First submission

The language of the journal is English, while it is inevitable that many authors will have English as their second or even third language. In such circumstances, when writing the paper, ask colleagues to comment on grammar, meaning and expressions. Use a spell checker on the manuscript before submitting. Carefully proofread the paper and cull mathematical misprints. Make sure that symbols are not used in several different meanings.

Don't invent notation if there is already a standard, lucid and accepted one already in existence. Try for simplicity and elegance in notation. Good notation is not only easier to read, it improves mathematical intuition and makes it easier to discover and prove results.

Do a thorough literature search and make sure that you are neither reinventing the wheel nor missing important results that would assist the depth and extent of your paper.

Good Pure Mathematics does not exist in a vacuum. Rather, it is often inspired by practical problems, perhaps by natural concepts, and usually relates to other areas. Try and address these precepts: don't just take a crisp concept and fuzzify it unless it is important in fuzzy applications or relates to existing fuzzy areas. Perhaps the easiest heuristic methodology here is to have a cohort of examples before you set about defining concepts and proving results.

Avoid e-papers: don't make trivial generalizations of existing results, nor introduce minuscule changes in the conditions of already extant theorems. Referees are not fools - they can see that the change is small, the techniques identical, the contribution an insignificant advance and become critical to the point of rejection.

If you have had a good idea going in a crisp field and produced a fruitful industry, please don't fuzzify it in a sham way, hoping to get the same thing going in fuzzy mathematics. Any fuzzification not only has to be genuine and usefully applicable to fuzzy mathematics, there also has to be some motivation dealing with vagueness or imprecision for it to be meaningful in the field.

Use simple ideas which relate to natural and intuitive concepts. Often, the same definitions can be formulated in a number of ways and the strictest, most formal, is not necessarily any more rigorous than the others. One example concerns the pleasant properties of the sup-inf form of the Extension Principle, uppersemicontinuity and fuzzy convexity. Taken together, these are equivalent to working with compact convex sets, and geometric intuition and ideas have been very successfully applied in this field. Again, the recent introduction of fuzzy lines and fuzzy Euclidean Geometry can be described in terms of translates of level sets of a ``fuzzy point'' in Rⁿ and related concepts, without using the Extension Principle.