10 research outputs found
Heterogeneous environment on examples
We propose a running example for heterogeneous approach based on new type of fuzzification that diversifies fuzziness of every object, fuzziness of every attribute and fuzziness of every table value in a formal context. Moreover we suggest another working examples on heterogeneous environment and provide additional utilization and illustration of this new model that allows to use Formal Concept Analysis also for heterogenenous data. An interpretation of heterogeneous formal concepts and the resulting concept lattice is included
Heterogeneous environment on examples
We propose a running example for heterogeneous approach based on new type of fuzzification that diversifies fuzziness of every object, fuzziness of every attribute and fuzziness of every table value in a formal context. Moreover we suggest another working examples on heterogeneous environment and provide additional utilization and illustration of this new model that allows to use Formal Concept Analysis also for heterogenenous data. An interpretation of heterogeneous formal concepts and the resulting concept lattice is included
A Recursive Bateson-Inspired Model for the Generation of Semantic Formal Concepts from Spatial Sensory Data
Neural-symbolic approaches to machine learning incorporate the advantages
from both connectionist and symbolic methods. Typically, these models employ a
first module based on a neural architecture to extract features from complex
data. Then, these features are processed as symbols by a symbolic engine that
provides reasoning, concept structures, composability, better generalization
and out-of-distribution learning among other possibilities. However, neural
approaches to the grounding of symbols in sensory data, albeit powerful, still
require heavy training and tedious labeling for the most part. This paper
presents a new symbolic-only method for the generation of hierarchical concept
structures from complex spatial sensory data. The approach is based on
Bateson's notion of difference as the key to the genesis of an idea or a
concept. Following his suggestion, the model extracts atomic features from raw
data by computing elemental sequential comparisons in a stream of multivariate
numerical values. Higher-level constructs are built from these features by
subjecting them to further comparisons in a recursive process. At any stage in
the recursion, a concept structure may be obtained from these constructs and
features by means of Formal Concept Analysis. Results show that the model is
able to produce fairly rich yet human-readable conceptual representations
without training. Additionally, the concept structures obtained through the
model (i) present high composability, which potentially enables the generation
of 'unseen' concepts, (ii) allow formal reasoning, and (iii) have inherent
abilities for generalization and out-of-distribution learning. Consequently,
this method may offer an interesting angle to current neural-symbolic research.
Future work is required to develop a training methodology so that the model can
be tested against a larger dataset
Bivalent and other solutions of fuzzy relational equations via linguistic hedges
Abstract We show that the well-known results regarding solutions of fuzzy relational equations and their systems can easily be generalized to obtain criteria regarding constrained solutions such as solutions which are crisp relations. When the constraint is empty, constrained solutions are ordinary solutions. The generalization is obtained by employing intensifying and relaxing linguistic hedges, conceived in this paper as certain unary functions on the scale of truth degrees. One aim of the paper is to highlight the problem of constrained solutions and to demonstrate that this problem naturally appears when identifying unknown relations. The other is to emphasize the role of linguistic hedges as constraints. © 2011 Elsevier B.V. All rights reserved. Motivation Fuzzy relational equations play an important role in fuzzy set theory and its applications, see and every fuzzy relation U satisfying the first or the second equality is called a solution of the respective fuzzy relational equation. The nature of the unknown relationship represented by U may impose additional constraints on U. For example, one may require that U be a bivalent (crisp) relation (see Section 3 for an illustrative example). More generally
Parameterizing the semantics of fuzzy attribute implications by systems of isotone Galois connections
We study the semantics of fuzzy if-then rules called fuzzy attribute
implications parameterized by systems of isotone Galois connections. The rules
express dependencies between fuzzy attributes in object-attribute incidence
data. The proposed parameterizations are general and include as special cases
the parameterizations by linguistic hedges used in earlier approaches. We
formalize the general parameterizations, propose bivalent and graded notions of
semantic entailment of fuzzy attribute implications, show their
characterization in terms of least models and complete axiomatization, and
provide characterization of bases of fuzzy attribute implications derived from
data
Reducing the size of fuzzy concept lattices by hedges
Abstract-We study concept lattices with hedges. The principal aim is to control, in a parametrical way, the size of a concept lattice. The paper presents theoretical insight, comments, and examples. We show that a concept lattice with hedges is indeed a complete lattice which is isomorphic to an ordinary concept lattice. We describe the isomorphism and its inverse. These mappings serve as translation procedures. As a consequence, we obtain a theorem characterizing the structure of concept lattices with hedges which generalizes the so-called main theorem of concept lattices. Furthermore, the isomorphism and its inverse enable us to compute a concept lattice with hedges using algorithms for ordinary concept lattices. Further insight is provided in case one uses hedges only for attributes. We demonstrate by experiments that the size reduction using hedges as a parameter is smooth. I. PROBLEM SETTING Tabular data describing objects and their attributes represents a basic form of data. Among the several methods for analysis of object-attribute data, formal concept analysis (FCA) is becoming increasingly popular, see In [4], we proposed a way to reduce the number of formal concepts extracted from data with attributes by using socalled (truth-stressing) hedges. Definitions, basic results, and illustrative examples are given in II. PRELIMINARIES We use sets of truth degrees equipped with operations (logical connectives) so that is becomes a complete residuated lattice with a truth-stressing hedge. A complete residuated lattice with truth-stressing hedge (shortly, a hedge) . Elements a of L are called truth degrees. â and â are (truth functions of) "fuzzy conjunction" and "fuzzy implication". Hedge * is a (truth function of) logical connective "very true", see A common choice of L is a structure with L = [0, 1] (unit interval), ⧠and âš being minimum and maximum, â being a left-continuous t-norm with the corresponding â. Three most important pairs of adjoint operations on the unit interval are: Gödel: Goguen (product): In applications, we usually need a finite linearly ordered L. For instance, one can put L = {a 0 = 0, a 1 , . . . , a n = 1} â [0, 1] (a 0 < · · · < a n ) with â given by a k â a l = a max(k+lân,0) and the corresponding â given by a k â a l = a min(nâk+l,n) . Such an L is called a finite Ćukasiewicz chain. Another possibility is a finite Gödel chain which consists of L and restrictions of Gödel operations on [0, 1] to L