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Associative classification (AC) integrates the task of mining association rules with the classification task to increase the efficiency of the classification process. AC algorithms produce accurate classification and generate easy to understand rules. However, AC algorithms suffer from two drawbacks: the large number of classification rules, and using different pruning methods that may remove vital information to achieve the right decision. In this paper, a new hybrid AC algorithm (HAC) is proposed. HAC applies the power of the Naïve Bayes (NB) algorithm to reduce the number of classification rules and to produce several rules that represent each attribute value. Two experiments are conducted on an Arabic textual dataset and the standard Reuters-21578 datasets using six different algorithms, namely J48, NB, classification based on associations (CBA), multi-class classification based on association rules (MCAR), expert multi-class classification based on association rules (EMCAR), and fast associative classification algorithm (FACA). The results of the experiments showed that the HAC approach produced higher classification accuracy than MCAR, CBA, EMCAR, FACA, J48 and NB with gains of 3.95%, 6.58%, 3.48%, 1.18%, 5.37% and 8.05% respectively. Furthermore, on Reuters-21578 datasets, the results indicated that the HAC algorithm has an excellent and stable performance in terms of classification accuracy and F measure. [ABSTRACT FROM AUTHOR]

A consistent connective system generated by nilpotent operators is not necessarily isomorphic to the Łukasiewicz system. Using more than one generator function, consistent nilpotent connective systems (so-called bounded systems) can be obtained with the advantage of three naturally derived negation operators and thresholds. In this paper, equivalences in bounded systems are examined. Here, three different types of operators are studied, and a paradox of the equivalence (i.e. there is no equivalence relation in a non-Boolean setting which fulfils ∀ x e ( x , x ) = 1 and e ( x , n ( x ) ) = 0 ) is resolved by aggregating the implication-based equivalence and its dual operator. We will also show that the aggregated equivalence has nice properties like associativity, threshold transitivity and T-transitiviy. [ABSTRACT FROM AUTHOR]

In this paper, a new product of tensors is given, which is a generalization of the product of tensors introduced by Gelfand, Kapranov, Zelevinsky. This product satisfies the associative law. Using the associative law, it is concluded that the product of tensors given by Bu and others and the general product of tensors introduced by Shao can be represented by this new tensors product. As an application of this new tensors product and the associative law, the hyperdeterminant of the product of a kind of tensors is studied, i.e., some formulas for the hyperdeterminant of boundary formats product are shown. [ABSTRACT FROM AUTHOR]

Abstract: The soft set theory, proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. By combining the interval-valued fuzzy set and soft set models, the purpose of this paper is to introduce the concept of the interval-valued fuzzy soft set. The complement, “AND” and “OR” operations are defined on the interval-valued fuzzy soft sets. The DeMorgan’s, associative and distribution laws of the interval-valued fuzzy soft sets are then proved. Finally, a decision problem is analyzed by the interval-valued fuzzy soft set. Some numerical examples are employed to substantiate the conceptual arguments. [Copyright &y& Elsevier]

Abstract: A class-bridge rule is the rule whose antecedent and consequent belong to different conceptual classes. This kind of rules stands for the correlation between conceptual classes. The study on class-bridge rules can benefit many domains such as criminal detection, chemical synthesis, biological grafting, etc. Class-bridge rules are different from other association rules as follows: (1) class-bridge rules can be generated from infrequent itemsets; (2) measurements of class-bridge rules include the distance between conceptual classes and the relation between the antecedents/consequents and their affiliated conceptual classes. This paper proposes an algorithm based on rough sets to mine and evaluate class-bridge rules. The experiment demonstrates its effectiveness. [Copyright &y& Elsevier]

In this paper we prove that the heart of a nondegenerate Jordan system (algebra, triple system or pair) is either simple or zero. We also obtain Herstein type results relating the hearts of associative systems and those of their corresponding Jordan systems. [Copyright &y& Elsevier]