Extension operators of circular intuitionistic fuzzy sets with triangular norms and conorms: Exploring a domain radius

• Published in: AIMS MATHEMATICS
• Main Authors: Pratama, Dian; Yuso, Binyamin; Abdullah, Lazim; Kilicman, Adem; Kamis, Nor Hanimah
• Format: Article
• Language: English
• Published: AMER INST MATHEMATICAL SCIENCES-AIMS 2024
• Subjects: Mathematics
• Online Access: https://www-webofscience-com.uitm.idm.oclc.org/wos/woscc/full-record/WOS:001194171900007

The circular intuitionistic fuzzy set (CIFS) extends the concept of IFS, representing each set element with a circular area on the IFS interpretation triangle (IFIT). Each element in CIFS is characterized not only by membership and non-membership degrees but also by a radius, indicating the imprecise areas of these degrees. While some basic operations have been defined for CIFS, not all have been thoroughly explored and generalized. The radius domain has been extended from [0, 1] to [0, 2]. However, the operations on the radius domain are limited to min and max. We aimed to address these limitations and further explore the theory of CIFS, focusing on operations for membership and nonmembership degrees as well as radius domains. First, we proposed new radius operations on CIFS with based on triangular norms and conorms, investigating their algebraic properties. Finally, we explored negation and modal operators based on proposed radius conditions and examined their characteristics. providing valuable insights into its potential applications, particularly in decision-making theory.