Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyz...Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.展开更多
The distribution function is an important tool in the study of the stochastic variances. The normal distribution is very popular in the nature and our society. The idea of membership functions is the foundation of the...The distribution function is an important tool in the study of the stochastic variances. The normal distribution is very popular in the nature and our society. The idea of membership functions is the foundation of the fuzzy sets theory. While the fuzzy theory is widely used, the completely certain membership function that has no any fuzziness at all has been the bottleneck of the applications of this theory. Cloud models are the effective tools in transforming between qualitative concepts and their quantitative expressions. It can represent the fuzziness and randomness and their relations of uncertain concepts. Also cloud models can show the concept granularity in multi-scale spaces by the digital characteristic Entropy (En). The normal cloud model not only broadens the form conditions of the normal distribution but also makes the normal membership function be the expectation of the random membership degree. In this paper, the universality of the normal cloud model is proved, which is more superior and easier, and can fit the fuzziness and gentleness of human cognitive processing. It would be more applicable and universal in the representation of uncertain notions.展开更多
The transition between the elastic and plastic states is sharp in the classical plasticity theory. To overcome this problem, many constitutive models, such as multi-yield-surface model and two-surface model, have been...The transition between the elastic and plastic states is sharp in the classical plasticity theory. To overcome this problem, many constitutive models, such as multi-yield-surface model and two-surface model, have been developed. However, these models can not represent the true deformation process in a material. In order to capture nonlinear hardening behavior and smooth transition from elastic to plastic state, a general model of fuzzy plasticity is developed. On the basis of the theory of fuzzy sets and TAKAGI-SUGENO fuzzy model, a fuzzy plastic model for monotonic and cyclic loadings in one dimension is established and it is generalized to six dimensions and unsymmetric cycles. The proposed model uses a set of surfaces to partition the stress space with individual plastic modulus. The plastic modulus between two adjacent surfaces is determined by a membership function. By means of a finite number of partitioning surfaces, the fuzzy plastic model can provide with a more realistic and practical description of the materials behavior than the classical plasticity model. The validity of the fuzzy plastic model is investigated by comparing the predicted and experimental stress-strain responses of steels. It was found that the fuzzy plasticity has the ability to handle many practical problems that cannot be adequately analyzed by the conventional theory of plasticity.展开更多
In this paper, a multi-item inventory model with storage space, number of orders and production cost as constraints are developed in both crisp and fuzzy environment. In most of the real world situations the cost para...In this paper, a multi-item inventory model with storage space, number of orders and production cost as constraints are developed in both crisp and fuzzy environment. In most of the real world situations the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. This model is solved with shortages and the unit cost dependent demand is assumed. Hence the cost parameters are imposed here in fuzzy environment. This model has been solved by Kuhn-Tucker conditions method. The results for the model without shortages are obtained as a particular case. The model is illustrated with numerical example.展开更多
The final diagnosis of some diseases depends on many factors and information. Considering all these factors and reviewing all of them is a difficult process, thus providing a mathematical model that can simultaneously...The final diagnosis of some diseases depends on many factors and information. Considering all these factors and reviewing all of them is a difficult process, thus providing a mathematical model that can simultaneously consider all these factors is a great help for physicians to diagnose and treat these diseases. In this paper, we propose a new fuzzy control model for kidney transplantation patients. For the inference and conclusion of this model, we use Mamdani approach. Also we employ a new method to smooth the well-known non-smooth piecewise membership functions, i.e. trapezoidal and half trapezoidal membership functions.展开更多
基金the Scientific Research and Development Project of Shandong Provincial Education Department(J06P01)the Science and Technology Fundation of University of Jinan (XKY0703).
文摘Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.
文摘The distribution function is an important tool in the study of the stochastic variances. The normal distribution is very popular in the nature and our society. The idea of membership functions is the foundation of the fuzzy sets theory. While the fuzzy theory is widely used, the completely certain membership function that has no any fuzziness at all has been the bottleneck of the applications of this theory. Cloud models are the effective tools in transforming between qualitative concepts and their quantitative expressions. It can represent the fuzziness and randomness and their relations of uncertain concepts. Also cloud models can show the concept granularity in multi-scale spaces by the digital characteristic Entropy (En). The normal cloud model not only broadens the form conditions of the normal distribution but also makes the normal membership function be the expectation of the random membership degree. In this paper, the universality of the normal cloud model is proved, which is more superior and easier, and can fit the fuzziness and gentleness of human cognitive processing. It would be more applicable and universal in the representation of uncertain notions.
基金supported by National Hi-tech Research and Development Program of China (863 Program, Grant No. 2008AA04Z407)
文摘The transition between the elastic and plastic states is sharp in the classical plasticity theory. To overcome this problem, many constitutive models, such as multi-yield-surface model and two-surface model, have been developed. However, these models can not represent the true deformation process in a material. In order to capture nonlinear hardening behavior and smooth transition from elastic to plastic state, a general model of fuzzy plasticity is developed. On the basis of the theory of fuzzy sets and TAKAGI-SUGENO fuzzy model, a fuzzy plastic model for monotonic and cyclic loadings in one dimension is established and it is generalized to six dimensions and unsymmetric cycles. The proposed model uses a set of surfaces to partition the stress space with individual plastic modulus. The plastic modulus between two adjacent surfaces is determined by a membership function. By means of a finite number of partitioning surfaces, the fuzzy plastic model can provide with a more realistic and practical description of the materials behavior than the classical plasticity model. The validity of the fuzzy plastic model is investigated by comparing the predicted and experimental stress-strain responses of steels. It was found that the fuzzy plasticity has the ability to handle many practical problems that cannot be adequately analyzed by the conventional theory of plasticity.
文摘In this paper, a multi-item inventory model with storage space, number of orders and production cost as constraints are developed in both crisp and fuzzy environment. In most of the real world situations the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. This model is solved with shortages and the unit cost dependent demand is assumed. Hence the cost parameters are imposed here in fuzzy environment. This model has been solved by Kuhn-Tucker conditions method. The results for the model without shortages are obtained as a particular case. The model is illustrated with numerical example.
文摘The final diagnosis of some diseases depends on many factors and information. Considering all these factors and reviewing all of them is a difficult process, thus providing a mathematical model that can simultaneously consider all these factors is a great help for physicians to diagnose and treat these diseases. In this paper, we propose a new fuzzy control model for kidney transplantation patients. For the inference and conclusion of this model, we use Mamdani approach. Also we employ a new method to smooth the well-known non-smooth piecewise membership functions, i.e. trapezoidal and half trapezoidal membership functions.
