Aggregation of the fuzzy logic sets in terms of the functions of the triangular norm and triangular co-norm
D. Gadjiev, I. Kochetkov, A. Rustanov
Dec 1, 2019
Citations
4
Citations
Journal
IOP Conference Series: Earth and Environmental Science
Full text
Semantic Scholar
Key Takeaway Key Takeaway: This paper explores the group of operators for aggregating fuzzy sets, focusing on triangular norm and triangular co-norm functions, and their properties, enabling the transformation of union into intersection and vice versa in fuzzy logic sets.
Abstract
The purpose of this article is to explore the group of the operators, which can be used for aggregation of the fuzzy sets. There were scrutinized operators to be used for the intersection and union such as the triangular norm and triangular co-norm in the article. All of those operators are defined as the binary operations, where there was indicated that the norms and co-norms are two-valued functions of [0, 1]. Furthermore, there were discussed properties of norm and co-norm functions such as symmetry, associativity, neutral entry and null entry properties, monotonicity properties. Moreover, the consideration of the properties of norm and co-norm functions have routed investigation of the norm and co-norm operators to go further to prove theorem, which converts the union into intersection and vice versa in terms to all possible norm and co-norm functions based on the fuzzy logic sets.