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The concept of q-rung orthopair fuzzy set (q-ROFS) is the extension of intuitionistic fuzzy set (IFS) in which the sum of the qth power of the support for and the qth power of the support against is bounded by one. Therefore, the q-ROFSs are an important way to express uncertain information in broader space, and they are superior to the IFSs and the Pythagorean fuzzy sets. In this paper, the familiarity degree of the experts with the evaluated objects is incorporated to the initial assessments under q-rung orthopair fuzzy environment. For this, some aggregation operators are proposed to combine these two types of information. Their some important properties are also well proved. Furthermore, these developed operators are utilized in a multicriteria decision-making approach and demonstrated with a real life problem of customers' choice. Then, the experimental results are compared with other existing methods to show its superiority over recent research works.

The concept of intuitionistic fuzzy set (IFS) theory plays an important role in dealing with real‐life issues under uncertain and imprecise environment. But it has certain limitations and further extended by many researchers by taking different situations. One of the extensions of IFS theory is Pythagorean fuzzy set (PFS), in which the condition of IFS theory, ie, sum of membership degree and nonmembership degree is less than (or equal to) one is related to the square sum of its membership degree and nonmembership degree is less than (or equal to) one. In this study, the concept of the generalized parameter is incorporated into the PFS theory and presented some generalized Pythagorean fuzzy average aggregation operators. Then, the operators are extended to a group‐based generalized parameter by taking the opinions of multiple senior experts/observers. Based on the defined operators, a multi‐criteria decision‐making (MCDM) approach is provided and illustrated with a numerical example to show the proposed approach effectively. Finally, a comparison analysis is also considered to validate the proposed approach over the existing ones.

Intuitionistic fuzzy sets introduced by Atanassov are generalization of fuzzy sets as they also handle the non-determinacy which is caused by degree of hesitation of decision maker. The present study proposes a computational method of forecasting for fuzzy time series. In the proposed method the notion of intuitionistic fuzzy set is used in fuzzy time series forecasting with simplified computational approach. The developed model has been tested on the movement of share market prices of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India. Further the method has been implemented for forecasting SENSEX of BSE. The suitability of the developed model has also been examined by comparing it with the other existing models to show its superiority.

Present study proposes a method for fuzzy time series forecasting based on difference parameters. The developed method has been presented in a form of simple computational algorithm. It utilizes various difference parameters being implemented on current state for forecasting the next state values to accommodate the possible vagueness in the data in an efficient way. The developed model has been simulated on the historical student enrollments data of University of Alabama and the obtained forecasted values have been compared with the existing methods to show its superiority. Further, the developed model has also been implemented in forecasting the movement of market prices of share of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India.

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