On the use of fuzzy inference techniques in assessment models : part I — theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules

A biophysical perspective on dispersal and the geography of evolution in marine and terrestrial systems

The fluid mechanics of marine and terrestrial systems are surprisingly similar at many spatial and temporal scales. Not surprisingly, the dispersal of organisms that float, swim or fly is influenced by the fluid environments of air and seawater. Nonetheless, it has been argued repeatedly that the geography of evolution differs fundamentally between marine and terrestrial taxa. Might this view emanate from qualitative contrasts between the pelagic ocean and terrestrial land conflated by anthropocentric perception of within- and between-realm variation? We draw on recent advances in biogeography to identify two pairs of biophysically similar marine and terrestrial settings—(i) aerial and marine microplankton and (ii) true islands and brackish seawater lakes—which have similar geographies of evolution. Commonalities at these scales, the largest and smallest biogeographic scales, delimit the geographical extents that can possibly characterize evolution in the remaining majority of species. The geographies of evolution therefore differ statistically, not fundamentally, between marine and terrestrial systems. Comparing the geography of evolution in diverse non-microplanktonic and non-island species from a biophysical perspective is an essential next step for quantifying precisely how marine and terrestrial systems differ and is an important yet under-explored avenue of macroecology