1 Introduction Currently,all six different continents have discovered potash deposits and potash-bearing salt lake saline water.However,the distribution is extremely uneven,which is mostly concentrated in Canada,Russi...1 Introduction Currently,all six different continents have discovered potash deposits and potash-bearing salt lake saline water.However,the distribution is extremely uneven,which is mostly concentrated in Canada,Russia,Middle-Asia and展开更多
Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is propo...Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.展开更多
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, seque...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.展开更多
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...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. .展开更多
基金funded by National Program on Key Basic Research Project of China - 973 Program" Potash formation mechanism, conditions and late evolution in Ordovician ancient epicontinental sea basin, Erdos" (No. 2011CB403001)China Geological survey work Program - " Potash resources investigation and evaluation in Northern Shaanxi Ordovician Salt Basin " (No. 1212011085516)
文摘1 Introduction Currently,all six different continents have discovered potash deposits and potash-bearing salt lake saline water.However,the distribution is extremely uneven,which is mostly concentrated in Canada,Russia,Middle-Asia and
文摘Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.
文摘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.
文摘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. .
