Interval Type-2 Fuzzy Environment Research Articles

Sensitivity analysis in multi-criteria decision making: A state-of-the-art research perspective using bibliometric analysis

In the present era, the implementation of scientifically grounded Multi-Criteria Decision Making (MCDM) has emerged as a pivotal solution to diverse decision-making challenges across various domains. Although a substantial body of exploratory, conceptual, and experimental studies exists, only 9.457% studies have incorporated sensitivity analyses to assess the robustness of MCDM methods. An exhaustive scientific exploration of sensitivity analysis within the scope of MCDM is thus lacking. This research aims to address this gap through Bibliometric Analysis while examining 1374 articles published between January 2000 and March 2023 from the Scopus database. Using RStudio (Biblioshiny), CiteSpace, and VOSviewer software, the study constructs a visual representation of the most prolific countries, institutions, and authors. Impressively, China takes the lead in article publications, while India excels in international collaboration. “An extended TODIM multi-criteria group decision-making method for green supplier selection in an interval type-2 fuzzy environment,” featured in the Journal of Environmental Management, emerges as the most cited paper with a total citation of 455. The study also identifies the top three most cited journals, namely “Journal of Cleaner Production,” “Expert Systems With Applications,” and “Computers and Industrial Engineering.” “North China Electric Power University” is the leading institute with the highest research outputs. “Pamučar D” is the most cited author, with 2594 citations and 39 articles, followed by “Kahraman C” and “Zavadskas EK. This study sheds light on trends in scientific developments and collaborations, providing a model for the application of sensitivity analysis in MCDM research and highlighting global trends. An understanding of the current state of sensitivity analysis research can assist researchers working in the entire domain of MCDM. Additionally, the visualization provides prescriptive data for future work and applications related to sensitivity analysis.

An interval type-2 fuzzy best-worst method and likelihood-based multi-criteria method in group decision-making

In real-world decision-making problems, a group of decision-makers (DMs) with different levels of expertise gathers to investigate the problem from various perspectives. Making the best choice from an analogous shortlist of competitors is challenging, even for an expert group. To address these types of problems, a new multi-criteria group decision-making (MCGDM) methodology under the interval type-2 trapezoidal fuzzy (IT2TrF) environment is proposed. The proposed IT2TrF MCGDM method comprises three phases. In the first phase, the IT2TrF cognitive best-worst method (IT2TrF-CBWM) is introduced to calculate the initial weights of criteria using the interval scale. Subsequently, a new consistency index (CI) and consistency ratio (CR) are presented. In the second phase, an optimization model is proposed to determine the final IT2TrF weights of criteria. Finally, a likelihood-based method for solving MCGDM problems is introduced in the third phase. The validity of the proposed method is illustrated by addressing a healthcare waste (HCW) treatment technology selection problem during the COVID-19 pandemic. Sensitivity and comparative analyses highlight the superiority and effectiveness of the presented MCGDM method.

A novel belief-based QFD-AHP model in interval type-2 fuzzy environment for lean after-sales service in automotive industry

PurposeThe purpose of this paper is to propose a novel lean management tool to provide a comprehensive and flexible evaluation model while converting customer voices into technical characteristics in lean implementations.Design/methodology/approachFor this purpose, the proposed model was constructed by belief space-evaluations, quality function deployment (QFD) and analytic hierarchy process (AHP) in interval type-2 fuzzy (IT2F) environment. This model involves three phases: determining the linguistic weights and belief-based relations with their IT2F-sets, processing information about IT2F-based belief-evaluations and ranking the technical characteristics using the defuzzified belief-based relative importance values.FindingsThe proposed model was applied to automotive after-sales service in Turkey to demonstrate its use in lean service-decisions. This model was compared with its classical and type-1 fuzzy versions. The ranking-results of the proposed model differed from those of the other versions. The reason is that the IT2F-environment offers a sensitive and flexible evaluation of the model’s linguistic scales.Research limitations/implicationsCalculations in the proposed model may be quite involved for practitioners. An Excel-dashboard was created to simplify the computational complexity.Practical implicationsResearchers/practitioners can apply this model to any lean manufacturing/service implementation.Social implicationsCompany managers/employees/customers can recognize their perception-mechanisms via belief space-evaluations and experience how uncertainty in the perception-mechanism affects their decisions.Originality/valueThe proposed model provides a new lean tool due to the Bayesian model combined with QFD-AHP in IT2F-environment. This model eliminates the ambiguity in conceptual change-based lean decisions.

