LearnFCA: A Fuzzy FCA and Probability Based Approach for Learning and Classification

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering. This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems. We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success. Adviser: Dr Jitender Deogu

LEARNFCA: A FUZZY FCA AND PROBABILITY BASED APPROACH FOR LEARNING AND CLASSIFICATION

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering. This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems. We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success. Adviser: Jitender Deogu

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas

Concept learning consistency under three‑way decision paradigm

Concept Mining is one of the main challenges both in Cognitive Computing and in Machine Learning. The ongoing improvement of solutions to address this issue raises the need to analyze whether the consistency of the learning process is preserved. This paper addresses a particular problem, namely, how the concept mining capability changes under the reconsideration of the hypothesis class. The issue will be raised from the point of view of the so-called Three-Way Decision (3WD) paradigm. The paradigm provides a sound framework to reconsider decision-making processes, including those assisted by Machine Learning. Thus, the paper aims to analyze the influence of 3WD techniques in the Concept Learning Process itself. For this purpose, we introduce new versions of the Vapnik-Chervonenkis dimension. Likewise, to illustrate how the formal approach can be instantiated in a particular model, the case of concept learning in (Fuzzy) Formal Concept Analysis is considered.This work is supported by State Investigation Agency (Agencia Estatal de Investigación), project PID2019-109152GB-100/AEI/10.13039/501100011033. We acknowledge the reviewers for their suggestions and guidance on additional references that have enriched our paper. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature

A Logic Approach to Granular computing

This article was originally published by the International Journal of Cognitive Informatics and Natural IntelligenceGranular computing is an emerging field of study that attempts to formalize and explore methods and heuristics of human problem solving with multiple levels of granularity and abstraction. A fundamental issue of granular computing is the representation and utilization of granular structures. The main objective of this article is to examine a logic approach to address this issue. Following the classical interpretation of a concept as a pair of intension and extension, we interpret a granule as a pair of a set of objects and a logic formula describing the granule. The building blocks of granular structures are basic granules representing an elementary concept or a piece of knowledge. They are treated as atomic formulas of a logic language. Different types of granular structures can be constructed by using logic connectives. Within this logic framework, we show that rough set analysis (RSA) and formal concept analysis (FCA) can be interpreted uniformly. The two theories use multilevel granular structures but differ in their choices of definable granules and granular structures.NSERC Canada Discovery gran

Mining for Unknown Unknowns

Unknown unknowns are future relevant contingencies that lack an ex ante description. While there are numerous retrospective accounts showing that significant gains or losses might have been achieved or avoided had such contingencies been previously uncovered, getting hold of unknown unknowns still remains elusive, both in practice and conceptually. Using Formal Concept Analysis (FCA) - a subfield of lattice theory which is increasingly applied for mining and organizing data - this paper introduces a simple framework to systematically think out of the box and direct the search for unknown unknowns.Comment: In Proceedings TARK 2023, arXiv:2307.0400

Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory. In 1965, L.A. Zadeh had published “Fuzzy Sets” [335]. After only one year, the first effects of this seminal paper began to emerge, with the pioneering paper on clustering by Bellman, Kalaba, Zadeh [33], in which they proposed a prototypal of clustering algorithm based on the fuzzy sets theory