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The control charts are used in many production areas because they give an idea about the quality characteristic(s) of a product. The control limits are calculated and the data are examined whether the quality characteristic(s) is/are within these limits. At this point, it may be confusing to comment, especially if it is slightly below or above the limit values. In order to overcome this situation, it is suitable to use fuzzy numbers instead of crisp numbers. The purpose of this paper is to demonstrate how to create control limits of X ¯ -R control charts for a specified data set of interval type-2 fuzzy sets.

There are methods in the literature, such as defuzzification, distance, ranking and likelihood, which may be applicable for interval type-2 fuzzy set. This study is the first that these methods are adapted to the X ¯ -R control charts. This methodology enables interval type-2 fuzzy sets to be used in X ¯ -R control charts.

It is demonstrated that the methods – such as defuzzification, distance, ranking and likelihood for interval type-2 fuzzy sets – could be applied to the X ¯ -R control charts. The fuzzy control charts created using the methods provide similar results in terms of in/out control situations. On the other hand, the sample points depicted on charts show similar pattern, even though the calculations are different based on their own structures. Finally, the control charts obtained with interval type-2 fuzzy sets and the control charts obtained with crisp numbers are compared.

Based on the related literature, research works on interval type-2 fuzzy control charts seem to be very limited. This study shows the applicability of different interval type-2 fuzzy methods on X ¯ -R control charts. For the future study, different interval type-2 fuzzy methods may be considered for X ¯ -R control charts.

The unique contribution of this research to the relevant literature is that interval type-2 fuzzy numbers for quantitative control charts, such as X ¯ -R control charts, is used for the first time in this context. Since the research is the first adaptation of interval type-2 fuzzy sets on X ¯ -R control charts, the authors believe that this study will lead and encourage the people who work on this topic.

For a nation to become a superpower, it's scientific and technological advancement is essential. Each country is exploring how to improve themselves in terms of science and technology. The authors analyzed the innovation capabilities of 35 OECD countries that have not recently joined Lithuania.

In recent years, a lot of research work has been done on trapezoidal interval type-2 fuzzy sets (TIT-2 FS), and many research works have been published. The trapezoidal interval type-2 fuzzy set helps effectively to represent the uncertainty comparatively than the type-1 fuzzy set. Taking advantage of this effectiveness, the authors extend the best multi-criteria decision making method (MCDM) for trapezoidal interval type-2 fuzzy sets. Here, ELimination and Choice Expressing REality III (ELECTRE III) method in the trapezoidal interval type-2 fuzzy set environment is proposed.

This analysis helps to the OECD countries to develop their level of innovation in the criteria. The authors are making this evaluation for the year 2018 based on the 31 criteria. Application of the proposed method expressed by evaluation of the national innovation capability problem. Based on the obtained results, the top five countries are United States, Switzerland, Canada, Germany and Japan.

The authors collected required data from different available data sources like OECD, IMD, USPTO, ITU and surveyed data reported by KISTEP. After collecting all the data from different sources, the authors calculated the standard values as KISTEP. After converting the standard values into trapezoidal interval type-2 fuzzy values, the authors construct a decision matrix based on these values. Then, the authors determined the possibility mean values and preference. Then, they calculated the concordance and discordance credibility degree values. Finally, they ranked OECD countries by the net credibility degree. The results are computed by using the MATLAB software.

The purpose of this paper is to present a new public bread factory location selection for Istanbul Metropolitan Municipality (IMM).

A two-stage methodology is proposed to determine the location for the public bread factory facility. This framework is based on both geographic information systems (GIS) and multi-criteria decision-making (MCDM) techniques. The first stage of the methodology aims to decrease the number of possible alternative locations to simplify the selection activity by applying GIS; the second stage utilises interval type-2 fuzzy MCDM approach to exactly determine the public bread factory site location.

In this study, the authors present weighted normalised-based interval type-2 hesitant fuzzy and interval type-2 hesitant fuzzy sets (IT2HFSs)-based compressed proportional assessment (COPRAS) methods to overcome facility location selection problem for a fourth public bread factory in Istanbul.

