Diamond Intuitionistic Fuzzy Sets and Their Applications

Abstract

The primary purpose of this study is to introduce diamond intuitionistic fuzzy sets ( $ \mathcal {D} - IFS$ s). Although several generalizations of intuitionistic fuzzy sets have been introduced in the literature, the constraints of IFSs limit decision-makers ability to freely choose the degree of membership (validity, etc.) and non-membership (non-validity, etc.). The $ \mathcal {D} - IFS$ , however, offers this flexibility, which is why these new sets are introduced. By applying a mild restriction on the $ \mathcal {D} - IFS$ , a novel generalization, known as the lozenge intuitionistic fuzzy set has been acquired. Some properties of these intuitionistic fuzzy sets are characterized geometrically. The main aim of this research is also to establish some basic operations and inclusions for $ \mathcal {D} - IFS$ s, along with some well-known rules. On the other hand, Szmidt and Kacprzyk’s forms of Hamming distance measures and, Euclidean distance measures for $ \mathcal {D} - IFS$ s are defined. Additionally, new score and accuracy functions are presented to compare newly defined diamond intuitionistic fuzzy relations ( $ \mathcal {D} - IFR$ s). Moreover, two new ${\mathscr {min}}- {\mathscr {max}}$ operations have been derived to analyze the decomposition of $ \mathcal {D} - IFR$ s. Finally, a practical assessment of medical diagnosis in patients is conducted to demonstrate the feasibility and value of the proposed approaches.

Keywords

• Diamond intuitionistic fuzzy set
• lozenge intuitionistic fuzzy set
• distance measures
• score function
• accuracy function
• max – min operations