Some operations on circular intuitionistic fuzzy sets.

Intuitionistic Fuzzy Set or IFS is a set that is used to describe problems related to uncertainty and vagueness. To deal with more complex problems that involve interval-based membership degrees, this set has been expanded to the Interval-Valued Intuitionistic Fuzzy Set or IVIFS. Theoretically, the difference between IFS and IVIFS lies in the area around the membership and non-membership coordinates. In IVIFS, the surrounding area is in the form of a rectangle with the center being the coordinates of membership and non-membership degrees. However, the use of intervals as approximations is still too general and broad, so that the idea to create other approximations is generated. Circular Intuitionistic Fuzzy Set (CIFS) was proposed as an alternative representation of uncertain and vague information. It is a set characterized by membership, non-membership, and radius on the element. Several basic operations have been introduced since then, accompanied by some operations on the radius. However, the operations on the radius are only limited to max and min. Hence, some other operations on the radius are proposed here to enrich the CIFS theory. The proposed operations are based on the previous operations on IFS and are reinforced by the t-norm and s-norm forms. The contribution of this paper lies in the expansion of basic operators, based on algebraic sums and products, which are not only applied to membership andxnon-membershipxdegrees but also to radius. In addition, it also applies to the negation operators which displays the operations based on the radius. The results of this paper are the modification of the basic operators and negation on the CIFS along with the adjustment of the properties that previously established for IFS. [ABSTRACT FROM AUTHOR]