Bán István: Selection mathematical method (2017)
A generalised new version of the Planned Method of Selection by Bán
26 Bán io Consequence 1: Two wanted entities differ if their state characteristic values, their relations and their specific features differ, too. Consequence 2: The optimum is the special case of the wanted entity. Definition 6.3: Of all specific features determined on the basis of the known relations Rt(aj,m) as interpreted over the values of the given state characteristics aJjm, j — 1,2,...; m — 1,2,..., the most advantageous one is called optimum and denoted by Optj,m,t,e o = {ßy,mi RtiPj.m'i Pso [a?,m, Rt (ßj,m)]} ^0 ^ (0*3) Theorem 6.2: Theorem of the optimum wanted entity ([10], p. 43): Be the state characteristic values ajtTn, j = 1, 2, ...; m = 1, 2, ... The relations where t = 1,2,..., should be existent. The specific features detected by the mathematical methods in the state characteristic values Oj,m and relations Rt(aj,m) should be Ps[aj,mi a — 1,2,... The most advantageous specific feature should be Feo[ajtm; Rt{aj,m)], e0 is fixed > 1. Statement: The optimum wanted entity Opij,m,t,eo is that of the existing wanted entities that has the most advantageous specific feature. Proof: [10], p. 44. Consequence 3: Two optima are equal if and only if their respective state characteristic values, relations and specific features are identical. Consequence f: Two optima differ if their state characteristic values, relations and specific features differ. Consequence 5: The wanted entity is not additive ([10], p. 44). Consequence 6: The optimum is not additive ([10], p. 45). Theorem 6.3: Theorem of the existence of local optima: Be the natural phenomenon T varying, and be its wanted entities CWl, Cw,2, ..., CWn. Statement: In the natural phenomenon T there exists the local optimum o\, 02, ..., on. Proof: [10], p. 48. Theorem 6.4: Theorem of the optima approximating the absolute optimum: Be the natural phenomenon T varying, and be its absolute optimum To. Statement: There exists To, a best approximating local optimum of the absolute optimum. Definitions: [10], p. 48. Proof: [10], p. 49. The definitions and features of the optimum of nature, the local optimum of nature and the absolute optimum of nature can also be found in [10], pp. 49-50. Theorem 6.5: Theorem of the existence of the local optima of nature: [10], p. 50. Theorem 6.6: Theorem of the natural local optima approximating the absolute optimum of nature: [10], p. 51.