Semiconcept and concept representations
Year: 2024
Type: article
Abstract: In FCA, we often deal with a formal context $ K=(G,M,I)$ that is only partially known, i.e. only the attributes that belong to an observable set $N \subset M $ are known. There must also exist a part $ H $ of the object set $ G $ - called a training set - that consists of elements with all attributes known. The concepts of $ K $ have to be determined using the subcontexts corresponding to $ H $ and to $ N $. In our paper, this problem is examined within the extended framework of the semiconcepts of $ K $, which are generalizations of the concepts of $ K $. Each semiconcept of $ K $ induces a semiconcept in both subcontexts. In this way, each semiconcept of $ K $ is represented by an induced pair of semiconcepts, which can also be considered its approximations - as in the case of rough sets. We describe the properties of the mapping defined by this representation and prove that the poset formed by these semiconcept pairs is a union of two complete lattices. We show that these induced semiconcept pairs can be generated by using a simplified representation of them. As the number of semiconcepts grows exponentially with the size of $ H $ and $ N $, an algorithm that selects the representation pairs for which their support and relevance reach a certain threshold is also presented.
Source: Knowledge-Based Systems
Authors: Dávid Gégény, László Kovács, Sándor Radeleczki
Language: English
Topic: Rough Sets and Fuzzy Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,250
OpenAlex ID: W4403157659