Bán István: Biomathematics - PMSB Methods in Forestry (2002)
2. The environment - 2.2. Algorithmization of a wanted phenomenon and its application in local optima
2. The environment tively, is accepted as the biomathematical definition of the natural phenomenon. The entity of the states observable by living and non-living observing systems, of interpretable projections and of deducible properties is called the entity of wanted phenomena, and one of its element is called a wanted phenomenon. Be all the possible state characteristic values of the states occurring in the nature °1, n> a2, n> a3, n’ ■■■> ai,n > where i = 1, 2, ... is the index of the state characteristic, indicator n = 1, 2, ... the index of the observed indicator. Definition: Out of all the former possible state characteristic values be the state characteristic values observed among the conditions ensured by the possibilities of the observing system: ai,m’a2,m’a3,m> m ’ where j<i,m<n. Definition. Under relation is understood the arbitrary correspondence between the state characteristic values. Among the relations between the state characteristics one has to distinguish among relations corresponding theoretically to all combinatorial possibilities between the previous state characteristics, the really existing relations, and relations conceivable among the possibilities of the observing system. Definition: Be the relations corresponding theoretically to all combinatorial possibilities among the previous state characteristics a; n: br = Rr(ai n) , r = 1, 2,... . Definition-. Be the really existing relations between the previous state characteristics a; n: bs = Rs(ai,n) . s = 1,2, ... <r. Definition: Be the relations between the previous state characteristics a,m conceivable on the basis of the observing system: bt = Rt(aj m) , t = 1, 2, ... <s. Definition: The properties of the state characteristic values and relations shown by mathematical methods are called features. Within the entity of the features deducible from the previous state characteristic values and relations, one has to distinguish among the theoretically possible all features, the really existing features and those ones which can be interpreted among the possibilities of the observing system.