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

Tabela III: Linguistic Variables Linguistic Variables Fuzzy Numbers ( , , , ) Verylow(VL) (0,0,1,2) low(L) (1,2,2,3) Mediumlow(ML) (2,3,4,5) Medium(M) (4,5,5,6) Medium high (MH) (5,6,7,8) high (H) (7,8,8,9) Very high (VH) (8,9,10,10) Therefore, the decision matrix is building by transforming linguistic variables into fuzzy trapezoidal numbers, using Table III as a reference. When there is more than one decision-maker, everyone should build their decision matrix, and a simple arithmetic average should be applied to obtain a single fuzzy result for each criterion, base on Tan et al. (2010) methodology. Subsequently, the next step consists of determining the maximum numerical variable ( ∗ ) of the evaluation alternatives for each factor through the equation: ∗ = (9) The numerical decision matrix is normalized to obtain the matrix with fuzzy data through the equation: ̃ = � ∗ , ∗ , ∗ , ∗ � (10) The normalization method mentioned above is designed to preserve the property in which the elements ̃ , ∀ i,jare standardized (normalized) trapezoidal fuzzy numbers(Chen et al. , 2006).Then, considering the different importance of each criterion evaluated, the normalized fuzzy matrix should be weighted using the equations: � = �̃ � (11) � =̃ (. )� (12) In the sequence, the next step in the TOPSIS method consists of calculating the positive ideal solution (A*) and negative ideal (A ˉ ) for each criterion. In this study, the positive ideal solution is the maximum weight, considering that the ideal scenario is to reach the highest score of each criterion; and the negative ideal solution is 0 since the un-ideal scenario is the minimum score. Then it is necessary to calculate the distance between each alternative from the positive ideal solution ( ∗ ) and the negative ideal solution ( − ), through the equations: ∗ = ∑ =1 � � , � ∗ � (13) − = ∑ =1 � � , � − � (14) where (. , . ) is the distance measured between the two fuzzy numbers (Chen et al. , 2006). With the values of the distances of each alternative, the proximity coefficient ( ) can be calculated. The The CCI determines the classification order of all alternatives, representing the distances from A* and A ˉ simultaneously, bringing relative proximity to the positive ideal fuzzy solution. It is calculated by the equation: = − ∗ + − (15) It is observed that = 1 if = ∗ and = 0 if = − . In other words, = 1 when the alternative is closer to A* and further away from A ˉ . Thus, once the set of alternatives is classified, it is possible to select the best among a set of viable alternatives (Chen et al. , 2006). Base on this result, the maturity level can be calculated using the synthetic indicator proposed by Aragão (2020), through the equation: = + (16) where is the valeuof the alternative to be evaluated (Reference DIPAT and Real DIPAT), and + is the of the Utopian alternative. From the synthetic indicator, it is possible to determine the maturity level (Table II). Table IV shows the values of each maturity level base on the methodology proposed by Aragão (2020). Table IV: Maturity Level Values Level Values Qualitative Evaluation 5 > 0,90 Optimized 4 0,90 - 0,75 Managed 3 0,75 – 0,50 Defined 2 0,50 – 0,25 Repetitive 1 < 0,25 Initial 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 59 © 2023 Global Journals