Bán István: Selection mathematical method (2017)
A generalised new version of the Planned Method of Selection by Bán
The Planned Method of Selection generalised9 As is evident, the system presented above by way of its major definitions is based on the state characteristic values. The largest portion of information is represented by the state characteristic values themselves. The entirety of non-cumulative mathematical exploration methods preserving the state characteristic values is called direct mathematical state set analysis. For the purpose of the direct mathematical state set analysis concepts like the following had to be introduced and then used: cognisability limit ([1], p. 56; [2], p. 31; [10], p. 29); distance ([1]; [2], p. 29; [9], p. 28; [10], p. 33); monotonisation ([2], p. 33; [9], p. 30; [10], p. 33); change of state ([1], pp. 56-59); effect ([1], p. 62; [2], pp. 28-35; [7], pp. 27-32); completeness ([10], pp. 33-39); porousness ([10], pp. 33-39); wanted element ([10], pp. 40-46); optima ([10], pp. 40-53). 6 Generalisation of the wanted entity Definition 6.1: There is an advantageous principle for all state characteristic values of all state characteristics that determines the criteria of evaluation. In a PMSB task elaborated in the 1970s the user determines the advantageous principle. When interpreting this task it is again the user who, based on the advantageous principle defined by the user, decides which one is the wanted state to him. This wanted state is the optimum. This understanding of the PMSB followed from the practical problems to be solved in the 1970s. Since then, a kind of scientific revolution has taken place, examples of which can be found in virtually all fields of science. It follows from the definition of natural phenomenon and the existence of the advantageous principle that the concepts of wanted state and optimum need to be generalised ([10], pp. 42-53). Definition 6.2: Of natural phenomenon T the set of states perceivable by living and nonliving observation systems and of interpretable relations and deducible specific features, i.e. the wanted entity Cj^ is ([10], p. 42), as follows from Equation (5.2): One element of the wanted entity is the wanted element C, i.e. as given for a fixed, arbitrary subscript j, m, t, e. Theorem 6.1: Two wanted entities are equal if and only if their respective state characteristic values, relations and specific features are identical. Proof: [10], p. 42.