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

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

Best matching processes in distributed systems

The growing complexity and dynamic behavior of modern manufacturing and service industries along with competitive and globalized markets have gradually transformed traditional centralized systems into distributed networks of e- (electronic) Systems. Emerging examples include e-Factories, virtual enterprises, smart farms, automated warehouses, and intelligent transportation systems. These (and similar) distributed systems, regardless of context and application, have a property in common: They all involve certain types of interactions (collaborative, competitive, or both) among their distributed individuals—from clusters of passive sensors and machines to complex networks of computers, intelligent robots, humans, and enterprises. Having this common property, such systems may encounter common challenges in terms of suboptimal interactions and thus poor performance, caused by potential mismatch between individuals. For example, mismatched subassembly parts, vehicles—routes, suppliers—retailers, employees—departments, and products—automated guided vehicles—storage locations may lead to low-quality products, congested roads, unstable supply networks, conflicts, and low service level, respectively. This research refers to this problem as best matching, and investigates it as a major design principle of CCT, the Collaborative Control Theory. The original contribution of this research is to elaborate on the fundamentals of best matching in distributed and collaborative systems, by providing general frameworks for (1) Systematic analysis, inclusive taxonomy, analogical and structural comparison between different matching processes; (2) Specification and formulation of problems, and development of algorithms and protocols for best matching; (3) Validation of the models, algorithms, and protocols through extensive numerical experiments and case studies. The first goal is addressed by investigating matching problems in distributed production, manufacturing, supply, and service systems based on a recently developed reference model, the PRISM Taxonomy of Best Matching. Following the second goal, the identified problems are then formulated as mixed-integer programs. Due to the computational complexity of matching problems, various optimization algorithms are developed for solving different problem instances, including modified genetic algorithms, tabu search, and neighbourhood search heuristics. The dynamic and collaborative/competitive behaviors of matching processes in distributed settings are also formulated and examined through various collaboration, best matching, and task administration protocols. In line with the third goal, four case studies are conducted on various manufacturing, supply, and service systems to highlight the impact of best matching on their operational performance, including service level, utilization, stability, and cost-effectiveness, and validate the computational merits of the developed solution methodologies

The Rise of Decentralized Autonomous Organizations: Coordination and Growth within Cryptocurrencies

The rise of cryptocurrencies such as Bitcoin is driving a paradigm shift in organization design. Their underlying blockchain technology enables a novel form of organizing, which I call the “decentralized autonomous organization” (DAO). This study explores how tasks are coordinated within DAOs that provide decentralized and open payment systems that do not rely on centralized intermediaries (e.g., banks). Guided by a Bitcoin pilot case study followed by a three-stage research design that uses both qualitative and quantitative data, this inductive study examines twenty DAOs in the cryptocurrency industry to address the following question: How are DAOs coordinated to enable growth? Results from the pilot study suggest that task coordination within DAOs is enabled by distributed consensus mechanisms at various levels. Further, findings from interview data reveal that DAOs coordinate tasks through “machine consensus” and “social consensus” mechanisms that operate at varying degrees of decentralization. Subsequent fuzzy-set qualitative comparative analyses (fsQCA), explaining when DAOs grow or decline, show that social consensus mechanisms can partially substitute machine consensus mechanisms in less decentralized DAOs. Taken together, the results unpack how DAO growth relies on the interplay between machine consensus, social consensus, and decentralization mechanisms. To conclude, I formulate three propositions to outline a theory of DAO coordination and discuss how this novel form of organizing calls for a revision of our conventional understanding of task coordination and organizational growth

Divergence vs. Decision P-values: A Distinction Worth Making in Theory and Keeping in Practice

There are two distinct definitions of 'P-value' for evaluating a proposed hypothesis or model for the process generating an observed dataset. The original definition starts with a measure of the divergence of the dataset from what was expected under the model, such as a sum of squares or a deviance statistic. A P-value is then the ordinal location of the measure in a reference distribution computed from the model and the data, and is treated as a unit-scaled index of compatibility between the data and the model. In the other definition, a P-value is a random variable on the unit interval whose realizations can be compared to a cutoff alpha to generate a decision rule with known error rates under the model and specific alternatives. It is commonly assumed that realizations of such decision P-values always correspond to divergence P-values. But this need not be so: Decision P-values can violate intuitive single-sample coherence criteria where divergence P-values do not. It is thus argued that divergence and decision P-values should be carefully distinguished in teaching, and that divergence P-values are the relevant choice when the analysis goal is to summarize evidence rather than implement a decision rule.Comment: 49 pages. Scandinavian Journal of Statistics 2023, issue 1, with discussion and rejoinder in issue

Congruencias y factorización como herramientas de reducción en el análisis de conceptos formales

