Author:
Jiří Močkoř
Affiliation:
University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
Keyword(s):
Semirings, Dual Pair of Semirings, Transformation of New Fuzzy Sets, Approximation of New Fuzzy Sets.
Abstract:
Many of the new types of fuzzy sets, such as intuitionistic, neutrosophic, multi-level or fuzzy soft sets and
their combinations, can be transformed into one common type of fuzzy sets, called (R,R*)-fuzzy sets, with
values in a set R that is a common underlying set of complete commutative idempotent semirings R and R*.
For (R,R*)-fuzzy sets, the theory of lower and upper approximations by (R,R*)-relations is defined and
the basic properties of these approximations are presented. Using examples of the transformation of some
new types of MV-valued fuzzy sets and corresponding fuzzy relations into R-fuzzy sets and R-fuzzy relations,
examples of approximation of these new types of fuzzy sets through their fuzzy relations are presented, without
having to define these operators separately for each new type of fuzzy set.