An approach version of fuzzy metric spaces including an ad hoc fixed point theorem

In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen's approach spaces and the probabilistic field of Kramosil and Michalek's fuzzymetric spaces, we present a family of spaces, called fuzzy approach spaces, that are appropriate to handle, at the same time, both measure conceptions. To do that, we study the underlying metric interrelationships between the above mentioned theories, obtaining six postulates that allow us to consider such kind of spaces in a unique category. As a result, the natural way in which metric spaces can be embedded in both classes leads to a commutative categorical scheme. Each postulate is interpreted in the context of the study of the evolution of fuzzy systems. First properties of fuzzy approach spaces are introduced, including a topology. Finally, we describe a fixed point theorem in the setting of fuzzy approach spaces that can be particularized to the previous existing measure spaces.

Survey- and fishery-derived estimates of Pacific cod (Gadus macrocephalus) biomass: implications for strategies to reduce interactions between groundfish fisheries and Steller sea lions (Eumetopias jubatus)

Survey- and fishery-derived biomass estimates have indicated that the harvest indices for Pacific cod (Gadus macrocephalus) within a portion of Steller sea lion (Eumetopias jubatus) critical habitat in February and March 2001 were five to 16 times greater than the annual rate for the entire Bering Sea-Aleutian Islands stock. A bottom trawl survey yielded a cod biomass estimate of 49,032 metric tons (t) for the entire area surveyed, of which less than half (23,329 t) was located within the area used primarily by the commercial fishery, which caught 11,631 t of Pacific cod. Leslie depletion analyses of fishery data yielded biomass estimates of approximately 14,500 t (95% confidence intervals of approximately 9,000–25,000 t), which are within the 95% confidence interval on the fished area survey estimate (12,846–33,812 t). These data indicate that Leslie analyses may be useful in estimating local fish biomass and harvest indices for certain marine fisheries that are well constrained spatially and relatively short in duration (weeks). In addition, fishery effects on prey availability within the time and space scales relevant to foraging sea lions may be much greater than the effects indicated by annual harvest rates estimated from stock assessments averaged across the range of the target spec