*4.1. Descriptive Analysis*

The sample is diverse when compared to the generic strategy: Leader in costs: 24%, Differentiation: 22%, Focus: 14%, Mixed: 29%, Doesn't know: 11%, Management profile. 60% claim to have defined their strategic objectives.

In addition, 54% state that they are a family-run business, 55% base their decisionmaking process on results, and 50% have a functional structure. Regarding decisionmaking, 84% indicate that they have a centralized system, 68% have defined their mission and/or vision, and 73% have their organizational values well defined. The analysis demonstrates that the majority of SMEs in the beliefs lever understand and have well-defined strategies, mission, vision, values, and strategic objectives. Furthermore, the diagnostics show that 69% of decision-making is based on rational and financial quantitative information. This is linked to the large number of organizational cultures that focus on results.

In retrospect, the values and answers in the boundary lever have weaker data as the majority of managers and directors who answered explained that role hierarchy does not apply in their organization. In fact, barely more than half of the sample define role profiles to their employees and take part in formalizing roles. The interactive lever highlights that the vast majority of decision-making (84%) is centralized and that slightly more than half include staff participation in the process. Similar numbers are found in the practice of benchmarking activities. Lastly, the diagnostics system could be improved by developing navigation routes and plans based on strategic maps, increasing knowledge of the results of the company, nurturing knowledge of the state of results, and developing budget and inventory systems. According to data, the latter is the most developed.

Taking into account performance, the financial field shows improvement with 64% of answers asseverating increased utility after using managemen<sup>t</sup> control tools within the last two years. In addition, 57% consider that their liquidity has improved, and less than half report improved levels of debt (lower debt levels). The non-financial performance indicates that 65% report improvement in the organizational environment after implementing managemen<sup>t</sup> control tools, while 58.2% feel that their sense of control has improved due to these applications.

By segmenting SMEs into two groups (small companies and medium-sized companies), we can appreciate the difference in the use of managemen<sup>t</sup> control tools between them. The larger a company grows, the higher the rate of use of these tools. A clear example in the beliefs lever is the important increase from 54.8% to 86% on employing strategic objectives to define strategy between small and medium-sized companies, respectively.

The interactive lever also demonstrates this difference in the section of "survey and investigate the activities of the competition", where only 58.7% of small companies do this compared to 70.3% of medium-sized companies. More interesting data pertains to the formalization of work contracts and the use of policies and procedures manuals between businesses. As observed, only 67% of small companies do this compared to 84.5% of medium-sized companies.

In the diagnostics lever the differences are very apparent in the use of costing systems (small: 56%, medium: 69%), state of results (small: 59.6%, medium: 76%), and budget (small: 68.4%, medium: 82.6%).

## *4.2. Measurement Scale*

Before proceeding with fuzzy logic analysis, it is important to determine whether the tools employed are appropriate to measure the levers of the study. This is done by proving the reliability and validity of the chosen scale. The survey's internal consistency serves to estimate reliability using Cronbach's Alpha [44], while the scale's validity is proven through factorial analysis to evaluate whether each scale measures a single concept. The KMO statistics (Kaiser–Meyer–Olkin) is applied, and for this research, the minimum value of the limits selected for the analysis to be acceptable is 0.5 [45].

Using Bartlett's test of sphericity to evaluate the presence of correlations among variables, we obtain a level that is significantly inferior to 0.05 [45]. In the case of Cronbach's Alpha, the accepted inferior limit is 0.7, and 0.6 for new scales [46]. In retrospect, as all results are satisfactory, a factorial analysis is convenient.

Hence, the "Belief" dimension's Cronbach Alpha value is 0.935, which is a higher value than the advised minimum. For the Kaiser–Meyer–Olkin (KMO) method, the investigation obtained satisfactory results of 0.764 > 0.5. Bartlett's test returns a chi-squared range (497.57, 549.95), and *p* = 0.000. This corroborates once again the recommendation of employing factorial analysis. The results return three factors; thus, it is recommended to (1) eliminate the following items: q3\_5 and q3\_11. (2) Use the remaining two factors to define two new belief variables (Strategy and Belief, Planning).

The "Interactive Control" dimension returns a Cronbach Alpha value of 0.692, which is within the acceptable limits (given that this scale is new and created specifically during this research). The KMO value is 0.596, and Bartlett's test returns a chi-squared range of (35.77, 37.56). Both results are satisfactory, and the factorial analysis identified two different factors, which makes it recommendable to eliminate item Q6\_4 and keep only one factor.

Regarding the "Boundary" dimension, the Cronbach Alpha value is 08.10 while KMO is 0.787. Bartlett's test returns a chi-squared range of (76.07, 84.08). The factorial analysis identified one factor, confirming that the scale measures one "Boundary" dimension.

The "Diagnostics" dimension has a Cronbach Alpha value of 0.882, KMO of 0.743, and Bartlett's test of chi-squared range (271.17, 299.73). Factorial analysis reveals the existence of three factors; thus, it is recommended to eliminate: q8\_6, q8\_7, and q8\_9. The other two factors are defined as 'Diagnostic-financial' (q8\_4, q8\_5, q8\_8, q8\_10, q8\_11) and 'Diagnostic-non-financial' (q8\_1, q8\_2, q8\_3).

