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In the last decade, several new construction methods of fuzzy implication functions from one or more given ones have been proposed. Following this line of research, in our paper some construction methods based on polynomial functions of three variables are presented. Concretely, these methods provide a (possibly new) fuzzy implication function from a given one and a quadratic polynomial function. A complete characterization of those quadratic functions adequate to obtain a fuzzy implication function through this strategy is presented. Moreover, the invariant fuzzy implication functions with respect to this method are determined. Finally, some quadratic construction methods preserving some specific additional properties are analysed. [ABSTRACT FROM AUTHOR]

Jobs with deterioration and learning effect co-exist in many industry engineering and logistics management situations. In this note, the general effects of deterioration and learning are considered. It is proved that some single machine scheduling problems are still polynomially solvable under the proposed model. The note also shows that some results in Lee and Lai’s recent paper (Lee and Lai, 2011) are incorrect by a counterexample. [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, 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 scheduling problems with learning effects, most of the research is based on specific learning functions. In this paper, we develop a general model with learning effects where the actual processing time of a job is not only a function of the total normal processing times of the jobs already processed, but also a function of the job’s scheduled position. In particular, it is shown that some single machine scheduling problems and m-machine permutation flowshop problems are still polynomially solvable under the proposed model. These results are significant extensions of some of the existing results on learning effects in the literature. [Copyright &y& Elsevier]