Initial and Stopping Condition in Possibility Principal Factor Rotation

Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as an example of its application. Since it is well known that the alternative problem leads to sequential Bayesian inference, the flow of subsequent research was to make the mapping formula multidimensional, to introduce the concept of time, and to derive a Markov (decision) process. Furthermore, we formulated stochastic differential equations to derive them [2]. This paper refers to type 2 vague events based on a second-order mapping equation. This quadratic mapping formula gives a certain rotation named as possibility principal factor rotation by transforming a non-mapping function by a relation between two mapping functions. In addition, the derivation of the Type 2 Complex Markov process and the initial and stopping conditions in this rotation are mentioned. .

Type 2 Possibility Factor Rotation in No-Data Problem

Uemura [1] discovered a mapping formula that transforms and maps the state of nature into fuzzy events with a membership function that expresses the degree of attribution. In decision theory in no-data problems, sequential Bayesian inference is an example of this mapping formula, and Hori et al. [2] made the mapping formula multidimensional, introduced the concept of time, to Markov (decision) processes in fuzzy events under ergodic conditions, and derived stochastic differential equations in fuzzy events, although in reverse. In this paper, we focus on type 2 fuzzy. First, assuming that Type 2 Fuzzy Events are transformed and mapped onto the state of nature by a quadratic mapping formula that simultaneously considers longitudinal and transverse ambiguity, the joint stochastic differential equation representing these two ambiguities can be applied to possibility principal factor analysis if the weights of the equations are orthogonal. This indicates that the type 2 fuzzy is a two-dimensional possibility multivariate error model with longitudinal and transverse directions. Also, when the weights are oblique, it is a general possibility oblique factor analysis. Therefore, an example of type 2 fuzzy system theory is the possibility factor analysis. Furthermore, we show the initial and stopping condition on possibility factor rotation, on the base of possibility theory.

A VERIFICATION ON DIVISION OF HYDROCLIMATIC AREA IN CHINA SEAS USING DIGITAL CHARACTERISTIC OF FREQUENCY DISTRIBUTION

oceanographic data files on the China Seas prepared by the National Marine Data and Information Service, SOA, China and the '30-year (1953-1982) Reports of Sea Surface Monthly Mean Temperature in the East China Sea by the Meteorological Agency, Japan,' were used to calculate the digital characteristics of frequency distribution of sea and air temperature in 153 areas in the China Seas. Principal factor analysis and fuzzy cluster ISODATA were used to divide the China hydroclimatic area into three climatic zones including ten climatic regions. It is concluded that the characteristic values derived by this method may completely show the characteristics of frequency distribution of sea and air temperature in the studied area and the final division of hydroclimatic area is fully coincident with the author's former result [2].

贵州省岩溶洼地发育的空间分布格局及控制因素

Karst depressions are common negative topographic landforms formed by the intense dissolution of soluble rocks and are widely developed in Guizhou province.In this work,an inventory of karst depressions in Guizhou was established,and a total of approximately 256,400 karst depressions were extracted and found to be spatially clustered based on multidistance spatial cluster analysis with Ripley’s K function.The kernel density(KD)can transform the position data of the depressions into a smooth trend surface,and five different depression concentration areas were established based on the KD values.The results indicated that the karst depressions are clustered and developed in the south and west of Guizhou,while some areas in the southeast,east and north have poorly developed or no clustering.Additionally,the random forest(RF)model was used to rank the importance of factors affecting the distribution of karst depressions,and the results showed that the influence of lithology on the spatial distribution of karst depressions is absolutely dominant,followed by that of fault tectonics and hydrological conditions.The research results will contribute to the resource investigation of karst depressions and provide theoretical support for resource evaluation and sustainable utilization.

Trace metals in atmospheric fine particles in one industrial urban city: Spatial variations, sources, and health implications

Trace metals in PM2.5 were measured at one industrial site and one urban site during September, 2010 in Ji＇nan, eastern China. Individual aerosol particles and PM2.5 samples were collected concurrently at both sites. Mass concentrations of eleven trace metals （i.e., Al, Ti, Cr, Mn, Fe, Ni, Cu, Zn, Sr, Ba, and Pb） and one metalloid （i.e., As） were measured by inductively coupled plasma atomic emission spectroscopy （ICP-AES）. The result shows that mass concentrations of PM2.5 （130μg/m3） and trace metals （4.03 μg/m3） at the industrial site were 1.3 times and 1.7 times higher than those at the urban site, respectively, indicating that industrial activities nearby the city can emit trace metals into the surrounding atmosphere. Fe concentrations were the highest among all the measured trace metals at both sites, with concentrations of 1.04 ixg/m 3 at the urban site and 2.41 Itg/m3 at the industrial site, respectively. In addition, Pb showed the highest enrichment factors at both sites, suggesting the emissions from anthropogenic activities existed around the city. Correlation coefficient analysis and principal component analysis revealed that Cu, Fe, Mn, Pb, and Zn were originated from vehicular traffic and industrial emissions at both sites; As, Cr, and part of Pb from coal-fired power plant; Ba and Ti from natural soil. Based on the transmission electron microscopy analysis, we found that most of the trace metals were internally mixed with secondary sulfate/organic particles. These internally mixed trace metals in the urban air may have different toxic abilities compared with externally mixed trace metals.