Lastly, the "Performance" variable has a Cronbach Alpha value of 0.859 and a KMO of 0.812. Bartlett's test results give a chi-squared range of (278.92, 308.28). Factorial analysis reveals the existence of one factor, confirming that the scale measures a "Performance" dimension.

#### *4.3. Fuzzy Inference Systems and Parameterization of Membership Functions*

This research has analyzed the proposed measurement tools for evaluating the presence of levers [10]) in SMEs while defining input and output variables, Table 2. The next step is to present the fuzzy inference surfaces that are present in each managemen<sup>t</sup> control lever related to organizational performance. This is accomplished by using Fuzzy Inference Systems (FIS) with regard to their fuzzy sets and membership functions.

The proposed methodology is based on [33], where the structure stems from Mamdani's fuzzy system. The process of analysis returns a fuzzy indicator that allows us to make strategic recommendations for SMEs.

The inference mechanism output is a fuzzy output. To ensure that the output of the fuzzy system can be interpreted only by elements that process numerical information, the fuzzy output from the inference mechanism must be converted in a process called defuzzification. The output of the inference mechanism comes as a fuzzy set. A numerical value can be generated from these sets through various means, such as through Centroid (Center of Gravity), which was used in this case. The fuzzy controller employed comes from [12]. This research is elaborated through the MATLAB module and the Fuzzy Logic Toolbox, and the process was applied to all dimensions of the model in the study.

The selection of relevant fuzzy membership functions considered the extremes as trapezoidal functions as this considers them as tolerance in case an interval increases or decreases beyond the limits. For all other functions, the research used triangular functions (quad-triangular) due to their higher adaptability to the research and variables as well as increased simplicity for interpretation. Considering the different degrees of membership returned by the fuzzification process, these must be processed to generate fuzzy output.

This is achieved by the inference system, which, based on the rules, can generate the output of a fuzzy system. Fuzzy membership function of output variables, where: High improvement: [25%; 100%], Medium improvement: [50%; −50%], No improvement: [−100%; −25%]. Hence, the following analysis develops the stages demonstrated in Figure 2. As a visual example, the FIS is presented for Beliefs.

**Figure 2.** Stages of a Fuzzy Inference System.

#### 4.3.1. FIS for Beliefs

The Fuzzy Inference Systems (FIS) for Beliefs and their respective fuzzy sets (with the membership parameters) are presented as follows: After factorial analysis, the dimension was divided into: "Beliefs = Corporate pillar": q3\_1, q3\_2, q3\_3, q3\_4, q3\_8, and "Beliefs = Strategic proposal": q3\_6, q3\_7, q3\_9, q3\_10. The output variables are H1(1) and H1(2), respectively, as shown in Figures 3–6. The input and output variable membership functions are displayed in Figure 2: Parameterization of Fuzzy Sets for Beliefs.

**Figure 3.** Inference system H1(1): Fuzzy model for Beliefs-CP dimension.


**Figure 4.** Employment of Centroid Defuzzification.

**Figure 5.** Surface of Fuzzy Inference for CP\_Beliefs.

4.3.2. CP-Beliefs (Corporate Pillar) Beliefs

The CP-Beliefs lever has the following managemen<sup>t</sup> tools: definition of mission, vision, and values. FIS analysis reveals that these are used at an average level (30.4512) by SMEs, as demonstrated in Figure 3. The presence or absence of a variable affects the stability of the Beliefs lever.

Figure 3 shows the fuzzy model structure for the CP-Beliefs dimension. It is composed of five input variables (q3\_1, q3\_2, q3\_3, q3\_4, q3\_8) and an output variable H1(1).

The following, through MATLAB, considers the output variable membership function for the CP-Beliefs dimension. It is seen that the use of the lever "CP-Beliefs" has a value of "medium", highlighting the positive (30.4512). Figure 5 has two inputs and one output, which shows the output surface of the system. By default, this output was plotted with the two initial input variables.

F (x) = 30.4512. A: medium level X(Input): Q3\_1 Y(input): Q3\_2 Z(output): H1\_1

As shown in Figure 5, the relationship between input variables Q3\_1 and Q3\_2 are displayed as a large volume close to the interval 2–5, returning a result of approximately 30.45%.

For the following variables under study, Appendix A can be reviewed.

#### *4.4. Summary of Fuzzy Indicators*

Table 3 shows a summary of the fuzzy indicators obtained in this research. Observations note a considerable degree of difference between small and medium-sized companies on the presence of managemen<sup>t</sup> control tools on their administration. Small businesses have a positive ye<sup>t</sup> lower degree of presence than medium-sized companies. Both segments have weaknesses, particularly in describing role profiles, the hierarchy of roles, organizational structure, use of policies and procedure manuals, and the use of formal contracts (in general, they both hit the 'medium' level).


**Table 3.** Summary of Fuzzy Indicators, SMEs (Small and Medium-sized companies).

Source: Self-elaboration.
