Distance measures on circular interval-valued intuitionistic fuzzy sets

Abstract

The region encircled by the circle of radius $\mathfrak{u}$ around an interval-valued intuitionistic fuzzy set is known as the circular interval-valued intuitionistic fuzzy set. Since intervals are used to represent them, interval-valued intuitionistic fuzzy sets can deal with ambiguity and uncertainty in a variety of ways, however, the area encircling them is not taken into account. As the area around it is taken into consideration, a circular interval-valued intuitionistic fuzzy set is therefore more able to handle uncertainty than an interval-valued intuitionistic fuzzy set. Effective decision-making can result in progress, happiness, and prosperity, making it crucial for both professional and personal success. All of the fuzzy extension's distance measures have applications in a variety of fields, including pattern recognition, clustering, medical diagnosis, and more. As a result, distance measures for circular interval-valued intuitionistic fuzzy sets are presented, and the proposed distance measures are used to solve a group decision-making challenge that is selected from the literature. TOPSIS is the method used for tackling the decision-making problem. The same problem is assessed using the existing distance measures in order to further validate the suggested distance measures of circular interval-valued intuitionistic fuzzy sets, and the outcomes are contrasted. In addition, to verify the robustness of the proposed distance measures on circular interval-valued intuitionistic fuzzy environment, sensitivity analysis is done using the operators ${\otimes }_{min}$ and ${\otimes }_{max}$ .