Improved q-rung orthopair and T-spherical fuzzy sets

Different extensions of fuzzy sets like intuitionistic, picture, Pythagorean, and spherical have been proposed to model uncertainty. Although these extensions are able to increase the level of accuracy, imposing rigid restrictions on the grades are the main problem of them. In these types of fuzzy sets, the value of grades and also the sum of them must be in the closed unit interval of [0, 1]. The sum condition seriously restricts the eligible values for grades. q-rung orthopair and T-spherical fuzzy sets have been introduced to establish a framework to tackle the mentioned problem for two-grade and three-grade fuzzy sets, respectively. Reducing the value of grades by means of power operator is the backbone idea of the both sets. However, these fuzzy sets are suffering from two drawbacks. The first one arises from the fact that there is no automatic structure to identify a proper power. Also, information loss is the other one which affects the accuracy of the decision-making process. This problem is a damaging consequence of changing the values of the grades. This paper introduces a novel reducing strategy to improve q-rung orthopair and T-spherical fuzzy sets by tackling the mentioned drawbacks. The proposed strategy solves out the former problem by establishing an automatic framework for finding a proper power which guarantee enough reduction of the values. The automatic framework is used for reducing the value of the maximum grade. Besides, the novel strategy reduces the rest of the grades according to their distance with the the maximum grade and its reduction rate. This paper proves mathematically that the ratio between the grades before and after of the reduction process will be intact, which results in solving information loss problem. Moreover, the higher accuracy level of the novel reduction strategy in comparison with the preceding methods, q-rung orthopair and T-sipherical fuzzy sets, is shown via different examples.