The results show that the proposed approach is practical and can be employed by the bakery industry.

In this study, the authors present a two-stage methodology for public bread factory site selection. In the first stage, the number of alternatives is reduced by the GIS. In the second stage, an interval type-2 fuzzy set is implemented for the evaluation of public bakery factory site alternatives. A new integrated approach based on COPRAS method and weighted normalised with IT2HFSs is proposed.

In recent times, fuzzy logic is gaining more and more attention, and this is because of the capability of understanding the functioning of the system as per human knowledge-based system. The main contribution of the work is dynamically adapting the important parameters throughout the execution of the flower pollination algorithm (FPA) using concepts of fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.

The fuzzy logic-based parameter adaptation in the FPA is proposed. In addition, type-2 fuzzy logic is used to design fuzzy inference system for dynamic parameter adaptation in metaheuristics, which can help in eliminating uncertainty and hence offers an attractive improvement in dynamic parameter adaption in metaheuristic method, and, in reality, the effectiveness of the interval type-2 fuzzy inference system (IT2 FIS) has shown to provide improved results as matched to type-1 fuzzy inference system (T1 FIS) in some latest work.

One case study is considered for testing the proposed approach in a fault tolerant control problem without faults and with partial loss of effectiveness of main actuator fault with abrupt and incipient nature. For comparison between the type-1 fuzzy FPA and interval type-2 fuzzy FPA is presented using statistical analysis which validates the advantages of the interval type-2 fuzzy FPA. The statistical Z-test is presented for comparison of efficiency between two fuzzy variants of the FPA optimization method.

The main contribution of the work is a dynamical adaptation of the important parameters throughout the execution of the flower pollination optimization algorithm using concepts of type-2 fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.

This study aims to create a model for defining the best supplier for a company and allocating order that considers sustainability criteria beyond the traditional selection criteria.

In this paper, sustainable supplier Selection and order allocation (SSS and OA) problem is managed based on a multiobjective linear programming (MOLP) model that incorporates sustainability dimensions. First, an interval type-2 fuzzy analytic hierarchy process (FAHP) method is applied for the main criteria and subcriteria to determine the weight of the selected criteria. Then, these values are used to convert the proposed MOLP model into a single-objective model.

The economic criterion (0.438) was the most important criterion for SSS in the agricultural machinery sector, followed by the social criterion (0.333) and the environmental criterion (0.229).

The results show that the proposed framework can be utilized by the agricultural machinery industry for SSS and OA.

The proposed framework provides to develop an integrated model by interval type-2 fuzzy sets for SSS and OA, taking into account the relationships between qualitative and quantitative evaluation criteria with different priorities. The validity of the developed model is confirmed by a case study of the agricultural machinery industry in Turkey.

The purpose of this paper is to combine the uncertain methods of type-2 fuzzy sets and data envelopment analysis (DEA) evaluation model together. A new type-2 fuzzy DEA efficiency assessment method is established. Then the proposed procedure is applied to the poverty alleviation problem.

The research method is the DEA model, which is an effective method for efficiency assessment of social–economic systems. Considering the existence of the same efficiency values that cannot be ranked in the proposed DEA model, the balance index is introduced to solve the ranking problem of decision-making units effectively.

The results show that the proposed method can not only measure the efficiency of the existence of uncertain information but also deal with the ranking of multiple efficient decision-making units.

This paper selects type-2 fuzzy DEA model to express a lot of uncertain information in efficiency evaluation problems. We use the parameter decomposition method of type-2 fuzzy programming or the type-2 expectation values indirectly. The balance index is proposed to further distinguish the multiple effective decision-making units. Furthermore, this paper selects rural poverty alleviation in Hainan Province as a case study to verify the feasibility of the method. The relative efficiency values in different years are calculated and analyzed.

