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The exact complexity of the Tutte polynomial
Published in Joanna A. Ellis-Monaghan, Iain Moffatt, Handbook of the Tutte Polynomial and Related Topics, 2022
Tomer Kotek, Johann A. Makowsky
Background on matroids can be found in Chapter 4. Recall a matroid is an ordered pair (E,C) consisting of a finite set E, called the ground set and a set C of subsets of E, called the circuits. Matroids have many equivalent definitions. Instead of C one can consider I, the independent sets, S, the spanning sets, F, the flats, B, the bases, H, the hyperplanes. Other definitions use a closure operator on the subsets of E, a rank function or a girth function. All these definitions of matroids are equivalent from an axiomatic point of view, but differ from an algorithmic point of view (cf. [602, 828]).
Topology and Logic Programming
Published in Pascal Hitzler, Anthony Seda, Mathematical Aspects of Logic Programming Semantics, 2016
3.1.3 Theorem Let C be a convergence class in a non-empty set X. For each A ⊆ X, let Ac = {s ∈ X |there is a net (si) in A with ((si), s) ∈ C}. Then .c is a closure operator on X and, hence, defines a topology τ on X, called the topology associated with C. Moreover, we have ((si), s) ∈ C if and only if si → s with respect to τ.
Fuzzy-Genetic Approach to Epidemiology
Published in Jyoti Mishra, Ritu Agarwal, Abdon Atangana, Mathematical Modeling and Soft Computing in Epidemiology, 2020
Minakshi Biswas Hathiwala, Jignesh Pravin Chauhan, Gautam Suresh Hathiwala
A closure operator on the set of genotypes is persuaded by recombination set through the closure operator cl(M)=∪(x,y)∈M×MR(x,y).
An alternative construction of uninorms on bounded lattices
Published in International Journal of General Systems, 2023
Let be a lattice and Then the mapping , defined by for all , is a closure operator on .Let be a complete lattice. Then the mapping , defined by for all , is a closure operator on , where , either or
On pattern setups and pattern multistructures
Published in International Journal of General Systems, 2020
Aimene Belfodil, Sergei O. Kuznetsov, Mehdi Kaytoue
Formal Concept Analysis (FCA) was introduced in Wille (1982) as a mathematical framework for analyzing concepts and dependencies in databases. FCA starts with a formal context where is a set of objects (Gegenstände, German), is a set of attributes (Merkmale, German) and is a binary relation on (i.e. Incidence relation). For , holds iff g has attribute m. Figure 3 presents an example of a formal context. Two following operations denoted by : and define Galois connection between and and closure operator . The Basic Theorem of FCA says that pairs of closed sets of objects and attributes make a complete lattice called concept lattice, and a complete lattice can be represented as a concept lattice under certain conditions, see Ganter and Wille (1999) for detail.
t-closure Operators
Published in International Journal of General Systems, 2019
Mehmet Akif İnce, Funda Karaçal
If a closure operator C provides and , then it is called topological closure operator. So, with the help of a topological closure operator, a topology is obtained. Since and , the t-closure operator is a topological closure operator at the same time.