The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy imp...The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.展开更多
Phosphorus is an essential element in agricultural production and chemical industry. However, since the risk of casualties and economic loss by mining accidents, the application of clean and safe production in phospho...Phosphorus is an essential element in agricultural production and chemical industry. However, since the risk of casualties and economic loss by mining accidents, the application of clean and safe production in phosphorus mines encounters great challenges. For this purpose, a man-machine-environment system composed of evaluation indexes was established, and the grading standards of indexes were defined. Firstly, the measurements of 39 qualitative indexes were obtained through the survey data. According to the measured values of 31 quantitative indexes, the measurements of quantitative indexes were calculated by linear measurement function(LM) and other three functions. Then the singleindex measurement evaluation matrixes were established. Secondly, the entropy weight method was used to determine the weights of each index directly. The analytic hierarchy process(AHP) was also applied to calculate the weights of index and index factor hierarchies after the established hierarchical model. The weights of system hierarchies were given by the grid-based fuzzy Borda method(GFB). The comprehensive weights were determined by the combination method of AHP and GFB(CAG). Furthermore, the multi-index comprehensive measurement evaluation vectors were obtained.Thirdly, the vectors were evaluated by the credible degree recognition(CDR) and the maximum membership(TMM)criteria. Based on the above functions, methods, and criteria, 16 combination evaluation methods were recommended.Finally, the clean and safe production grade of Kaiyang phosphate mine in China was evaluated. The results show that the LM-CAG-CDR is the most reasonable method, which can not only determine the clean and safe production grade of phosphorus mines, but also improve the development level of clean and safe mining of phosphorus mines for guidance.In addition, some beneficial suggestions and measures were also proposed to advance the clean and safe production grade of Kaiyang phosphorus mine.展开更多
Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the...Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the design variables as independent optimization variables. However, at each iteration of the conventional optimization procedure, multidisciplinary analysis (MDA) is numerously performed that results in extreme expense and low optimization efficiency. The intrinsic weakness of MDF is due to the times that it loop fixed-point iterations in MDA, which drive us to improve MDF by building inexpensive approximations as surrogates for expensive MDA. An simple example is presented to demonstrate the usefulness of the improved MDF. Results show that a significant reduction in the number of multidisciplinary analysis required for optimization is obtained as compared with original MDF and the efficiency of optimization is increased.展开更多
基金supported by the National Natural Science Foundation of China(60774100)the Natural Science Foundation of Shandong Province of China(Y2007A15)
文摘The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.
基金Project(51974362) supported by the National Natural Science Foundation of ChinaProject(2282020cxqd055) supported by the Fundamental Research Funds for the Central Universities,ChinaProject(2021-QYC-10050-25631) supported by the Department of Emergency Management of Hunan Province,China。
文摘Phosphorus is an essential element in agricultural production and chemical industry. However, since the risk of casualties and economic loss by mining accidents, the application of clean and safe production in phosphorus mines encounters great challenges. For this purpose, a man-machine-environment system composed of evaluation indexes was established, and the grading standards of indexes were defined. Firstly, the measurements of 39 qualitative indexes were obtained through the survey data. According to the measured values of 31 quantitative indexes, the measurements of quantitative indexes were calculated by linear measurement function(LM) and other three functions. Then the singleindex measurement evaluation matrixes were established. Secondly, the entropy weight method was used to determine the weights of each index directly. The analytic hierarchy process(AHP) was also applied to calculate the weights of index and index factor hierarchies after the established hierarchical model. The weights of system hierarchies were given by the grid-based fuzzy Borda method(GFB). The comprehensive weights were determined by the combination method of AHP and GFB(CAG). Furthermore, the multi-index comprehensive measurement evaluation vectors were obtained.Thirdly, the vectors were evaluated by the credible degree recognition(CDR) and the maximum membership(TMM)criteria. Based on the above functions, methods, and criteria, 16 combination evaluation methods were recommended.Finally, the clean and safe production grade of Kaiyang phosphate mine in China was evaluated. The results show that the LM-CAG-CDR is the most reasonable method, which can not only determine the clean and safe production grade of phosphorus mines, but also improve the development level of clean and safe mining of phosphorus mines for guidance.In addition, some beneficial suggestions and measures were also proposed to advance the clean and safe production grade of Kaiyang phosphorus mine.
文摘Multidisciplinary feasible method (MDF) is conventional method to multidisciplinary optimization (MDO) and well-understood by users. It reduces the dimensions of the multidisciplinary optimization problem by using the design variables as independent optimization variables. However, at each iteration of the conventional optimization procedure, multidisciplinary analysis (MDA) is numerously performed that results in extreme expense and low optimization efficiency. The intrinsic weakness of MDF is due to the times that it loop fixed-point iterations in MDA, which drive us to improve MDF by building inexpensive approximations as surrogates for expensive MDA. An simple example is presented to demonstrate the usefulness of the improved MDF. Results show that a significant reduction in the number of multidisciplinary analysis required for optimization is obtained as compared with original MDF and the efficiency of optimization is increased.