With numerous and ambiguous sets of information and often conflicting requirements, construction management is a complex process involving much uncertainty. Decision makers may be challenged with satisfying multiple criteria using vague information. Fuzzy multi-criteria decision-making (FMCDM) provides an innovative approach for addressing complex problems featuring diverse decision makers’ interests, conflicting objectives and numerous but uncertain bits of information. FMCDM has therefore been widely applied in construction management. With the increase in information complexity, extensions of fuzzy set (FS) theory have been generated and adopted to improve its capacity to address this complexity. Examples include hesitant FSs (HFSs), intuitionistic FSs (IFSs) and type-2 FSs (T2FSs). This chapter introduces commonly used FMCDM methods, examines their applications in construction management and discusses trends in future research and application. The chapter first introduces the MCDM process as well as FS theory and its three main extensions, namely, HFSs, IFSs and T2FSs. The chapter then explores the linkage between FS theory and its extensions and MCDM approaches. In total, 17 FMCDM methods are reviewed and two FMCDM methods (i.e. T2FS-TOPSIS and T2FS-PROMETHEE) are further improved based on the literature. These 19 FMCDM methods with their corresponding applications in construction management are discussed in a systematic manner. This review and development of FS theory and its extensions should help both researchers and practitioners better understand and handle information uncertainty in complex decision problems.

Fuzzy-based metaheuristic algorithm is used to optimize the fuzzy controllers for the nonlinear level control system subject to uncertainty specially in the main actuator that has lost effectiveness (LOE). To optimize the fuzzy controller, type-1 harmonic search (HS) and interval type-2 (HS) will be used.

The type-1 and type-2 fuzzy-based HS algorithms are designed for optimization of fuzzy controllers for Fault-Tolerant Control (FTC) applications, and this research proposes a fuzzy-based HS metaheuristic method. The performance of a fuzzy logic-based HS algorithm applied to a nonlinear two-tank level control process with a main actuator that has lost effectiveness (LOE) and also the same controller will be tested on DC motor angular position control with and without noise.

The key contribution of this work is the discovery of the best approach for generating an optimal vector of values for the fuzzy controller's membership function optimization. This is done in order to improve the controller's performance, bringing the process value of the two-tank level control process closer to the target process value (set point). It is worth noting that the type-1 fuzzy controller that has been optimized is an interval type-2 fuzzy system, which can handle more uncertainty than a type-1 fuzzy system.

The type-1 and type-2 fuzzy-based HS algorithms are designed for optimization of fuzzy controllers for FTC applications, and this research proposes a fuzzy-based HS metaheuristic method. The performance of a fuzzy logic-based HS algorithm applied to a nonlinear two-tank level control process with a main actuator that has LOE will be tested on DC motor angular position control with noise. Two nonlinear uncertain processes are used to demonstrate the effectiveness of the proposed control scheme.

This study aims to propose, as the first time, the interval type-2 adaptive network-fuzzy inference system (ANFIS) structure, which is given better results compared to previously presented in the open literature. So, the ANFIS can be used effectively for training of interval type-2 fuzzy logic system (IT2FLS) parameters.

Karnik–Mendel algorithm (KMA) is modified to use in interval type-2 ANFIS. The modified Karnik–Mendel algorithm (M-KMA) is implemented to change the uncertain ANFIS parameters into known ones. In this way, the interval type-2 ANFIS removes uncertainties of IT2FLS. Therefore, the interval type-2 ANFIS is reduced to a simple one, i.e. less mathematical operation required. Only consequent parameters are trained, and the consequent parameters are chosen in the form of crisp.

By applying the mentioned procedure, it can be shown that interval type-2 ANFIS has generally better results compared to type-1 ANFIS. However, it was noticed that the worst results obtained in the case of interval type-2 ANFIS are equal to the best result obtained in the case of type-1 ANFIS. Therefore, users in this field can use this approach in solving nonlinear problems.

The interval type-2 ANFIS can be used as controller for highly nonlinear systems such as air vehicles.

As stated in the open literature, it is ineffective to use ANFIS for IT2FLS. In this study, the KMA is modified for IT2FLS, and it is seen that the ANFIS can be used effectively for IT2FLS.

This study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers.

The emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert's imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis.

A real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures.

This study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account.

Our contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.