Name
Abstract | ||
|---|---|---|
Constructions and characterizations of triangular norms(t-norms) have been discussed in many different contexts. In this paper, we present two methods to construct t-norms on lattices from given partial information. Since the idea is to follow from part-to-whole, we especially consider the lattices with -decompositions. Firstly, we investigate the structure of the partially ordered set of -irreducible elements. Then, for a given t-norm T on the complete distributive lattice [0, 1]2, we study the restriction of T to the poset of -irreducible elements of [0, 1]2. Furthermore, we give a method for generating t-norms on a finite distributive lattice L by means of -irreducible elements in L. We show that a t-norm on a finite distributive lattice is idempotent if and only if it is idempotent on the set of -irreducible elements. Finally, we introduce a formula to obtain t-norms on L[n] from given t-norms on -irreducible elements of L[n]. We present the dual statements for t-conorms. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.ins.2017.02.041 | Inf. Sci. |
Keywords | Field | DocType |
∧-semilattice,∨-semilattice,Lattice,Triangular norm,Irreducible element | Discrete mathematics,Congruence lattice problem,Combinatorics,Distributive lattice,Lattice (order),Irreducible element,If and only if,Semilattice,Idempotence,Partially ordered set,Mathematics | Journal |
Volume | Issue | ISSN |
397 | C | 0020-0255 |
Citations | PageRank | References |
1 | 0.36 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| S. Yilmaz | 1 | 1 | 1.04 |
| O. Kazancı | 2 | 50 | 5.37 |