Global Journal of Management and Business Research, A: Administration and Management, Volume 23 Issue 10

From the comparison matrix, the priority vector is calculated using the eigenvector method. With the eigenvector w of the matrix , = , considering that is the maximum eigenvector of the A matrix, it is possible to estimate the priority of the criteria (Saaty, 1994). It is also necessary to calculate the consistency rate ( CR ) that aims to capture whether decision-makers were consistent in their opinions, through the equation: CR= CI RI (1) where is the consistency index and is the random index. and values depend on the number of criteria ( n ). The is calculated by using the formula: = λ− −1 (2) where is the average value of the consistency vector. For comparisons to be consistent, the CR value must be less than 0.1 (Saaty, 1994). In order to calculate the weighting of a series of criteria weights base on more than one decision-maker, the method of entropy of Zeleny (1976) is used. The entropy method is considered a measure of the uncertainty of the information, where the first step consists of normalized the decision matrix through the equations: = � � (3) = ∑ =1 (4) where represents the normalized performance of the alternative ( = 1, … , ) in relation to the criterion ( = 1, … , ) . After the normalization process, the following equations are used: = − ∑ =1 � � (5) = 1/ ( ) (6) = 1 − (7) = ∑ =1 (8) where means the entropy of the set of alternatives for the criterion ; means the degree of diversification of the information provided by the results of the criterion ; and is the weight of the criterion . ii. Fuzzy-TOPSIS Method After defining the capacity weights, the Aragão methodology (2020) is used to generate a synthetic indicator that makes it possible to measure the maturity level of the model. Aragão's (2020) proposes the use of the so- called “evaluation alternatives”, being the basis to compose a synthetic indicator, which determines the level of final maturity. The evaluation alternatives are: (i) the Utopian alternative ( + ) , with the data considered ideal for the highest level of maturity; (ii) the Reference alternative ( ), with the data obtained from a maturity reference to the user (sector, processes, department, etc.) for possible comparison with the data from where the model will be applied (sector, process, department, etc.); and the Real Alternative ( A ), which is the data where the model will be applied (sector, process, department, etc.); and the alternative Limit ( 0 ) which has the minimum values among the main references. From these definitions, the evaluation alternatives of this study are composed by the variables: Utopian DIPAT alternative Limit ( 0 ) was not used in this study, as we chose to use only the values of the Utopian alternative ( + ) to calculate the priorities for applying improvements. Aragão (2020) used the TOPSIS method to generate a synthetic indicator. In this study, the method was changed to Fuzzy-TOPSIS, since the proposed maturity model has only qualitative variables. The Fuzzy methodology allows the transformation of qualitative variables into numerical variables. The Fuzzy-TOPSIS method was created by Chen (2000) and consists of a version of the TOPSIS method to be used when the decision-maker needs to use linguistic values based on a scale. The Fuzzy-TOPSIS method was created by Chen (2000) and consists of a version of the TOPSIS method to be used when the decision-maker needs to use linguistic values based on a scale. The metho- dology allows the decision-maker to identify the best alternatives concerning its approximation with the positive ideal solution (PIS) and greater distance from the negative ideal solution (NIS). Here, the maturity model is applied to the evaluation alternatives Reference DIPAT ( ), Real DIPAT ( A ), and Utopian DIPAT ( + ) . The Utopian DIPAT is the ideal DIPAT, that is, the best possible alternative. Subsequently, the decision matrix must be filled by the decision-maker, who chooses a linguist variable for each criterion. This linguistic variable is used to represents the importance of the criteria and the classifications of the alternatives regarding the qualitative criteria. All linguistic variable option is expressed by positive trapezoidal fuzzy numbers, where the weight of the importance of each criterion is attributed directly or indirectly using the paired comparison (CHEN; LIN; HUANG, 2006; COOK, 1992), as expressed in Table III (Chen, 2000). Innovative Multicriteria Approach to Business Process Management Maturity in the Public Sector Global Journal of Management and Business Research ( A ) XXIII Issue X Version I Year 2023 58 © 2023 Global Journals ( + ) ; Reference DIPAT ( ) and Real DIPAT ( A ). The