Coalition and distribution in fuzzy dynamic supply chain systems

In this paper, two models of coalition and income's distribution in FSCS (fuzzy supply chain systems) are proposed based on the fuzzy set theory and fuzzy cooperative game theory. The fuzzy dynamic coalition choice's recursive equations are constructed in terms of sup-t composition of fuzzy relations, where t is a triangular norm. The existence of the fuzzy relations in FSCS is also proved. On the other hand, the approaches to ascertain the fuzzy coalition through the choice's recursive equations and distribute the fuzzy income in FSCS by the fuzzy Shapley values are also given. These models are discussed in two parts: the fuzzy dynamic coalition choice of different units in FSCS; the fuzzy income's distribution model among different participators in the same coalition. Furthermore, numerical examples are given aiming at illustrating these models., and the results show that these models are feasible and validity in FSCS.

The level and distribution of chromosomal aberration of tomato seeds at different penetration depths of carbon ions

The relationship between the penetration depth and the level and distribution of chromosomal aberration of the root tip cells were investigated by exposure of the superposed tomato seeds to 80 MeV/u carbon ions. The results showed that on the entrance of the beam the chromosomal aberration level was low. Damage such as breaks and gaps were dominant. At the Bragg peak, the chromosomal aberration level was high. The yields of dicentrics, rings and disintegrated small chromosomes increased but the yields of breaks and gaps decreased. These results are consistent with the distribution of the physical depth dose pro. le of carbon ions. It is effective to deposit the Bragg peak on the seeds to induce hereditary aberration in the mutation breeding with heavy ions.