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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.

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.

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The fuzzy time series forecasting model is a powerful tool in forecasting the time series data. The nature of the fuzzy set exhibits its role in handling the uncertainty of the data. The intuitionistic fuzzy set (IFS) is a generalization of a fuzzy set that makes the forecasting process more precise and accurate. This paper proposes a new fuzzy forecasting model based on IFS via the de-i-fuzzification approach, namely equal distribution of hesitancy. The proposed model consists of four main parts; the fuzzification of historical data; the establishment of the IFS; the de-i-fuzzification; and the defuzzification. For the fuzzification, the historical data is partitioned into 14 intervals using the frequency density-based method and trapezoidal fuzzy numbers are used to fuzzify the data. The data are then converted into IFS. The data in IFS form is reduced to fuzzy set using equally distributed with the degree of hesitancy approach. The arithmetic rules based on centroid defuzzification is used to calculate the forecasted output. The proposed model shows a better performance than the existing forecasting models based on IFS, indicating that the equal distribution of hesitancy de-i-fuzzification managed to handle the non-determinism in the forecasting with simplified procedure. In the future, an improved method will be proposed to defuzzify the IFS into crisp values without going through the de-i-fuzzification process, yet preserving the nature of IFS.

The analytic hierarchy process (AHP) is a powerful multi-criteria and multi-alternative decision-making model which helps decision makers in giving preferences using pairwise comparison matrices. The development of AHP using fuzzy numbers got attention from many researchers due to the capability of fuzzy numbers in handling vagueness and uncertainty. The integration of AHP with fuzzy Z-numbers has improved the model since the reliability of decision makers is considered, in which the judgement is followed by the degree of certainty or sureness. Most of the existing decision-making models based on Znumbers transform the Z-numbers into regular fuzzy numbers by integrating the reliability parts into the restriction parts which has caused a great loss of information. Hence, this research develops the AHP based on the magnitude of Z-numbers, in which the magnitude 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.

Z-numbers and intuitionistic fuzzy numbers are both important as they consider the reliability of the judgement, membership and non-membership functions of the numbers. The combination of these two numbers produce intuitionistic Z-numbers which need to be defuzzified before aggregation of multiple experts' opinions could be done in the decision making problems. This paper presents the generalised intuitionistic Z-numbers and proposes a centroid-based defuzzification of such numbers, namely intuitive multiple centroid. The proposed defuzzification is used in the decision making model and applied to the supplier selection problem. The ranking of supplier alternatives is evaluated using the ranking function based on centroid. In the present paper, the ranking is improved since the intuitionistic fuzzy numbers (IFN) are integrated within the evaluations which were initially in form of Z-numbers, considering their membership and non-membership grades. The ranking of the proposed model gives almost similar ranking to the existing model, with simplified but detailed defuzzification method.

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