Desde su introducción a principios de los años ochenta por B. Ganter y R. Wille, el Análisis de Conceptos Formales (FCA, de sus siglas en inglés) ha sido una de las herramientas matemáticas para el análisis de datos que más desarrollo ha experimentado. El FCA es una teoría matemática que determina estructuras conceptuales entre conjuntos de datos. En particular, las bases de datos se interpretan formalmente en esta teoría con la noción de contexto, que viene determinado por un conjunto de objetos, un conjunto de atributos y una relación entre ambos conjuntos. Las herramientas que proporciona el FCA permiten manipular adecuadamente los datos y extraer información relevante de ellos. Una de las líneas de investigación con más importancia es la reducción del conjunto de atributos que contienen estos conjuntos de datos, preservando la información esencial y eliminando la redundancia que puedan contener. La reducción de atributos también ha sido estudiada en otros ambientes, como en la Teoría de Conjuntos Rugosos, así como en las distintas generalizaciones difusas de ambas teorías. En el FCA, se ha demostrado que cuando se lleva a cabo una reducción de atributos de un contexto formal, se induce una relación de equivalencia sobre el conjunto de conceptos del contexto original. Esta relación de equivalencia inducida tiene una particularidad, sus clases de equivalencia tienen una estructura de semirretículo superior con un elemento máximo, es decir, no forman estructuras algebraicas cerradas, en general. En esta tesis estudiamos cómo es posible complementar las reducciones de atributos dotando a las clases de equivalencia con una estructura algebraica cerrada. La noción de congruencia consigue este propósito, sin embargo, el uso de este tipo de relación de equivalencia puede desembocar en una gran pérdida de información debido a que las clases de equivalencia agrupan demasiados conceptos. Para abordar este problema, en esta tesis se introduce una noción debilitada de congruencia que denominamos congruencia local. La congruencia local da lugar a clases de equivalencia con estructura de subretículo convexo, siendo más flexible a la hora de agrupar conceptos pero manteniendo propiedades interesantes desde un punto de vista algebraico. Se presenta una discusión general de los principales resultados relativos al estudio y aplicación de las congruencias locales que se han obtenido a lo largo de la investigación desarrollada durante la tesis. En particular, se introduce la noción de congruencia local junto con un análisis de las propiedades que satisface, así como una relación de orden sobre el conjunto de las clases de equivalencia. Además, realizamos un análisis profundo del impacto que genera el uso de las congruencias locales en el FCA, tanto en el contexto formal como en el retículo de conceptos. En este análisis identificamos aquellas clases de equivalencia de la relación inducida por una reducción de atributos, sobre las cuales actuaría la congruencia local, realizando una agrupación de conceptos diferente para obtener subretículos convexos. Adicionalmente, llevamos a cabo un estudio sobre el uso de las congruencias locales cuando en la reducción de atributos considerada se han eliminado todos los atributos innecesarios del contexto, obtienen resultados interesantes. Presentamos diversos mecanismos que permiten calcular congruencias locales y aplicarlas sobre retículos de conceptos, detallando las modificaciones que se realizan sobre el contexto formal para proporcionar un método de reducción basado en congruencias locales. Por otra parte, otra de las estrategias que nos permite reducir la complejidad del análisis de los contextos formales son los mecanismos de factorización. Los procedimientos utilizados para factorizar permiten dividir un contexto en dos o más subcontextos formales de menor tamaño, pudiéndose estudiar por separado más fácilmente. Se presenta un estudio preliminar sobre la factorización de contextos formales difusos usando operadores modales, que no se ha publicado aún en una revista. Estos operadores modales ya han sido utilizados para extraer subcontextos independientes de un contexto formal clásico obteniéndose así una factorización del contexto original. En esta tesis estudiamos también diversas propiedades que nos ayudan a comprender mejor cómo funciona la descomposición de tablas de datos booleanos, para luego realizar una adaptación de dichas propiedades al marco de trabajo multiadjunto. El estudio de estas propiedades generales en el marco de trabajo multiadjunto será de gran relevancia para poder obtener en el futuro un procedimiento que nos permita factorizar contextos formales multiadjuntos. Por tanto, la obtención de mecanismos de factorización de contextos multiadjuntos será clave para el análisis y tratamiento de grandes bases de dato

Instrumental Variables: An Econometrician's Perspective

I review recent work in the statistics literature on instrumental variables methods from an econometrics perspective. I discuss some of the older, economic, applications including supply and demand models and relate them to the recent applications in settings of randomized experiments with noncompliance. I discuss the assumptions underlying instrumental variables methods and in what settings these may be plausible. By providing context to the current applications, a better understanding of the applicability of these methods may arise.Comment: Published in at http://dx.doi.org/10.1214/14-STS480 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org