Under the traditional positivist methodology of the categorical value logic,the quantitative sociological analysts tend to focus on the accuracy in social measurement.People’s experience from daily life and the devel...Under the traditional positivist methodology of the categorical value logic,the quantitative sociological analysts tend to focus on the accuracy in social measurement.People’s experience from daily life and the development of fuzzy mathematics,however,has challenged this traditional approach.In this paper,the author discuss the neccssity of applying fuzzy mathematics to sociological research,analyze briefly some basic concepts in fuzzy mathematics,such as subordination measures,fuzzy set,fuzzy relations,clustering analysis,fuzzy logic and fuzzy languages,and then exemplify their application in sociological research.展开更多
[Objective] This study was to evaluate the ecological suitability of agricultural land in western Jilin Province, with the aim to provide basis for the effective application of agricultural resources and the structura...[Objective] This study was to evaluate the ecological suitability of agricultural land in western Jilin Province, with the aim to provide basis for the effective application of agricultural resources and the structural adjustment of land use. [Method] The evaluation index system was constructed based on fuzzy mathematic method according to the principles of systematic, dominant, effectiveness and feasibility; based on law of tolerance, reasonable evaluation criteria were determined according to the ecological amplitude of crops; based on GIS processing, the initial data completed the mathematical operation by using the VBA program in Excel. [Result] The area of agricultural land grade I was 5 512 km2, grade II of 25 985 km2, grade Ill of 7 907 km2, and area of land not suitable for agriculture was 6 312 km2. According to the evaluation results, the key areas for land use adjustment were Zhenlai County, Da＇an County, Tongyu County and western Changling County. The directions of land use adjustment included improving irrigation and drainage conditions, governing land salinization and conversion of cropland to forest and grassland. [Conclusion] This study provided basis for the effective application of agricultural resources and ecological environment construction in western Jilin Province.展开更多
By employing the knowledge（R-element equivalence class） in one direction S-rough sets and dual of one direction S-rough sets, the concept of knowledge law is given; the generation theorem of knowledge law, the excur...By employing the knowledge（R-element equivalence class） in one direction S-rough sets and dual of one direction S-rough sets, the concept of knowledge law is given; the generation theorem of knowledge law, the excursion theorem of knowledge law, and the attribute disturbance discernible theorem of knowledge law are proposed. Knowledge law is a new characteristic of S-rough sets.展开更多
By using the dynamic characteristic of one direction S-rough sets（one direction singular rough sets） and dual of one direction S-rough sets（dual of one direction singular rough sets）, the concepts of attribute dis...By using the dynamic characteristic of one direction S-rough sets（one direction singular rough sets） and dual of one direction S-rough sets（dual of one direction singular rough sets）, the concepts of attribute disturbance of knowledge, the attribute disturbance degree of knowledge, and the disturbance coefficient of knowledge are given. By employing these concepts, the cardinal order theorem of the attribute disturbance knowledge, the unit circle theorem of the attribute disturbance knowledge, and the discernible theorem of the attribute disturbance knowledge are presented.展开更多
The numerical characteristics of fuzzy numbers include the optimistic value, pessimistic value, expected value, and the variance. We mainly provide the calculation formulae of several numerical characteristics of fuzz...The numerical characteristics of fuzzy numbers include the optimistic value, pessimistic value, expected value, and the variance. We mainly provide the calculation formulae of several numerical characteristics of fuzzy numbers based on credibility measure. Especially, the variance of symmetric fuzzy numbers is formulated, and a super bound for the variance of fuzzy numbers is presented. Meanwhile, some conclusions relative to credibility measure, optimistic and pessimistic values are also given.展开更多
This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub latt...This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras.展开更多
In the past, the probabilities of basic events were described as triangular or trapezoidal fuzzy number that cannot characterize the common distribution of the primary events in engineering, and the fault tree analyze...In the past, the probabilities of basic events were described as triangular or trapezoidal fuzzy number that cannot characterize the common distribution of the primary events in engineering, and the fault tree analyzed by fuzzy set theory did not include repeated basic events. This paper presents a new method to analyze the fault tree by using normal fuzzy number to describe the fuzzy probability of each basic event which is more suitably used to analyze the reliability in safety systems, and then the formulae of computing the fuzzy probability of the top event of the fault tree which includes repeated events are derived. Finally, an example is given.展开更多
According to the information provided by engineer, technicians and workers,there exist four factors related to the existence of cracksat the pressing place of vehicle axletree. i. e.The rate of attenuation,the moving ...According to the information provided by engineer, technicians and workers,there exist four factors related to the existence of cracksat the pressing place of vehicle axletree. i. e.The rate of attenuation,the moving of the ware form,the width of the waveform and the height of the penetrating wave as the supersonic wave id being used to detecting cracks. To decide the possibility of crack existence (PCE),this article should firstly give the relationship between every one of the four factors and the PCE,respectively. Secondly,synthestically consider the degrees of influence of the four factors on the existence of crack,and finally determine the PCE.展开更多
The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy rand...The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy random variables and fuzzy stochastic processes etc.. But, a large part of this theory heavily depends on the condition that fuzzy number has to have compact support set and so fails to analyze and apply noncompact fuzzy numbers. The purpose of this paper is to introduce three classes of metrics on noncompact fuzzy number space and to discuss their basic properties, completeness and separability in detail.展开更多
文摘Under the traditional positivist methodology of the categorical value logic,the quantitative sociological analysts tend to focus on the accuracy in social measurement.People’s experience from daily life and the development of fuzzy mathematics,however,has challenged this traditional approach.In this paper,the author discuss the neccssity of applying fuzzy mathematics to sociological research,analyze briefly some basic concepts in fuzzy mathematics,such as subordination measures,fuzzy set,fuzzy relations,clustering analysis,fuzzy logic and fuzzy languages,and then exemplify their application in sociological research.
