1. What are unknown unknowns?
Unknown unknowns refer to contingencies that cannot be anticipated or analyzed beforehand. They are unforeseen events or situations that are not known or recognized in advance. Examples of unknown unknowns can be found in various fields such as public policy, business strategy, entrepreneurship, contracts, and security. The Covid-19 pandemic serves as a recent reminder of the existence of unknown unknowns. Despite extensive research efforts, capturing and understanding unknown unknowns remains a challenging task. However, various approaches and theories, such as Knightian uncertainty, undescribable events, unforeseen contingencies, unawareness, and surprises, have been developed to provide a conceptual grasp on the notion of unknown unknowns. This paper aims to uncover concrete unknown unknowns by utilizing Formal Concept Analysis (FCA) as a rigorous and operational framework.
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2. What is a seed in FCA?
In FCA, a seed is an incompletely specified concept, i.e., a list that misses some object and attributes. It is a specific preconcept that already contains some data from the existing context. For example, the list (B;a) is a seed of the concept (B,D;a), as B and attribute a could already be seen in the existing context of Table 1. Seeds play a crucial role in discovering unknown unknowns and can lead to the generation of new concepts in the discovery context.
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3. What is a context in Formal Concept Analysis?
In Formal Concept Analysis (FCA), a context is a matrix showing relationships between 'objects' and 'attributes'. It represents the properties, features, or characteristics of items, events, or other entities. The context is crucial for decision-making as it provides value-weighted properties. In practice, FCA users encounter complex contexts with numerous rows and columns, mitigated relationships, and value-weighted properties. The initial objects and attributes are represented in a simple matrix, which can be expanded with new discoveries, experiments, or inventions, resulting in an updated context matrix.
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4. What are Birkhoff Operators in FCA?
Birkhoff Operators in FCA are set-to-set functions I R and E R defined for sets of objects S and attributes T. I R (S) gives all attributes in T that objects in S have in common, while E R (T) gives all objects in S that share these attributes. These operators are duals of each other, meaning knowing I R completely determines E R and vice versa. They play a crucial role in defining formal concepts in the context of FCA.
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