No abstract

De-i-fuzzification is a process of converting the intuitionistic fuzzy set into a fuzzy set. It becomes one of the core procedures in fuzzy time series forecasting model based on the intuitionistic fuzzy set. In this paper, we propose a fuzzy time series forecasting model based on intuitionistic fuzzy set via de-i-fuzzification. The de-i-fuzzification approach used is assigning the hesitancy degree to the major grade. The data are partitioned into a few intervals using the frequency density-based method. The data in the fuzzy set form is then transformed into an intuitionistic fuzzy set using the definition of intuitionistic fuzzy set. The arithmetic rules based on centroid defuzzification is used to obtain the forecasted output. The model is implemented on the data of student enrolment at the University of Alabama. The results are then compared to forecasting method using classical fuzzy set and similar de-i-fuzzification approach using max-min operation. The proposed method outperforms the other two methods, thus supports the fact that intuitionistic fuzzy set is a generalization of a classical fuzzy set and gives better performance in forecasting.

Due to the COVID-19 pandemic, the enforcement of the Movement Control Order (MCO) by theMalaysian government since March 2020 significantly impacted many sectors such as the economy, society, and others. MCO enforcement has made Malaysians spend most of their time staying at home, and even some have lost their income source. Another sector that has been greatly affected is the educational sector. Today’s landscape of education has changed dramatically with the phenomenal rise of virtual classes from home. Learning and teaching processes are undertaken remotely and on digital platforms to curb the spreading of the virus. This situation has affected the lesson and learning process from home to many of the several students in Malaysia. Therefore, this study investigates the challenges of home learning during MCO among students in the Universiti Teknologi MARA (UiTM) Pahang Branch. A simple random sampling technique was used to distribute the online survey questionnaires, involving a sample of 213 students. Besides, a descriptive statistic was used to study the students’ demographic characteristics according to the challenges. In contrast, logistic regression analysis was used to determine the factors associated with home learning challenges during MCO. Based on the findings, most male and female students were not well prepared for home learning during MCO, with a percentage of 71.60% and 69.70%, respectively. As a result, 79.81% agreed that home learning is more stressful than the physical classes on the campus. In comparison, 79.63% of Social Science and 83.02% of Science and Technology students claimed that the workload given is way more significant during online classes. Furthermore, this study concludes that the most associated challenges of home learning faced by the students during MCO are the abundance of workload and loss of interest in the subject.

A Z-number is very powerful in describing imperfect information, in which fuzzy numbers are paired such that the partially reliable information is properly processed. During a decision-making process, human beings always use natural language to describe their preferences, and the decision information is usually imprecise and partially reliable. The nature of the Z-number, which is composed of the restriction and reliability components, has made it a powerful tool for depicting certain decision information. Its strengths and advantages have attracted many researchers worldwide to further study and extend its theory and applications. The current research trend on Z-numbers has shown an increasing interest among researchers in the fuzzy set theory, especially its application to decision making. This paper reviews the application of Z-numbers in decision making, in which previous decision-making models based on Z-numbers are analyzed to identify their strengths and contributions. The decision making based on Z-numbers improves the reliability of the decision information and makes it more meaningful. Another scope that is closely related to decision making, namely, the ranking of Z-numbers, is also reviewed. Then, the evaluative analysis of the Z-numbers is conducted to evaluate the performance of Z-numbers in decision making. Future directions and recommendations on the applications of Z-numbers in decision making are provided at the end of this review.

Intuitionistic fuzzy numbers incorporate the membership and nonmembership degrees. In contrast, Z-numbers consist of restriction components, with the existence of a reliability component describing the degree of certainty for the restriction. The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers, namely intuitionistic Z-numbers (IZN). The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are characterized by the membership and non-membership functions, exhibiting the degree of the hesitancy of decision-makers. This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems. A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives. The proposed model is then implemented in a supplier selection problem. The obtained ranking is compared to the existing models based on Znumbers. The results show that the ranking order is slightly different from the existing models. Sensitivity analysis is performed to validate the obtained ranking. The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80% to 100% consistency despite the drastic change of criteria weights. Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers' opinions in solving decision-making problems.

Fuzzy time series is a powerful tool to forecast the time series data under uncertainty. Fuzzy time series was first initiated with fuzzy sets and then generalized by intuitionistic fuzzy sets. The intuitionistic fuzzy sets consider the degree of hesitation in which the degree of non-membership is incorporated. In this paper, a fuzzy set time series forecasting model based on intuitionistic fuzzy sets via delegation of hesitancy degree to the major grade de-i-fuzzification approach was developed. The proposed model was implemented on the data of student enrollments at the University of Alabama. The forecasted output was obtained using the fuzzy logical relationships of the output, and the performance of the forecasted output was compared with the fuzzy time series forecasting model based on fuzzy sets using the mean square error, root mean square error, mean absolute error, and mean absolute percentage error. The results showed that the forecasting model based on induced fuzzy sets from intuitionistic fuzzy sets performs better compared to the fuzzy time series forecasting model based on fuzzy sets.

The Analytic Hierarchy Process (AHP) is a powerful multi-criteria and multi-alternative decision-making model, which assists decision-makers in giving preferences using pairwise comparison matrices. The development of the AHP using fuzzy numbers has received attention from many researchers due to the ability of fuzzy numbers to handle vagueness and uncertainty. The integration of the AHP with fuzzy Z-numbers has improved the model since the reliability of the decision-makers is considered, in which the judgment is followed by a degree of certainty or sureness. Most of the existing decision-making models based on Z-numbers transform the Z-numbers into regular fuzzy numbers by integrating the reliability parts into the restriction parts, causing a significant loss of information. Hence, this study develops the AHP based on the magnitude of Z-numbers, which is used to represent the criteria weights. A numerical example of criteria ranking for the prioritization of public services for digitalization is implemented to illustrate the proposed AHP model.

<abstract> <p>Decision science has a wide range of applications in daily life. Decision information is usually incomplete and partially reliable. In the fuzzy set theory, Z-numbers are introduced to handle this situation because they contain the restriction and reliability components, which complement the impaired information. The ranking of Z-numbers is a challenging task since they are composed of pairs of fuzzy numbers. In this research, the vectorial distance and spread of Z-numbers were proposed synergically, in which the vectorial distance measures how much the fuzzy numbers are apart from the origin, which was set as a relative point, and their spreads over a horizontal axis. Furthermore, a ranking method based on the convex compound was proposed to combine the restriction and reliability components of Z-numbers. The proposed ranking method was validated using several empirical examples and a comparative analysis was conducted. The application of the proposed ranking method in decision-making was illustrated via the development of the Analytic Hierarchy Process-Weighted Aggregated Sum Product Assessment (AHP-WASPAS) model to solve the prioritization of public services for the implementation of Industry 4.0 tools. Sensitivity analysis was also conducted to evaluate the performance of the proposed model and the results showed that the proposed model has improved its consistency from 66.67% of the existing model to 83.33%. This research leads to a future direction of the application of ranking based on the vectorial distance and spread in multi-criteria decision-making methods, which use Z-numbers as linguistic values.</p> </abstract>