Characterizing One-Sided Formal Concept Analysis by Multi-Adjoint Concept Lattices

Managing and extracting information from databases is one of the main goals in several fields, as in Formal Concept Analysis (FCA). One-sided concept lattices and multi-adjoint concept lattices are two frameworks in FCA that have been developed in parallel. This paper shows that one-sided concept lattices are particular cases of multi-adjoint concept lattices. As a first consequence of this characterization, a new attribute reduction mechanism has been introduced in the one-side framework.This research was partially supported by the 2014-2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in Project PID2019-108991GB-I00 and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in Project FEDER-UCA18-108612 and by the European Cooperation in Science & Technology (COST) Action CA17124

Interpretation of Fuzzy Attribute Subsets in Generalized One-Sided Concept Lattices

In this paper we describe possible interpretation and reduction of fuzzy attributes in Generalized One-sided Concept Lattices (GOSCL). This type of concept lattices represent generalization of Formal Concept Analysis (FCA) suitable for analysis of datatables with different types of attributes. FCA as well as generalized one-sided concept lattices represent conceptual data miningmethods. With growing number of attributes the interpretation of fuzzy subsets may become unclear, hence another interpretation of this fuzzy attribute subsets can be valuable. The originality of the presented method is based on the usage of one-sided concept lattices derived from submodels of former object-attribute model by grouping attributes with the same truth value structure. This leads to new method for attribute reduction in GOSCL environment

Distributed Computation of Generalized One-Sided Concept Lattices on Sparse Data Tables

In this paper we present the study on the usage of distributed version of the algorithm for generalized one-sided concept lattices (GOSCL), which provides a special case for fuzzy version of data analysis approach called formal concept analysis (FCA). The methods of this type create the conceptual model of the input data based on the theory of concept lattices and were successfully applied in several domains. GOSCL is able to create one-sided concept lattices for data tables with different attribute types processed as fuzzy sets. One of the problems with the creation of FCA-based models is their computational complexity. In order to reduce the computation times, we have designed the distributed version of the algorithm for GOSCL. The algorithm is able to work well especially for data where the number of newly generated concepts is reduced, i.e., for sparse input data tables which are often used in domains like text-mining and information retrieval. Therefore, we present the experimental results on sparse data tables in order to show the applicability of the algorithm on the generated data and the selected text-mining datasets

Sacrificing Civil Liberties to Reduce Terrorism Risk

The results of a survey conducted by Viscusi and Zeckhauser demonstrate that targeted screening of airline passengers raises conflicting concerns of efficiency and equity. Support for profiling increases if there is a substantial reduction in avoided delays to other passengers. The time cost and benefit components of targeting affect support for targeted screening in an efficiency-oriented manner. Nonwhite respondents are more reluctant than whites to support targeting or to be targeted. Terrorism risk assessments are highly diffuse, reflecting considerable risk ambiguity. People fear highly severe worst-case terrorism outcomes, but their best estimates of the risk are more closely related to their lower bound estimates than their upper bound estimates. Anomalies evident in other risk perception contexts, such as hindsight biases and embeddedness effects, are particularly evident for terrorism risk beliefs.

Impact of Local Congruences in Attribute Reduction

Local congruences are equivalence relations whose equivalence classes are convex sublattices of the original lattice. In this paper, we present a study that relates local congruences to attribute reduction in FCA. Specifically, we will analyze the impact in the context of the use of local congruences, when they are used for complementing an attribute reduction

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

The detection of redundant or irrelevant variables (attributes) in datasets becomes essential in different frameworks, such as in Formal Concept Analysis (FCA). However, removing such variables can have some impact on the concept lattice, which is closely related to the algebraic structure of the obtained quotient set and their classes. This paper studies the algebraic structure of the induced equivalence classes and characterizes those classes that are convex sublattices of the original concept lattice. Particular attention is given to the reductions removing FCA's unnecessary attributes. The obtained results will be useful to other complementary reduction techniques, such as the recently introduced procedure based on local congruences