Modification of AHP to improve the accuracy of measurements in the method of effective projects selection and other fields of science

The author continues the series of publications in the field of development of the previously formulated (Parts 1 and 2) core and two fundamental provisions in the methodology of selecting effective projects through different solutions of AHP modification for financial and mathematical science. In the article, the author pays special attention to improving the accuracy of measurements of matrix, normalized and vector estimates for the development of AHP universal properties using the following solutions with different qualities of scientific novelty: introduction of new formulas for calculating matrix estimates with detailed instructions for their application; proposals of nine different combinations of AHP, each of them including four classifiers (AHPMS-M1.N, AHPMS(AM) - M1.N, FAHPMS-M1.N and AHPDD-M1.N) on the basis of integer and fractional 9-point scale T. Saati; description of solutions to the problems of measuring matrix estimates formed by non-standard measured elements of the matrix. The prospects of applying modifications of AHP of the first generation are described based on fractional numeric scales, where there is a new scientific category for the methods of selection of effective projects and other fields of science: “Super Challenge”, “Super Matrix”; “Super Hierarchy”; “Super Array Data”. There is also a classifier - AHPMS(AM)-M1.N, which allows you to work with matrix elements that are indifferent to natural dimensions, but sensitive to artificial dimensions. In its turn, the classifier AHPDD-M1.N allows you to work with deterministic data and completely exclude the expert component from the study. These solutions are developed as a result of the analysis of the fundamental and historical representation of the scale of measurement of expert judgments in AHP over the past 40 years and other properties/characteristics of AHP. In conclusion, the horizons for further research on modification of AHP of the first and second generation are defined.