基金Supported by the National Natural Science Foundation of China(41072196)~~
文摘[Objective] This study was to evaluate the ecological suitability of agricultural land in western Jilin Province, with the aim to provide basis for the effective application of agricultural resources and the structural adjustment of land use. [Method] The evaluation index system was constructed based on fuzzy mathematic method according to the principles of systematic, dominant, effectiveness and feasibility; based on law of tolerance, reasonable evaluation criteria were determined according to the ecological amplitude of crops; based on GIS processing, the initial data completed the mathematical operation by using the VBA program in Excel. [Result] The area of agricultural land grade I was 5 512 km2, grade II of 25 985 km2, grade Ill of 7 907 km2, and area of land not suitable for agriculture was 6 312 km2. According to the evaluation results, the key areas for land use adjustment were Zhenlai County, Da＇an County, Tongyu County and western Changling County. The directions of land use adjustment included improving irrigation and drainage conditions, governing land salinization and conversion of cropland to forest and grassland. [Conclusion] This study provided basis for the effective application of agricultural resources and ecological environment construction in western Jilin Province.
基金Foundation item： Supported by the Nature Science Foundation of Shandong Province（Y2007H02）
文摘By employing the knowledge（R-element equivalence class） in one direction S-rough sets and dual of one direction S-rough sets, the concept of knowledge law is given; the generation theorem of knowledge law, the excursion theorem of knowledge law, and the attribute disturbance discernible theorem of knowledge law are proposed. Knowledge law is a new characteristic of S-rough sets.
基金Foundation item： Supported by the Nature Science Foundation of Shandong Province（Y2007H02）
文摘By using the dynamic characteristic of one direction S-rough sets（one direction singular rough sets） and dual of one direction S-rough sets（dual of one direction singular rough sets）, the concepts of attribute disturbance of knowledge, the attribute disturbance degree of knowledge, and the disturbance coefficient of knowledge are given. By employing these concepts, the cardinal order theorem of the attribute disturbance knowledge, the unit circle theorem of the attribute disturbance knowledge, and the discernible theorem of the attribute disturbance knowledge are presented.
文摘The numerical characteristics of fuzzy numbers include the optimistic value, pessimistic value, expected value, and the variance. We mainly provide the calculation formulae of several numerical characteristics of fuzzy numbers based on credibility measure. Especially, the variance of symmetric fuzzy numbers is formulated, and a super bound for the variance of fuzzy numbers is presented. Meanwhile, some conclusions relative to credibility measure, optimistic and pessimistic values are also given.
文摘This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras.
文摘In the past, the probabilities of basic events were described as triangular or trapezoidal fuzzy number that cannot characterize the common distribution of the primary events in engineering, and the fault tree analyzed by fuzzy set theory did not include repeated basic events. This paper presents a new method to analyze the fault tree by using normal fuzzy number to describe the fuzzy probability of each basic event which is more suitably used to analyze the reliability in safety systems, and then the formulae of computing the fuzzy probability of the top event of the fault tree which includes repeated events are derived. Finally, an example is given.
文摘According to the information provided by engineer, technicians and workers,there exist four factors related to the existence of cracksat the pressing place of vehicle axletree. i. e.The rate of attenuation,the moving of the ware form,the width of the waveform and the height of the penetrating wave as the supersonic wave id being used to detecting cracks. To decide the possibility of crack existence (PCE),this article should firstly give the relationship between every one of the four factors and the PCE,respectively. Secondly,synthestically consider the degrees of influence of the four factors on the existence of crack,and finally determine the PCE.
文摘The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy random variables and fuzzy stochastic processes etc.. But, a large part of this theory heavily depends on the condition that fuzzy number has to have compact support set and so fails to analyze and apply noncompact fuzzy numbers. The purpose of this paper is to introduce three classes of metrics on noncompact fuzzy number space and to discuss their basic properties, completeness and separability in detail.
