on the multi-criteria group decision-making (MAGDM) framework in the Fermatean fuzzy (FF) domain for smartphone brand selection. We derive the criteria using the UTAUT2 (unified theory of acceptance and ese of technology) model. A group of 15 decision makers (DMs) participated in our study. We compare 14 leading smartphone brands in India and find that the brands having superior features of a good quality and selling a brand image at a affordable price outperform other smartphones. To check the validity of our framework, we compare the results using extant multi-criteria decision-making (MCDM) models. We observe our model provides a consistent solution. Furthermore, we carry out a sensitivity analysis for ascertaining the robustness and stability of the results generated by our model. The results of the sensitivity analysis show that our proposed framework delivers a stable and robust solution.

Assessment of distribution center locations using a multi-expert subjective-objective decision-making approach

Distribution is a strategic function of logistics in different companies. Establishing distribution centers (DCs) in appropriate locations helps companies to reach long-term goals and have better relations with their customers. Assessment of possible locations for opening new DCs can be considered as an MCDM (Multi-Criteria Decision-Making) problem. In this study, a decision-making approach is proposed to assess DC locations. The proposed approach is based on Stepwise Weight Assessment Ratio Analysis II (SWARA II), Method based on the Removal Effects of Criteria (MEREC), Weighted Aggregated Sum Product Assessment (WASPAS), simulation, and the assignment model. The assessment process is performed using the subjective and objective criteria weights determined based on multiple experts' judgments. The decision matrix, subjective weights and objective weights are modeled based on the triangular probability distribution to assess the possible alternatives. Then, using simulation and the assignment model, the final aggregated results are determined. A case of DC locations assessment is addressed to show the applicability of the proposed approach. A comparative analysis is also made to verify the results. The analyses of this study show that the proposed approach is efficient in dealing with the assessment of DC locations, and the final results are congruent with those of existing MCDM methods.

Grey relational analysis method based on cumulative prospect theory for intuitionistic fuzzy multi-attribute group decision making

The Multi-attribute group decision making (MAGDM) problem is an interesting everyday problem full of complexity and ambiguity. As an extended form of fuzzy sets, intuitionistic fuzzy sets (IFSs) can provide decision-makers (DMs) with a wider range of preferences for MAGDM. The grey relational analysis (GRA) is an effective method for dealing with MAGDM problems. However, in view of the incomplete and asymmetric information and the influence of DMs’ psychological factors on the decision result, we develop a new model that GRA method based on cumulative prospect theory (CPT) under the intuitionistic fuzzy environment. Moreover, the weight of attribute is calculated by entropy weight, so as to distinguish the importance level of attributes, which greatly improves the credibility of the selected scheme. simultaneously, the proposed method is used to the selection of optimal green suppliers for testifying the availability of this new model and the final comparison between this new method and the existing methods further verify the reliability. In addition, the proposed method provides some references for other selection problems.

Developing an interplay among the psychological barriers for the adoption of industry 4.0 phenomenon

This research aims to identify, rank, and create an interplay among the psychological barriers to adopting Industry 4.0 technologies in the manufacturing sector. A comprehensive literature review tracked by a discussion with industry and academic experts recognized 20 barriers. Based on three widely acclaimed statistical techniques, hybrid AHP-TOPSIS (Analytical Hierarchy Process-Technique for Order Performance by Similarity to Ideal Solution) and ISM (Interpretative Structural Modeling), critical psychological barriers have been investigated. A group of 8 experts from industry and academia with at least 10 years of experience was consulted for AHP and ISM techniques. Whereas TOPSIS was conducted by 443 operational-level users, including managers and supervisors of different functional areas of the manufacturing industry located in Pakistan. The findings reveal that ‘Fear of job losses’, ‘Fear of data loss/Risk of security breaches, ‘Lack of advanced & continued education of employees’ and ‘Lack of standards and reference architecture’, with highest importance weights, emerged as the most prominent psychological barriers in developing economies. Then the interrelations among these barriers resulted in a four-layered structural model. The driver barriers identified in the final model advocate that development in ‘advanced & continued education of employees’, ‘standards & reference architecture’ and ‘minimization of fear of job & data loss’ can expedite the adoption of industry 4.0 (i4.0) technologies. The study uniquely develops hierarchical relationships among the psychological barriers for adopting i4.0 in the manufacturing context using AHP-TOPSIS and ISM techniques. The study would be valuable for practitioners, decision-makers and companies that wish to focus their efforts and resources on removing the most critical barriers and challenges for the seamless implementation of Industry 4.0.

Application of Fuzzy-TOPSIS Method in Supporting Supplier Selection with Focus on HSE Criteria: A Case Study in the Oil and Gas Industry

Supply chain management is an emerging topic in the oil and gas industry. There is higher exposure of contractors to undesirable incidents and supplier selection is a multicriteria decision problem (MCDM). A fuzzy-TOPSIS method was employed in the evaluation of three suppliers regarding four HSE criteria. This method was applied in a case study of the oil and gas industry involving a contractor bidding process. Results reinforced that fuzzy-TOPSIS is a versatile and suitable method for supplier selection problems, with low computational complexity and promoting a better user experience. This method contributes to greater effectiveness and agility in the selection processes of suppliers regarding HSE management. The fuzzy-TOPSIS model is suitable for supplier selection problems and some of the benefits of applying this method are that it allows the attribution weights according to the level of importance of each criterion and considers the complexity, subjectivity, and uncertainty of the decision process. One has determined that it was essential to have a robust and consistent process for weighting the criteria and defining the most appropriate linguistic variables.

An Integrated Decision-Making Approach for Green Supplier Selection in an Agri-Food Supply Chain: Threshold of Robustness Worthiness

Along with the increased competition in production and service areas, many organizations attempt to provide their products at a lower price and higher quality. On the other hand, consideration of environmental criteria in the conventional supplier selection methodologies is required for companies trying to promote green supply chain management (GSCM). In this regard, a multi-criteria decision-making (MCDM) technique based on analytic hierarchy process (AHP) and fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) is used to evaluate and rate the suppliers. Then, considering the resource constraint, weight of criteria and a rank of suppliers are taken into account in a multi-objective mixed-integer linear programming (MOMILP) to determine the optimum order quantity of each supplier under uncertain conditions. To deal with the uncertain multi-objectiveness of the proposed model, a robust goal programming (RGP) approach based on Shannon entropy is applied. The offered methodology is applied to a real case study from a green service food manufacturing company in Iran in order to verify its applicability with a sensitivity analysis performed on different uncertainty levels. Furthermore, the threshold of robustness worthiness (TRW) is studied by applying different budgets of uncertainty for the green service food manufacturing company. Finally, a discussion and conclusion on the applicability of the methodology is provided, and an outlook to future research projects is given.