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In this paper we extend our previous results on sets of graded attribute implications with witnessed non-redundancy. We assume finite residuated lattices as structures of truth degrees and use arbitrary idempotent truth-stressing linguistic hedges as parameters which influence the semantics of graded attribute implications. In this setting, we introduce algorithm which transforms any set of graded attribute implications into an equivalent non-redundant set of graded attribute implications with saturated consequents whose non-redundancy is witnessed by antecedents of the formulas. As a consequence, we solve the open problem regarding the existence of general systems of pseudo-intents which appear in formal concept analysis of object-attribute data with graded attributes and linguistic hedges. Furthermore, we show a polynomial-time procedure for determining bases given by general systems of pseudo-intents from sets of graded attribute implications which are complete in data. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an effective particle swarm optimization (PSO) is proposed for polynomial models for time varying systems. The basic operations of the proposed PSO are similar to those of the classical PSO except that elements of particles represent arithmetic operations and variables of time-varying models. The performance of the proposed PSO is evaluated by polynomial modeling based on various sets of time-invariant and time-varying data. Results of polynomial modeling in time-varying systems show that the proposed PSO outperforms commonly used modeling methods which have been developed for solving dynamic optimization problems including genetic programming (GP) and dynamic GP. An analysis of the diversity of individuals of populations in the proposed PSO and GP reveals why the proposed PSO obtains better results than those obtained by GP. [Copyright &y& Elsevier]

Abstract: In this paper, rough approximations of Cayley graphs are studied, and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition for pseudo-Cayley graphs containing Cayley graphs is proposed, and a rough approximation is expanded to pseudo-Cayley graphs. In addition, rough vertex pseudo-Cayley graphs and rough pseudo-Cayley graphs are introduced. Some theorems are provided from which properties such as connectivity and optimal connectivity are derived. This approach opens new research fields, such as data networks. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the notion of a reference point and provide local approximations for a subset of the universe. The notion of a reference point naturally gives rise to a rough approximations framework, wherein several approximations are possible on the same set. Also, we present an extension to the decision theoretic rough set model by using reference points. [Copyright &y& Elsevier]

Abstract: In this paper we show that, for given a pogroupoid (X,·), the associated poset (X,⩽) is (C 2 + 1)-free if and only if the relation is transitive for any fuzzy subset μ of X. Also we determine the set C(X,·) of fuzzy subsets μ such that μ(x · y)= μ(y · x) for all x, y ∈ X. Furthermore, with a given finite poset (X,⩽) or the associated pogroupoid (X,·) we may then associate a polynomial whose coefficients count the number of congruence classes mod(X, ·) of fuzzy subsets of X along with another polynomial invariant of interest. [Copyright &y& Elsevier]