A new risk quantification method in project-driven supply chain by MABACODAS method under interval type-2 fuzzy environment with a case study

Simultaneous decision-making in the supply chain and project management has attracted much attention. The integration of these two areas is called the project-driven supply chain. Timely supply of materials and services from the supply chain is significant for project activities. For this purpose, this paper presents a new method for the first time in the literature to quantify the supply risks in project activities and objectives. At first, the project’s critical path is specified according to the time, cost, risk, and quality criteria through a new decision model, namely MABACODAS, under parametric fuzzy values. The MABACODAS consists of two parts; One is about the degree of criticality of the paths, and the other is about determining the weight of experts in group decision-making. Then, a dynamic view is investigated under type-2 fuzzy numbers in the project, and it is observed that the critical path changes for different alpha values. The project suppliers’ resilience and each activity’s resilience are determined through the proposed MABACODAS model to obtain the appropriate alpha value. In other words, by using the resilience of each activity, the alpha value is selected, and the critical path is specified by considering the risk of the supply chain. Notably, the MABACODAS model is extended under interval type-2 fuzzy sets for uncertainty considerations. The main contribution of this study is introducing a risk quantification method. This method uses the MABACODAS method for specifying the criticality index of paths and resilience scores of suppliers. Also, this method is expanded under the IT2FSs. Finally, a real case study of the construction project is presented to show the applicability of the introduced model.

MALE UAV selection in interval Type-2 fuzzy sets environment

Unmanned Aerial Vehicles (UAVs) are increasingly used in the military field. Especially in recent years, UAVs have been a very effective instrument in gaining airspace superiority and military success. Many countries compete with each other to develop better UAV technology or improve the technical features of UAVs. Therefore, it is critical to determine which UAV has the best performance, considering technical and operational characteristics, because the vehicles with more advanced performance can provide countries with strategic superiority. The purpose of this study is to investigate the technical, cost, and operational performance of Medium Altitude Long Endurance UAVs (MALE UAVs). In the study, as a result of a wide literature review, we determined a performance criterion for this type of vehicle. The model presented here uses an Interval Type-2 Fuzzy Analytical Hierarch Process (IT2FAHP) and an Interval Type-2 Fuzzy Technique for Order of Preference by Similarity to an Ideal Solution (IT2FTOPSIS) hybrid method. The findings indicate that some MALE UAVs have superior technical and operational performance over others and demonstrate that range, max take-off weight, and payload are important criteria in determining the performance and superiority of these vehicles.

Two-Stage Fuzzy Interactive Multi-Objective Approach under Interval Type-2 Fuzzy Environment with Application to the Remanufacture of Old Clothes

In this study, a two-stage approach is introduced to obtain a more interactive and flexible solution to deal with the multi-objective programming under interval type-2 fuzzy environment. In the first stage, the fuzzy multi-objective chance-constrained programming with regular symmetric triangular interval type-2 fuzzy set parameters is proposed and transferred into its crisp equivalent form. In the second stage, we use the fuzzy interactive approach to address the crisp multi-objective programming obtained in the first stage by introducing the trade-off rate, which helps the decision maker react via updating their reference member values to obtain a satisfactory solution. Finally, taking a remanufacture of old clothes problem as an example, the comparison of experimental results obtained using a non-interactive method and interactive method shows that the proposed approach is conducive to obtaining satisfactory solutions effectively and efficiently, which broadens the application scope of the multi-objective programming with regular symmetric triangular interval type-2 fuzzy set parameters for sustainable manufacturing.

