scholarly journals FI-FG: Frequent Item Sets Mining from Datasets with High Number of Transactions by Granular Computing and Fuzzy Set Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Zhong-jie Zhang ◽  
Jian Huang ◽  
Ying Wei
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Granular Computing ◽  
Sampling Methods ◽  
High Reliability ◽  
Exact Algorithms ◽  
Frequent Item ◽  
Frequent Item Sets ◽  
Progressive Sampling

Mining frequent item set (FI) is an important issue in data mining. Considering the limitations of those exact algorithms and sampling methods, a novel FI mining algorithm based on granular computing and fuzzy set theory (FI-GF) is proposed, which mines those datasets with high number of transactions more efficiently. Firstly, the granularity is applied, which compresses the transactions to some granules for reducing the scanning cost. During the granularity, each granule is represented by a fuzzy set, and the transaction scale represented by a granule is optimized. Then, fuzzy set theory is used to compute the supports of item sets based on those granules, which faces the uncertainty brought by the granularity and ensures the accuracy of the final results. Finally, Apriori is applied to get the FIs based on those granules and the new computing way of supports. Through five datasets, FI-GF is compared with the original Apriori to prove its reliability and efficiency and is compared with a representative progressive sampling way, RC-SS, to prove the advantage of the granularity to the sampling method. Results show that FI-GF not only successfully saves the time cost by scanning transactions but also has the high reliability. Meanwhile, the granularity has advantages to those progressive sampling methods.

Application of Fuzzy Set Theory in the Scheduling of a Tandem Cold-Rolling Mill

1999 ◽  
Vol 122 (3) ◽  
pp. 494-500 ◽  
Author(s):  
U. S. Dixit ◽  
P. M. Dixit
Keyword(s):  
Cold Rolling ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rolling Mill ◽  
High Reliability ◽  
Specific Power ◽  
Cold Rolling Mill ◽  
Tandem Cold Rolling ◽  
First Pass

In a tandem cold-rolling mill, a strip is successively reduced in gauge at each stand as it passes through the mill. The optimal scheduling of a tandem mill is an important but difficult task. In this work, a scheduling problem is considered as an optimization problem which minimizes the total specific power and satisfies certain constraints. Since the material properties and friction coefficient are not known precisely, they are treated as fuzzy numbers. The fuzzy set theory is applied to find out an optimum drafting pattern. The methodology is illustrated by means of a few examples. It is observed that the schedule in which the maximum reduction is achieved in the first pass results in minimum specific power; however, its reliability is poor. Optimization using fuzzy set theory provides a solution which meets the twin requirements of high reliability and minimum power. [S1087-1357(00)00902-3]

Granular Computing Based Data Mining in the Views of Rough Set and Fuzzy Set

2010 ◽  
pp. 148-178 ◽  
Author(s):  
Guoyin Wang ◽  
Jun Hu ◽  
Qinghua Zhang ◽  
Xianquan Liu ◽  
Jiaqing Zhou
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Rule Sets ◽  
Incomplete Information Systems

Granular computing (GrC) is a label of theories, methodologies, techniques, and tools that make use of granules in the process of problem solving. The philosophy of granular computing has appeared in many fields, and it is likely playing a more and more important role in data mining. Rough set theory and fuzzy set theory, as two very important paradigms of granular computing, are often used to process vague information in data mining. In this chapter, based on the opinion of data is also a format for knowledge representation, a new understanding for data mining, domain-oriented data-driven data mining (3DM), is introduced at first. Its key idea is that data mining is a process of knowledge transformation. Then, the relationship of 3DM and GrC, especially from the view of rough set and fuzzy set, is discussed. Finally, some examples are used to illustrate how to solve real problems in data mining using granular computing. Combining rough set theory and fuzzy set theory, a flexible way for processing incomplete information systems is introduced firstly. Then, the uncertainty measure of covering based rough set is studied by converting a covering into a partition using an equivalence domain relation. Thirdly, a high efficient attribute reduction algorithm is developed by translating set operation of granules into logical operation of bit strings with bitmap technology. Finally, two rule generation algorithms are introduced, and experiment results show that the rule sets generated by these two algorithms are simpler than other similar algorithms.

Granular Computing

2011 ◽  
pp. 774-780
Author(s):  
Georg Peters
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Sets ◽  
Granular Computing ◽  
Information Granularity ◽  
Relationship Of ◽  
The Relationship

It is well accepted that in many real life situations information is not certain and precise but rather uncertain or imprecise. To describe uncertainty probability theory emerged in the 17th and 18th century. Bernoulli, Laplace and Pascal are considered to be the fathers of probability theory. Today probability can still be considered as the prevalent theory to describe uncertainty. However, in the year 1965 Zadeh seemed to have challenged probability theory by introducing fuzzy sets as a theory dealing with uncertainty (Zadeh, 1965). Since then it has been discussed whether probability and fuzzy set theory are complementary or rather competitive (Zadeh, 1995). Sometimes fuzzy sets theory is even considered as a subset of probability theory and therefore dispensable. Although the discussion on the relationship of probability and fuzziness seems to have lost the intensity of its early years it is still continuing today. However, fuzzy set theory has established itself as a central approach to tackle uncertainty. For a discussion on the relationship of probability and fuzziness the reader is referred to e.g. Dubois, Prade (1993), Ross et al. (2002) or Zadeh (1995). In the meantime further ideas how to deal with uncertainty have been suggested. For example, Pawlak introduced rough sets in the beginning of the eighties of the last century (Pawlak, 1982), a theory that has risen increasing attentions in the last years. For a comparison of probability, fuzzy sets and rough sets the reader is referred to Lin (2002). Presently research is conducted to develop a Generalized Theory of Uncertainty (GTU) as a framework for any kind of uncertainty whether it is based on probability, fuzziness besides others (Zadeh, 2005). Cornerstones in this theory are the concepts of information granularity (Zadeh, 1979) and generalized constraints (Zadeh, 1986). In this context the term Granular Computing was first suggested by Lin (1998a, 1998b), however it still lacks of a unique and well accepted definition. So, for example, Zadeh (2006a) colorfully calls granular computing “ballpark computing” or more precisely “a mode of computation in which the objects of computation are generalized constraints”.

Estimating construction waste generation in residential buildings: A fuzzy set theory approach in the Brazilian Amazon

2020 ◽  
Vol 265 ◽  
pp. 121779 ◽  
Author(s):  
Luiz Maurício Furtado Maués ◽  
Brisa do Mar Oliveira do Nascimento ◽  
Weisheng Lu ◽  
Fan Xue
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Residential Buildings ◽  
Brazilian Amazon ◽  
Theory Approach ◽  
Waste Generation ◽  
Construction Waste

Knowledge fusion method based on fuzzy set theory

2020 ◽  
Vol 38 (4) ◽  
pp. 3971-3979
Author(s):  
Yana Yuan ◽  
Huaqi Chai
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fusion Method ◽  
Knowledge Fusion
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