New methods for constructing generalized triangular operators, using a minimum and maximum fuzziness approach are outlined. Based on the entropy of a fuzzy subset, defined by using the equilibrium of the generalized fuzzy complement, the concept of elementary entropy function and its generalizations are introduced. These functions assign a value to each element of a fuzzy subset that characterizes its degree of fuzziness. It is shown that these functions can be used to construct the entropy of a fuzzy subset. The new generalized T-norm and generalized T-conorms are defined as minimum and maximum entropy operations. They are commutative semigroup operations on [0,1] with identity elements but they are not monotonic.
ASJC Scopus subject areas
- Artificial Intelligence