Building epistemology of multicultural education to the indigenous Javanese Islam

This research is intended to find out the epistemological building of multicultural education in the indigenous Javanese Islam. This theme is important to be investigated because multicultural education is still considered to be lacking. This research uses qualitative research. The data used in this study were sourced from books, journals and written results related to the indigenization (pribumisasi) of Islam, Javanese culture and multicultural education. The study focused on the indigenous Javanese Islam because of the high level of multiculturalism. The results of the study were then analyzed using an interactive data analysis model. The results of the study show that multicultural education components such as integration of content with syncretic Islam, knowledge construction lead to inclusive knowledge, reduction of prejudice with Sufism, equality education with boarding school (pesantren) and culture that empowers practiced by strengthening civil society.

A dynamic knowledge base and its data compression with homomorphism

In reality there are always a large number of complex massive databases. The notion of homomorphism may be a mathematical tool for studying data compression in knowledge bases. This paper investigates a knowledge base in dynamic environments and its data compression with homomorphism, where “dynamic” refers to the fact that the involved information systems need to be updated with time due to the inflow of new information. First, the relationships among knowledge bases, information systems and relation information systems are illustrated. Next, the idea of non-incremental algorithm for data compression with homomorphism and the concept of dynamic knowledge base are introduced. Two incremental algorithms for data compression with homomorphism in dynamic knowledge bases are presented. Finally, an experimental analysis is employed to demonstrate the applications of the non-incremental algorithm and the incremental algorithms for data compression when calculating the knowledge reduction of dynamic knowledge bases.

A Parallel Attribute Reduction Method Based on Classification

Parallel processing as a method to improve computer performance has become a development trend. Based on rough set theory and divide-and-conquer idea of knowledge reduction, this paper proposes a classification method that supports parallel attribute reduction processing, the method makes the relative positive domain which needs to be calculated repeatedly independent, and the independent relative positive domain calculation could be processed in parallel; thus, attribute reduction could be handled in parallel based on this classification method. Finally, the proposed algorithm and the traditional algorithm are analyzed and compared by experiments, and the results show that the proposed method in this paper has more advantages in time efficiency, which proves that the method could improve the processing efficiency of attribute reduction and makes it more suitable for massive data sets.

Reduction of fuzzy-crisp concept lattice based on order-class matrix

Knowledge reduction is one of critical problems in data mining and information processing. It can simplify the structure of the lattice during the construction of fuzzy-crisp concept lattice. In terms of fuzzy-crisp concept, we develop an order-class matrix to represent extents and intents of concepts, respectively. In order to improve the computing efficiency, it is necessary to reduce the size of lattices as much as possible. Therefore the judgement theorem of meet-irreducible elements is proposed. To deal with attribute reductions, we develop a discernibility Boolean matrix in formal fuzzy contexts by preserving extents of meet-irreducible elements via order-class matrix. A heuristic attribute-reduction algorithm is proposed. Then we extend the proposed model to consistent formal fuzzy decision contexts. Our methods present a new framework for knowledge reduction in formal fuzzy contexts.

Relative Reduction of Neighborhood-Covering Pessimistic Multigranulation Rough Set Based on Evidence Theory

Relative reduction of multiple neighborhood-covering with multigranulation rough set has been one of the hot research topics in knowledge reduction theory. In this paper, we explore the relative reduction of covering information system by combining the neighborhood-covering pessimistic multigranulation rough set with evidence theory. First, the lower and upper approximations of multigranulation rough set in neighborhood-covering information systems are introduced based on the concept of neighborhood of objects. Second, the belief and plausibility functions from evidence theory are employed to characterize the approximations of neighborhood-covering multigranulation rough set. Then the relative reduction of neighborhood-covering information system is investigated by using the belief and plausibility functions. Finally, an algorithm for computing a relative reduction of neighborhood-covering pessimistic multigranulation rough set is proposed according to the significance of coverings defined by the belief function, and its validity is examined by a practical example.