A new regret theory-based risk decision-making method for renewable energy investment under uncertain environment

Renewable energy is considered as a promising solution to alleviate the exploitation of fossil fuel energy and to keep sustainable development. Hence, renewable energy investments are attracting more and more attention. To solve the renewable energy investment problems under uncertain environment, this paper proposes a new multi-criteria risk decision-making method based on interval type-2 fuzzy sets (IT2FSs) and regret theory. First, to describe the uncertainty of real-world situation, the evaluation information is expressed by linguistic terms and encoded into IT2FSs. Second, a new interval type-2 fuzzy projection model is proposed to measure the relationships between alternatives under interval type-2 fuzzy environment. Then, to determine the criteria weights, a new interval type-2 fuzzy entropy weight determination model is developed. Moreover, some new rules are provided to explore the difference between alternatives under different spaces (i.e., positive space and negative space). Finally, the regret theory is extended to describe the psychological behavior of decision makers and select the optimal alternative under risk and uncertainty environment. A case study including comparative analysis is provided to manifest the feasibility and advantages of the proposed method.

An interval type-2 fuzzy axiomatic design method: A case study for evaluating blockchain deployment projects in supply chain

This study is concerned with the development of the axiomatic design (AD) method under an interval type-2 fuzzy (IT2F) environment and its application in evaluating blockchain deployment projects in supply chains. Blockchain is a transformative technology that has received significant attention recently. Blockchain technology can process various business transactions by offering a reliable and decentralized infrastructure. Supply chain management is an important application area of blockchains due to its desirable properties, including data security, extended visibility, product traceability, digitalization, and disintermediation. Since blockchain technologies are in their infancy, adopting them to supply chains requires proper design methodologies. Fuzzy AD offers valuable computational mechanisms to evaluate design options in the presence of functional requirements. However, extending AD to different fuzzy extensions is not an easy task, and area-based calculations hinder its widespread applicability. In this study, an IT2F-AD method is developed based on the concept of fuzzy subsethood. The potential of the fuzzy subsethood measure as the main computation engine within type-1 and IT2F-AD is demonstrated. Finally, an integrated multiple criteria decision-making (MCDM) model is proposed by using IT2F Best-Worst Method (IT2F-BWM) and IT2F-AD. The proposed model is used to prioritize blockchain deployment projects in a real-life case study.

A Combined Interval Type-2 Fuzzy MCDM Framework for the Resilient Supplier Selection Problem

Selecting the most resilient supplier is a crucial problem for organizations and managers in the supply chain. However, due to the inherited high degree of uncertainty in real-life projects, developing a decision-making framework in a crisp or fuzzy environment may not present accurate or reliable results for the managers. For this reason, it is better to evaluate the potential suppliers in an Interval Type-2 Fuzzy (IT2F) environment for better dealing with this ambiguity. This study developed an improved combined IT2F Best Worst Method (BWM) and IT2F technique for Order Preference by Similarity to Ideal Solution (TOPSIS) model “Atieh Sazan” Co. as a case study, such that the IT2FBWM was employed for obtaining the weight of criteria. The IT2FTOPSIS was utilized for ranking the potential suppliers based on Hamming distance measure. In both phases, the opinions of experts as IT2F linguistic terms were employed for weighting the criteria and obtaining the relative importance of the alternatives in terms of the evaluative criteria. After obtaining the final results, the proposed model was validated by replacing Analytical Hierarchy Process (AHP) and Simple Additive Weighting (SAW) approaches separately instead of BWM for weighting the criteria. After executing both new models, it was found that the final ranking was similar to the final ranking of the proposed model, representing the reliability and accuracy of the obtained results. Moreover, it was concluded that the resilient criteria of “Reorganization” and “Redundancy” are the most determinant measures for selecting the best supplier rather than measures in the Iranian Construction Industry.

