On Two Intuitionistic Fuzzy Modal Topological Structures

The concept of an Intuitionistic Fuzzy Modal Topological Structure (IFMTS) was introduced previously, and some of its properties were studied. So far, there are two different IFMTSs based on the classical intuitionistic fuzzy operations: union (?) and intersection (n). In the present paper, two new IFMTSs are developed. They are based on new intuitionistic fuzzy topological operators from closure and interior types, introduced here for the first time, and on the two standard intuitionistic fuzzy modal operators ? and ?. Some basic properties of the new IFMTSs are discussed. The newly presented IFMTSs could be considered as a basis for the next research on the IFMTSs. Some ideas for the future development of the IFMTS theory and open problems are formulated, related to the existence of other intuitionistic fuzzy operations that can generate new intuitionistic fuzzy topological operators and, respectively, new IFMTSs.

Automated summary

The concept of an Intuitionistic Fuzzy Modal Topological Structure (IFMTS) was introduced, and some of its properties were studied. Two new IFMTSs were developed based on new intuitionistic fuzzy topological operators and the two standard intuitionistic fuzzy modal operators ?. The basic properties of the new IFMTSs were discussed, and ideas for future development and open problems were presented.