Fuzzy logic and logical-mathematical argumentation in biometrical methods and inferences.

In biological sciences, logical–mathematical argumentation implies previous determination of concept biometrical unit of observation and then, using integers, argumentation of probability (relative frequency) of apperance in the given conditions, i.e. determination of the explained and unexplained (residual) variation of defined biometrical unit of observation. Therefore, if we are aware that concept and number are outcomes of a prior and rational thinking, then we consider certain correspondence between a concept and a number, defined in such a way. Particularly, in biological and, thus, agricultural sciences biometrical units of observation are mostly existing, so the determination of concept implies the abstraction of its objectiveness (concept is defined as a process of the abstaction of objectiveness). It follows that, in biometrical analysis, a number is the abstraction of quantity of biometrical unit objectiveness, previously abstracted. For such a correspondence, logic and mathematics are closely related, but not identical. However, in biometrical analyses, there is a methodological query, considering the logic of abstraction of the appointed numbers, and determination of attributive value quantity (abstracted property of biometrical units of observation). Two questions are imposed here: 1) in biometrics, a zero represents an attributive property (do not exist, is not recorded, have no characteristics etc.) and 2) abstraction and classification of quantity of attributive properties by linguistic variables (a classification of fruits by their size: small, medium–small, medium–large, large, very large etc.). It is evident that one can not draw a conclusion here by mathematization, i.e. based on the binary logic predicates, by notions like true (┬) or false (┴) [1 or 0], so principles of polyvalent (many–valued) logical systems, like fuzzy–logic, have emerged as an alternative. The objective of this research was to reconsider the question of logical–mathematical argumention in biometrical inferences in biological and agricultural sciences.