In the context of environmental, social, political, and other circumstances, people make three sorts of judgements to indicate importance, preference, or likelihood and use them to pick the best among choices. They make these decisions based on recalled information or analysis of advantages, costs, and dangers. We can occasionally construct standards of excellence and poorness based on prior information and use them to rank the choices one by one. This is important in instances when established norms must be followed, such as student admissions and wage increases. Without standards, one compares rather than rates options. Comparisons must be consistent within a reasonable range. The rating and comparison procedures are both included in the analytic hierarchy process (AHP). To decide the optimum choice, rationality necessitates the creation of a trustworthy hierarchic structure or feedback network that contains criteria of many forms of impact, stakeholders, and decision alternatives [8].

The AHP technique was applied by Saaty and other writers in a wide range of human activity areas, including planning, business, education, health-care, and so on, but especially in management. In this work, we present two additional proofs for the well-known assertion that for the eigenvector problem Aw = w, the maximal eigenvalue, max, equals n. the solution vector w that represents the probability components of discontinuous occurrences, and the consistent matrix of pairwise comparisons of type n × n (n ≥ 2) We also provide an approach for determining the eigenvalue issue solution Aw = nw, as well as a flowchart to go with it. It is simple to design and apply the algorithm for arbitrary consistent matrix A.

Author(s) Details:

Miron Pavlus,
Faculty of Management, University of Prešov, Konštantínova 16, 080 01 Prešov, Slovakia.

Rostislav Tomeš,
University College of Business in Prague, Spálená 14, 110 00 Prague, Czech Republic.

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