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Abstract: Web service process reuse can help us efficiently to construct a new service or service process by using the existing service processes generated by service composition. Since service requests are characteristic of multiformity, the existing service processes can hardly be reused unless they are modified and transformed to some specific scenarios. In this paper, a service process is modeled as a service net (SN) using logic Petri nets. Inspired by the relational algebra, service net algebra (SNA) is proposed to provide a formal foundation for structural transformations of SNs including composition and decomposition. It is constructed on the basis of logic Petri nets and consists of structure algebra, evolution algebra and synthesis algebra. Some algebra operators of SNA are defined, and their corresponding operational rules are presented. The properties and soundness preservation of SNA are analyzed. A framework for service process reuse is also given based on SNA. [Copyright &y& Elsevier]

Abstract: In this paper, we first analyze the rationality of weak transitivity of a fuzzy preference relation defined by Tanino [Fuzzy preference orderings in group decision making, Fuzzy Sets and Systems 12 (1984) 117–131]. We then propose a revised definition of weak transitivity (we call it ordinal consistency). We propose the ordinal consistency index (OCI) to measure the degree of ordinal consistency of a fuzzy preference relation, which is to count the unreasonable 3-cycles in a directed graph that represents the fuzzy preference relation. Afterwards, a procedure to compute the order consistency index and to locate each cycle, as well as to find the inconsistent judgments in the fuzzy preference relation is proposed. In order to repair the inconsistency of a fuzzy preference relation, an algorithm is developed to find and remove 3-cycles in the graph. The algorithm eliminates 3-cycles in a graph more effectively and the proposed method for improving consistency method aims to preserve the initial preference information of the decision maker. Furthermore, the method can be used not only for a strict fuzzy preference relation, but also for non-strict fuzzy preference relation. Finally, we provide some examples to show the effectiveness and validity of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper presents an extension of relational algebra suitable for the handling of bipolar concepts. The type of queries considered involves two parts: a first one which expresses a (possibly flexible) constraint, and a second one that corresponds to a (possibly flexible) wish. The framework considered is that of bipolar fuzzy relations where each tuple is associated with a pair of satisfaction degrees. [Copyright &y& Elsevier]

Abstract: Rough set theory was proposed by Pawlak to deal with the vagueness and granularity in information systems. The classical relation-based Pawlak rough set theory has been extended to covering-based generalized rough set theory. The rough set axiom system is the foundation of the covering-based generalized rough set theory, because the axiomatic characterizations of covering-based approximation operators guarantee the existence of coverings reproducing the operators. In this paper, the equivalent characterizations for the independent axiom sets of four types of covering-based generalized rough sets are investigated, and more refined axiom sets are presented. [Copyright &y& Elsevier]

Abstract: A T-fuzzy equivalence relation is a fuzzy binary relation on a set which is reflexive, symmetric and T-transitive for a t-norm T. Recently, Mesiar et al. [R. Mesiar, B. Reusch, H. Thiele, Fuzzy equivalence relations and fuzzy partitions, J. Multi-Valued Logic Soft Comput. 12 (2006) 167–181] have generalised the t-norm T to any general conjunctor C and investigated the minimal assumptions required on such operations, called duality fitting conjunctors, such that the fuzzification of the equivalence relation admits any value from the unit interval and also the one–one correspondence between the fuzzy equivalence relations and fuzzy partitions is preserved. In this work, we conduct a similar study by employing a related form of C-transitivity, viz., I-transitivity, where I is an implicator. We show that although every I-fuzzy equivalence relation can be shown to be a C-fuzzy equivalence relation, there exist C-fuzzy equivalence relations that are not I-fuzzy equivalence relations and hence these concepts are not equivalent. Most importantly, we show that the class of duality fitting implicators I is much richer than the residuals of the duality fitting conjunctors in the study of Mesiar et al. We also show that the I-fuzzy partitions have a “constant-wise” structure. [Copyright &y& Elsevier]

Discusses several candidate notions of determinacy in Kleene algebras. Definitions of Kleene algebras; Types of Boolean abstract relation algebra; Candidates from relation algebra; Technique for constructing Kleene algebras.

Discusses the application of the H.S. Leonard and N. Goodman's notion of a multigrade relation to the phenomenon of variable polyacidity in natural language. Definition of relational grammar; Application of multigrade relations to a fragment of English; Differences between multigrade relations and the use of predicates with no fixed valency.

Presents a structural and calculational approach to depth-first-search (DFS) algorithms for searching a directed graph. Basics about relational algebra; Relational specification of the DFS method; Applications of DFS method.

Presents a study which discussed BK-relational products and their role in the analysis and synthesis of complex systems. Application of similarity relations on the products; Information on similarity phenomenon approach in fuzzy set theory.

Focuses on the relation-algebraic monomorphic characterization of n-ary direct products (n-tuple-forming products). Generalization of binary products; Discussion on basic laws of homogeneous and heterogeneous relation algebras; Introduction of relational concepts; Proofs of monomorphicity.

Introduces an extended approach to graphical relation calculi towards relation matching, hierarchical relational diagrams. Discussion on algebraic notation; Introduction of the concept of rules and rewriting; Conclusion.

Provides a notion of Zadeh categories as a categorical structure formed by fuzzy relations. Information on Dedekind categories; Properties of fuzzy algebra; Connection of Zadeh category representation theorem with simple representation theorem.

Presents information on a study which defined a language for polymorphic typed relations and which introduced a typing discipline for terms of that language. Language for heterogenous relation algebras; Theorems and proofs; Conclusion.

Shows how to derive imperative programs for relation-based discrete structures by combining relational calculus and Dijkstra-Gries method. Description of algorithms; Concepts of relational calculus; Illustration of the Dijkstra-Gries method.

Evaluates the effectiveness of relational model of pointer structure in calculating standard algorithms on singly link list, both acyclic and cyclic. Definition of pointer structure and shape of records; Implementation of pointer structure; How to calculate with acyclic and cyclic cases using relational methods.

Focuses on fuzzy relation compositions. Proposition of similarity relations; What they can do; Use of compositions to expand compressed data; Information on object classification process.