An efficiency-based interval type-2 fuzzy multi-criteria group decision making for makeshift hospital selection

Since makeshift hospitals have strong ability in blocking the spread of the virus, how to design some methods to select the reasonable sites of makeshift hospitals is vitally important for containing COVID-19. This paper investigates an efficiency-based multi-criteria group decision making (MCGDM) method by combining the best-worst method (BWM) and data envelopment analysis (DEA) in trapezoidal interval type-2 fuzzy (TrIT2F) environment. This MCGDM method is called TrIT2F-BWM-DEA, where the TrIT2F-BWM is used to determine the weights of criteria and decision-makers, and the TrIT2F-DEA is employed to rank alternatives by measuring their overall efficiencies. Based on cut set theory, the expectation and average expectation (AE) of TrIT2FSs are successively defined. To solve three key issues in the development of the TrIT2F-BWM, this paper proposes a flexible ranking relation of TrIT2FSs to transform the TrIT2F constraints, initiates an efficient theorem to normalize the TrIT2F weights, and designs an input-based consistency ratio to check the reliability of the determined weights. A fully TrIT2F-DEA model is originally built to measure the TrIT2F efficiencies of alternatives. The alternatives are finally ranked according to the AEs of alternatives’ TrIT2F efficiencies. A site selection case of Fangcang hospitals and some comparative analyses are provided to confirm the validity and merits of the proposed TrIT2F-BWM-DEA.

An interval type-2 fuzzy Kano-prospect-TOPSIS based QFD model: Application to Chinese e-commerce service design

Owing to the rapidly changing customer preferences and demands, the e-commerce industry encounters various uncertainties and risks to enhance competitiveness. Quality function deployment (QFD) is a commonly used model, which can translate customer requirements (CRs) into products or service design requirements (DRs), to improve competitiveness by launching a new business. To measure the uncertainties and behavioral risk factors in e-commerce service design, we propose a new QFD model based on the Kano model and TOPSIS method by considering the behavior of experts with prospect theory under interval type-2 fuzzy linguistic environment. The categories of CRs are identified using the Kano model and the weights of CRs are determined dynamically according to the development stages of enterprises. The priorities of DRs are ranked using the extended TOPSIS method with prospect theory. A case study of China’s e-commerce service design is used to show the application of the proposed QFD model. The prioritizing results show the flexibility of the proposed model on determining the weights of CRs and the priorities of DRs for enterprises at different development stages.

Interval type-2 fuzzy inference-based failure mode and effect analysis model in a group decision-making setting

PurposeThis paper proposes an integrated IT2F-FMEA model under a group decision-making setting. In risk assessment models, experts' evaluations are often aggregated beforehand, and necessary computations are performed, which in turn, may cause a loss of information and valuable individual opinions. The proposed integrated IT2F-FMEA model aims to calculate risk priority numbers from the experts' evaluations and then fuse experts' judgments using a novel integrated model.Design/methodology/approachThis paper presents a novel failure mode and effect analysis (FMEA) model by integrating the fuzzy inference system, best-worst method (BWM) and weighted aggregated sum-product assessment (WASPAS) methods under interval type-2 fuzzy (IT2F) environment. The proposed FMEA approach utilizes the Mamdani-type IT2F inference system to calculate risk priority numbers. The individual FMEA results are combined by using integrated IT2F-BWM and IT2F-WASPAS methods.FindingsThe proposed model is implemented in a real-life case study in the furniture industry. According to the case study, fifteen failure modes are considered, and the proposed integrated method is used to prioritize the failure modes.Originality/valueMamdani-type singleton IT2F inference model is employed in the FMEA. Additionally, the proposed model allows experts to construct their membership functions and fuzzy rules to capitalize on the experience and knowledge of the experts. The proposed group FMEA model aggregates experts' judgments by using IT2F-BWM and IT2F-WASPAS methods. The proposed model is implemented in a real-life case study in the furniture company.

