It is well known that the system (1 + 1) can be unequal to 2, because this system has both observation error and system error. Furthermore, we must provide our mustered service within our cool head and warm heart, whe...It is well known that the system (1 + 1) can be unequal to 2, because this system has both observation error and system error. Furthermore, we must provide our mustered service within our cool head and warm heart, where two states of nature are existing upon us. Any system is regarded as the two-dimensional variable error model. On the other hand, we consider that the fuzziness is existing in this system. Though we can usually obtain the fuzzy number from the possibility theory, it is not fuzzy but possibility, because the possibility function is as same as the likelihood function, and we can obtain the possibility measure by the maximal likelihood method (i.e. max product method proposed by Dr. Hideo Tanaka). Therefore, Fuzzy is regarded as the only one case according to Vague, which has both some state of nature in this world and another state of nature in the other world. Here, we can consider that Type 1 Vague Event in other world can be obtained by mapping and translating from Type 1 fuzzy Event in this world. We named this estimation as Type 1 Bayes-Fuzzy Estimation. When the Vague Events were abnormal (ex. under War), we need to consider that another world could exist around other world. In this case, we call it Type 2 Bayes-Fuzzy Estimation. Where Hori et al. constructed the stochastic different equation upon Type 1 Vague Events, along with the general following probabilistic introduction method from the single regression model, multi-regression model, AR model, Markov (decision) process, to the stochastic different equation. Furthermore, we showed that the system theory approach is Possibility Markov Process, and that the making decision approach is Sequential Bayes Estimation, too. After all, Type 1 Bays-Fuzzy estimation is the special case in Bayes estimation, because the pareto solutions can exist in two stochastic different equations upon Type 2 Vague Events, after we ignore one equation each other (note that this is Type 1 case), we can obtain both its system solution and its decision solution. Here, it is noted that Type 2 Vague estimation can be applied to the shallow abnormal decision problem with possibility reserved judgement. However, it is very important problem that we can have no idea for possibility reserved judgement under the deepest abnormal envelopment (ex. under War). Expect for this deepest abnormal decision problem, Bayes estimation can completely cover fuzzy estimation. In this paper, we explain our flowing study and further research object forward to this deepest abnormal decision problem.展开更多
Let Kdenote the complete graph consisting of n vertices,every pair of which forms an edge.We want to know the least possible number of the intersections,when we draw the graph Kon the plane or on the sphere using cont...Let Kdenote the complete graph consisting of n vertices,every pair of which forms an edge.We want to know the least possible number of the intersections,when we draw the graph Kon the plane or on the sphere using continuous arcs for edges.In a paper published in 1960,Richard K.Guy conjectured that the least possible number of the intersections is 1/64(n-1)^(2)(n-3)^(2) if n is odd,or 1/64 n(n-2)^(2)(n-4)if n is even.A virgin road V_(n)is a drawing of a Hamiltonian cycle in Kconsisting of n vertices and n edges such that no other edge-representing arcs cross V.A drawing of Kis called virginal if it contains a virgin road.All drawings considered in this paper will be virginal with respect to a fixed virgin road V.We will present a certain drawing of a subgraph of K,for each n(≥5),which is"characteristic"in the sense that any minimal virginal drawing of Kcontaining this subdrawing satisfies Guy’s conjecture.展开更多
文摘It is well known that the system (1 + 1) can be unequal to 2, because this system has both observation error and system error. Furthermore, we must provide our mustered service within our cool head and warm heart, where two states of nature are existing upon us. Any system is regarded as the two-dimensional variable error model. On the other hand, we consider that the fuzziness is existing in this system. Though we can usually obtain the fuzzy number from the possibility theory, it is not fuzzy but possibility, because the possibility function is as same as the likelihood function, and we can obtain the possibility measure by the maximal likelihood method (i.e. max product method proposed by Dr. Hideo Tanaka). Therefore, Fuzzy is regarded as the only one case according to Vague, which has both some state of nature in this world and another state of nature in the other world. Here, we can consider that Type 1 Vague Event in other world can be obtained by mapping and translating from Type 1 fuzzy Event in this world. We named this estimation as Type 1 Bayes-Fuzzy Estimation. When the Vague Events were abnormal (ex. under War), we need to consider that another world could exist around other world. In this case, we call it Type 2 Bayes-Fuzzy Estimation. Where Hori et al. constructed the stochastic different equation upon Type 1 Vague Events, along with the general following probabilistic introduction method from the single regression model, multi-regression model, AR model, Markov (decision) process, to the stochastic different equation. Furthermore, we showed that the system theory approach is Possibility Markov Process, and that the making decision approach is Sequential Bayes Estimation, too. After all, Type 1 Bays-Fuzzy estimation is the special case in Bayes estimation, because the pareto solutions can exist in two stochastic different equations upon Type 2 Vague Events, after we ignore one equation each other (note that this is Type 1 case), we can obtain both its system solution and its decision solution. Here, it is noted that Type 2 Vague estimation can be applied to the shallow abnormal decision problem with possibility reserved judgement. However, it is very important problem that we can have no idea for possibility reserved judgement under the deepest abnormal envelopment (ex. under War). Expect for this deepest abnormal decision problem, Bayes estimation can completely cover fuzzy estimation. In this paper, we explain our flowing study and further research object forward to this deepest abnormal decision problem.
文摘Let Kdenote the complete graph consisting of n vertices,every pair of which forms an edge.We want to know the least possible number of the intersections,when we draw the graph Kon the plane or on the sphere using continuous arcs for edges.In a paper published in 1960,Richard K.Guy conjectured that the least possible number of the intersections is 1/64(n-1)^(2)(n-3)^(2) if n is odd,or 1/64 n(n-2)^(2)(n-4)if n is even.A virgin road V_(n)is a drawing of a Hamiltonian cycle in Kconsisting of n vertices and n edges such that no other edge-representing arcs cross V.A drawing of Kis called virginal if it contains a virgin road.All drawings considered in this paper will be virginal with respect to a fixed virgin road V.We will present a certain drawing of a subgraph of K,for each n(≥5),which is"characteristic"in the sense that any minimal virginal drawing of Kcontaining this subdrawing satisfies Guy’s conjecture.
