Proto-Fuzzy Concepts Generation Technique Using Fuzzy Graph
01 Jan 2015-pp 63-74
TL;DR: This paper begins with defining a fuzzy graph corresponding to the L-context (fuzzy context), and goes on to demonstrate that t-concepts can be found to correspond with each maximal cliques of t-level graph of the defined fuzzy graph.
Abstract: Since one major disadvantage of application of fuzzy formal concept analysis is that large numbers of fuzzy concepts are generated from fuzzy context, it is practically impossible to analyze such a large amount of concepts. Often it may be required to consider some particular concepts. For example, one might be interested to find out the fuzzy concepts containing all those objects which share some specific property with a specific/required degree from a given fuzzy context. Given such a situation, proto-fuzzy concepts may play a very useful role. This paper proposes a proto-fuzzy concept generation technique using fuzzy graph on uncertainty data. In this paper, we begin with defining a fuzzy graph corresponding to the L-context (fuzzy context). We then go on to demonstrate that t-concepts can be found to correspond with each maximal cliques of t-level graph of the defined fuzzy graph. After that, we determine all those cliques which corresponds to the proto-fuzzy concepts of degree \(t\). Finally, a demonstration has been made using an example with the proposed technique.
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TL;DR: A novel Hybrid Fuzzy Semi-Supervised Forecasting Framework is proposed, which combines fuzzy logic, semi- supervised clustering and semi-supervised classification in order to model Big Data sets in a faster, simpler and more essential manner.
Abstract: Mining hidden knowledge from available datasets is an extremely time-consuming and demanding process, especially in our era with the vast volume of high-complexity data. Additionally, validation of results requires the adoption of appropriate multifactor criteria, exhaustive testing and advanced error measurement techniques. This paper proposes a novel Hybrid Fuzzy Semi-Supervised Forecasting Framework. It combines fuzzy logic, semi-supervised clustering and semi-supervised classification in order to model Big Data sets in a faster, simpler and more essential manner. Its advantages are clearly shown and discussed in the paper. It uses as few pre-classified data as possible while providing a simple method of safe process validation. This innovative approach is applied herein to effectively model the air quality of Athens city. More specifically, it manages to forecast extreme air pollutants’ values and to explore the parameters that affect their concentration. Also it builds a correlation between pollution and general climatic conditions. Overall, it correlates the built model with the malfunctions caused to the city life by this serious environmental problem.
58 citations
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...The same boundary has been used in similar cases in the literature several times [30, 31]....
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DOI•
16 Aug 2021
TL;DR: A FCA-based teaching methodology for the learners on the basis of their background knowledge is proposed, using a mathematical model to calculate the learners’ prior knowledge on the subjects of pursuing course based on the learner’s background knowledge.
Abstract: In multidisciplinary courses, learners have diverse educational background and training on varying subjects. Subjects that such learners have studied may or may not relate to those of a course now being pursued. A requirement, therefore, arises to ascertain the level of understanding that the learners’ have acquired respectively in their chosen subjects. This paper proposes a FCA-based teaching methodology for the learners on the basis of their background knowledge. In our approach, we first present a mathematical model to calculate the learners’ prior knowledge on the subjects of pursuing course based on the learners’ background knowledge. Using the calculated prior knowledge on the pursuing subjects, the learners are then clustered by generating proto-fuzzy to deliver appropriate learning material to each of the learners. Finally, we discuss the proposed model with an example.
1 citations
References
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"Proto-Fuzzy Concepts Generation Tec..." refers background in this paper
...In this sub-section we first recall the basics of fuzzy logic [14, 19, 22, 33] and fuzzy...
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5,861 citations
"Proto-Fuzzy Concepts Generation Tec..." refers background in this paper
...In this sub-section we first recall the basics of fuzzy logic [14, 19, 22, 33] and fuzzy...
[...]
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04 Dec 1998
TL;DR: This is the first textbook on formal concept analysis that gives a systematic presentation of the mathematical foundations and their relation to applications in computer science, especially in data analysis and knowledge processing.
Abstract: From the Publisher:
This is the first textbook on formal concept analysis. It gives a systematic presentation of the mathematical foundations and their relation to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. Theory and graphical representation are thus closely coupled together. The mathematical foundations are treated thoroughly and illuminated by means of numerous examples.
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12 May 2009
TL;DR: Restructuring lattice theory is an attempt to reinvigorate connections with the authors' general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattices theory.
Abstract: Lattice theory today reflects the general Status of current mathematics: there is a rich production of theoretical concepts, results, and developments, many of which are reached by elaborate mental gymnastics; on the other hand, the connections of the theory to its surroundings are getting weaker and weaker, with the result that the theory and even many of its parts become more isolated. Restructuring lattice theory is an attempt to reinvigorate connections with our general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattice theory.
2,407 citations
"Proto-Fuzzy Concepts Generation Tec..." refers background in this paper
...The work on Formal Concept Analysis (FCA) by Wille and Ganter [15, 16, 31] has introduced a new perspective and opened up new areas of its application....
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TL;DR: Two backtracking algorithms are presented, using a branchand-bound technique [4] to cut off branches that cannot lead to a clique, and generates cliques in a rather unpredictable order in an attempt to minimize the number of branches to be traversed.
Abstract: Description bttroductian. A maximal complete subgraph (clique) is a complete subgraph that is not contained in any other complete subgraph. A recent paper [1] describes a number of techniques to find maximal complete subgraphs of a given undirected graph. In this paper, we present two backtracking algorithms, using a branchand-bound technique [4] to cut off branches that cannot lead to a clique. The first version is a straightforward implementation of the basic algorithm. It is mainly presented to illustrate the method used. This version generates cliques in alphabetic (lexicographic) order. The second version is derived from the first and generates cliques in a rather unpredictable order in an attempt to minimize the number of branches to be traversed. This version tends to produce the larger cliques first and to generate sequentially cliques having a large common intersection. The detailed algorithm for version 2 is presented here. Description o f the algorithm--Version 1. Three sets play an important role in the algorithm. (1) The set compsub is the set to be extended by a new point or shrunk by one point on traveling along a branch of the backtracking tree. The points that are eligible to extend compsub, i.e. that are connected to all points in compsub, are collected recursively in the remaining two sets. (2) The set candidates is the set of all points that will in due time serve as an extension to the present configuration of compsub. (3) The set not is the set of all points that have at an earlier stage already served as an extension of the present configuration of compsub and are now explicitly excluded. The reason for maintaining this set trot will soon be made clear. The core of the algorithm consists of a recursively defined extension operator that will be applied to the three sets Just described. It has the duty to generate all extensions of the given configuration of compsub that it can make with the given set of candidates and that do not contain any of the points in not. To put it differently: all extensions of compsub containing any point in not have already been generated. The basic mechanism now consists of the following five steps:
2,405 citations
"Proto-Fuzzy Concepts Generation Tec..." refers background in this paper
...There are several number of algorithm exists for this problem [7, 8, 13, 23, 30], and time complexity of most of these algorithms depends on the number of vertices and number of cliques of G....
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