An evaluation of ship investment in interval type-2 fuzzy environment

Investment is one of the most crucial factors for a company. The decisions that a company makes in an investment uncertainty environment with high global competition, such as in the shipping industry, affects the life of the company either positively or negatively. Therefore, correct decision-making is extremely important particularly in an environment of investment uncertainty. Fuzzy set theory can be used to represent uncertainty and vagueness to generate decisions in decision-making problems. In this study, the aim is to evaluate ship investment by means of Net Present Value (NPV), Profitability Index (PI), and Payback Period (PP) under the Trapezoidal Interval Type-2 Fuzzy environment. In addition, two methods, Interval Type-2 Fuzzy Payback Period (IT2FPP) and Interval Type-2 Fuzzy Profitability Index (IT2FPI), were developed for the first time in the literature by integrating Interval Type-2 Fuzzy with traditional methods. These methods were then successfully applied to a real case study of ship investment for evaluation in the shipping industry in an uncertain environment.

A large-scale group decision-making method for site selection of waste to energy project under interval type-2 fuzzy environment

The waste to energy (WTE) project provides a promising solution for managing the rapidly generated municipal solid waste (MSW). To achieve the sustainable MSW management, it is essential to select an appropriate WTE plant site. Thus, this paper proposes a large-scale group decision-making method to select the optimal site. First, a sustainable evaluation index system is constructed based on the Strengths, Weaknesses, Opportunities, and Threats (SWOT) analysis from the perspectives of economic, environment, and society. Second, considering the linguistic terms provided by the decision makers cannot be directly computed, an interval data driven-based computing with word model is presented to transform the linguistic terms into the Gaussian interval type-2 fuzzy sets (IT2FSs). Then, a Gaussian interval type-2 fuzzy clustering approach is provided to conquer the inefficiency caused by the increase of the number of decision makers. Finally, the TODIM method is extended to compare and rank the alternative sites in the context of Gaussian IT2FSs. A case study is provided to illustrate the effectiveness of the proposed method, meanwhile, some discussions are conducted to illustrate the superiority and flexibility of the proposed method. The results indicate that the proposed method can successfully select the optimal plant site and has the potential to provide practical reference for the policymakers.

Multi-criteria group decision-making for portfolio allocation with consensus reaching process under interval type-2 fuzzy environment

The portfolio allocation problem is a hot topic in modern economics and management science. It involves many immeasurable criteria and uncertainties. Given the advantage of interval type-2 fuzzy sets (IT2FSs) in modeling complexities and uncertainties, this study provides an integrated methodology to deal with portfolio allocation problem based on the multiple criteria group decision-making (MCGDM) method considering the consensus reaching process in an interval type-2 fuzzy environment. First, some new information measures for IT2FSs include the weighted mean, and the weighted semi-absolute deviation measures are defined. They are used to describe the return and risk of the portfolio allocation, respectively. Second, a two-stage MCGDM framework is constructed for portfolio allocation: one is to achieve the group consensus, and the other is to obtain the optimal portfolio ratios. Finally, an example on calculating the optimal portfolio ratios for four newly listed stocks in China is offered to elaborate on the performance of our approach. Sensitivity and comparative analyses are also given to show the effectiveness and advantages of the proposed method.

Hazard identification, risk assessment and control for dam construction safety using an integrated BWM and MARCOS approach under interval type-2 fuzzy sets environment

Undoubtedly, dams are one of the projects developed by people to make optimal water use and generate hydroelectric energy power. In addition to the importance of detailed project planning, faultless production, and optimal working conditions in dam constructions, it is equally important to identify and analyze the risks from the occupational health and safety (OHS) perspective that may arise during construction and operation. In this context, hazard identification, risk analysis, and control, which are the main issues of dam safety, have gained importance. In this study, a novel approach is developed for dam construction safety. Two newly proposed multi-criteria decision-making (MCDM) methods of “Best-Worst Method-BWM” and “measurement of alternatives and ranking to Compromise solution-MARCOS”, are merged under the context of interval type-2 fuzzy sets (IT2FSs). Severity and probability, two essential parameters of the risk score, have been weighted using BWM. Subsequently, the priority orders of hazards have been determined by the MARCOS. In implementing the approach to the blasting process in dam construction, several control measures are suggested for stakeholders. Some comparative works and sensitivity analyses are performed to test the approach's validity and solidity from the methodological viewpoint.

