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Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. It has been used in various domains such as data mining, machine learning, semantic web, Sciences, for the purpose of data analysis and Ontology over the last few decades. Various extensions of FCA are being researched to expand it's scope over more departments. In this thesis,we review the theory of Formal Concept Analysis(FCA) and its ex- tension Fuzzy FCA. Many studies to use FCA in data mining and text learning have been pursued. We extend these studies to include classification problems as well. Formal Concept Analysis is a mathematical theory of concepts and conceptual hierarchies, called concept lattices. It studies how objects can hierarchically be grouped together according to their common attributes. FCA is based on a mathematical order theory for data analysis, which extracts concepts and builds a conceptual hierarchy from given data. In order to analyze vague data set of uncertainty information, Fuzzy Formal Concept Analysis(Fuzzy FCA) incorporates fuzzy set theory into FCA. We propose an implementation of fuzzy FCA, a novel approach based on FCA and probability theory for learning and classification problems. It 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 unlabeled features. We also propose a novel approach to generate intents and extents for each of the nodes in the lattice. We intend to scan the MNIST image database and classify using Fuzzy FCA. Our proposed algorithm for Fuzzy FCA generates a concept lattice creating clusters of images that share similar attributes which meet a minimum threshold value. We evaluate the algorithm on the MNIST images and compare the results with well- known classification algorithms.
Advisor: Jitender Deogun