BIPOLAR INTUITIONISTIC FUZZY MATRICES AND ITS DETERMINANT

BIPOLAR INTUITIONISTIC FUZZY MATRICES AND ITS DETERMINANT

N. Deva, A. Felix

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Abstract

The theory of fuzzy sets has earned a lot of applications in science and en- gineering  elds. Fuzzy sets include extensions such as intuitionistic and bipolar fuzzy sets. These concepts have now become signi cant in recent research projects. The union of these sets can be de ned as a bipolar intuitionistic fuzzy set that o ers more exi- bility in analyzing real-life problems. It e ectively 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 de ned when a precise solution cannot be ob- tained from the crisp matrix. The theory of fuzzy matrix plays a vital role in the  eld of decision-making systems. The fuzzy matrix o ers 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 exibility, its three-dimensional representations are visualized. Also, the fundamental operations such as addition, multiplication, max-min and min-max compositions are de ned with illus- trations. Moreover, some examples and properties are provided to support the proposed study.

Keywords

Bipolar intuitionistic fuzzy matrix, Bipolar intuitionistic fuzzy determinant, Max-min, Min-max