A possibilistic approach for interval type-2 fuzzy linguistic summarization of time series

Linguistic summarization with fuzzy sets, extracting explicit and concise knowledge from data, has received a great attention because of its compatibility with human cognitive mechanism. The most crucial step in linguistic summarization is certainly the evaluation of linguistic summaries. In this study, a new fuzzy cardinality based possibilistic approach is proposed for evaluating linguistic summaries in interval type-2 fuzzy environment. It is proved that the proposed possibilistic approach satisfies the desired properties defined in the literature. An application of the proposed possibilistic approach is presented on financial time series including the three stocks in Borsa Istanbul (BIST) covering the period for the last 10 years. It is noticed that the proposed possibilistic approach generates more stable results than the probabilistic approach of Boran and Akay (IEEE Trans Cybern 44:1632–1645, 2014).

Interval type-2 Fuzzy ARAS method for recycling facility location problems

The management of end-of-life vehicles (ELVs) is currently one of the most important ecological topics. The recycling process has essential importance for the environmental and economic sustainability of the ELV management. Istanbul has the highest rate of car ownership population in Turkey as well as an old vehicle fleet. There is a strong motivation to open an additional ELV recycling facility in this mega-city. Facility location is one of the crucial strategic problems for decision-makers. Addressing multi-criteria and highly uncertain nature of the ELV recycling facility location problem, this paper introduces a novel approach to support the facility location process. For the first time, an extension of the Additive ratio assessment (ARAS) method under the interval type-2 fuzzy environment is presented. The novel method is utilized for solving the ELV recycling facility location problem. The potentials and applicability of the presented interval type-2 fuzzy ARAS method are demonstrated throughout the real-life case study of Istanbul. The comparison with the available state-of-the-art interval type-2 fuzzy set based MCDM methods approves its validity and consistency.

Evaluation of energy management system for regional integrated energy system under interval type-2 hesitant fuzzy environment

Selecting an energy management system for regional integrated energy system (EMS-RIES) is essential to improve energy management. But there lacks an EMS-RIES selection research. Meanwhile, some main issues, such as information loss, criteria interaction, properties of criteria, and risk preference, can influence the decision precision largely and have not been handled together in current decision researches. To fill these gaps, this study develops an integrated decision framework. Firstly, an evaluation criteria system is established from five dimensions. Secondly, double uncertainties on the degree of impact between criteria and criteria performances of each alternative are depicted by credibility-based hesitant fuzzy linguistic term set to reduce information loss. Thirdly, a combination weight method is used to determine criteria weight and interaction between criteria are investigated. Then, a cumulative prospect theory modified PROMETHEE II model considering properties of criteria and risk preference simultaneously is applied to rank the alternatives. Finally, a case study verifies the feasibility and practicability of the developed framework, and the final performances of alternatives are influenced by weight changing, properties of criteria, and risk preference. Furthermore, the comparative analysis shows that the proposed model has superiority to reveal the differences between alternatives due to its big distinction degree.

A new multi-criteria group decision-making method based on consensus mechanism in an interval type-2 fuzzy environment

The consensus problem is a very important aspect of group decision making (GDM). In order to deal with the multiple criteria group decision consensus problem in the interval type-2 fuzzy environment, a consensus measure based on similarity measurement is proposed in this paper. In this paper, first, a new similarity measure of two interval type-2 fuzzy sets (IT2FSs) is defined and the consensus measure is defined by the similarity measure between two IT2FSs. Then, a new consensus feedback mechanism is proposed. In the stage of alternatives selection, the entropy of IT2FSs is defined, and the entropy weight method is used to determine the weights of the criteria. Finally, the feasibility of the method proposed in this paper is illustrated by a comprehensive evaluation of old-age institutions.