Papers by Keyword: Category Theory

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Authors: Hong Feng Lai
Abstract: This paper proposes a categorical foundation for composing multi-resource in manufacturing systems. The composing procedures of overall system can be explained by pushout of category theory. The purpose of this paper is to resolve the issue involves in resource sharing, coordination and conflict for modeling the distributed manufacturing systems. We will propose a method for modeling discrete event system. The mathematical foundation lies in assuring that the constructed models have mathematical properties, e.g. consistency and completeness, and overcome the drawbacks of traditional function models, since it can show not only the static structure of resources but also the behavioral semantics of resources. The categorical notations and properties are to be expressed by a workcell example.
4131
Authors: Alexander Pavlovich Sokolov, Anton Yurievich Pershin
Abstract: In this work, a new software for computer-aided design of composite materials with predefined thermomechanical properties is presented in case of incomplete input data. The mathematical basis of underlying computational method of the properties identification is a modified method of multiscale homogenization named reversible multiscale homogenization method. The system has a modular architecture and includes software implementation of the reversible multiscale homogenization method based on a new technique of construction of software implementations of complex computational methods. The latter was named «Graph-based software engineering» (GBSE) and is based on category and graph theories. The corresponding numerical and experimental results were obtained and compared. The expediency of GBSE approach is discussed for the case of the development of complex computational methods required when solving the applied problems of the design of new heterogeneous materials.
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Authors: Hong Li, Xiao Ping Ma
Abstract: In order to solve the problem of conversion from the finer level of granularity to the coarser level of granularity, this paper proposes a formal method for Granular structure merging based on category theory. Firstly, it takes the granular structure as the granular object and the granular structure mapping as the granular morphism, then the granular object and the granular morphism compose the granular structure category. Secondly, it uses the granular morphism and the granular pushout to achieve the granular structure merging , then gets the granular structure merging algorithm (GrSM). Finally, the author illustrates the method with the concrete examples, which solves the granular structure merging issue. This method has a solid mathematical foundation and methodology, which is worth further study.
390
Authors: Hong Feng Lai, Kuang Yao Wu
Abstract: This paper proposes a categorical foundation for integrating various types of manufacturing knowledge in manufacturing systems. The composing procedures of overall system can be explained by pushout of category theory. The purpose of this paper is to resolve the issue involves in sharing and coordination for modeling knowledge application in distributed manufacturing systems. We will propose a method for modeling discrete event system. The mathematical foundation lies in assuring that the constructed models have mathematical properties, e.g. consistency and completeness, and overcome the drawbacks of traditional function models, since it can show not only the static structure but also the dynamic semantics. The categorical notations and properties are expressed by an example of flexible assembly workcell.
1218
Authors: Wei Dong Huang, Mei Rong Wu, Li Yan
Abstract: Focusing on the semantic heterogeneity existing in the representation and storage of emergency information vocabulary, the top concept of emergency plan is refined, generalized, and associated by introducing category theory. Furthermore, semantic model of emergency plan ontology is established, and field concepts are united and standardized. Based on the structure template, knowledge segments of emergency plan are categorized to mine the implied semantic relations between concepts. Finally, the understanding of a particular concept set in a specific field is analyzed by using examples.
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