Bipolar intuitionistic fuzzy matrices and its determinant

Abstract

The theory of fuzzy sets has earned a lot of applications in science and engineering fields. Fuzzy sets include extensions such as intuitionistic and bipolar fuzzy sets. These concepts have now become significant in recent research projects. The union of these sets can be defined as a bipolar intuitionistic fuzzy set that offers more flexibility in analyzing real-life problems. It effectively analyses the systems by examining the involvement and non-involvement grades of the element in a bipolar view. A matrix is a collection of crisp numbers arranged in a rectangular array with rows and columns. The concept of the fuzzy matrix can be defined when a precise solution cannot be obtained from the crisp matrix. The theory of fuzzy matrix plays a vital role in the field of decision-making systems. The fuzzy matrix offers a clear outcome, when examined with a bipolar intuitionistic fuzzy environment. Therefore, the present study coined the Notion of bipolar intuitionistic fuzzy matrix and its determinant. To depict the flexibility, its three-dimensional representations are visualized. Also, the fundamental operations such as addition, multiplication, max-min and min-max compositions are defined with illustrations. Moreover, some examples and properties are provided to support the proposed study.