This cross-sectional and modeling study was conducted in 2019 among five oil platforms located in the Persian Gulf in southern Iran. The statistical population consisted of 564 workers in five oil platforms. The sample size was determined by applying the Cochran formula with a margin of error of 0.04 equal to 291 employees. They were selected by systematic random sampling from the staff of five oil platforms. Finally, according to the response rate and elimination of incomplete and confusing questionnaires, 280 workers were studied (response rate was 96%). Before conducting the study and completing the questionnaires and checklists, the necessary coordination was done and sufficient information was provided to the participants. Inclusion criteria were having at least one year of work experience and exclusion criteria were also defined as lack of enough consent to participate in the study. employees were allowed to withdraw from the study at any stage if they did not have consent.
Data collection tools
Leadership style measurement
Multifactor leadership questionnaire (MLQ) designed by Bass and Avolio in 1977 was used to measure leadership style. This questionnaire evaluates three different leadership styles: transformational, transactional (exchange), and passive-avoidant. It allows individuals to measure how they perceive themselves with regard to specific leadership behaviors, but the heart of the MLQ comes in the rater/other feedback that is enabled with the rater form. The MLQ was designed with the 360-degree feedback method. Participants are asked to respond to 45 items in the MLQ 5x-Short (the current, classic version) using a five-point behavioral scale (“Not at all” to “Frequently if not always”).21
Safety climate measurement
To measure safety climate, a standard questionnaire of occupational safety climate with 37 questions including 8 components (management commitment for safety and priority of safety matters (10 questions), the knowledge of the workers and following safety rules (7 questions), the attitude of the workers regarding safety (4 questions), cooperation of the workers and commitment to following safety (5 questions), safety of workplace (4 questions), priority of safety over products (2 questions), and neglecting dangers (2 questions) were used. Scoring was performed on a five-point Likert scale (1 = strongly disagree, 2 = disagree, 3 = no idea, 4 = agree, 5 = strongly agree). The validity and reliability of this questionnaire have been confirmed in previous studies.22,23
Matching variables measurement tools
Since the number of factors in leadership style and safety climate questionnaires are different for various dimensions, and in order to uniformed expression and facilitate comparison of different dimensions of leadership style and safety climate in oil platforms, fuzzy scaling was used to eliminate the effect of the number of questions. The fuzzy scaling formula is as follows:
Where Fi is a questionnaire rating for answering the number i, which ranges from zero to one, ij is the score of the question j according to Likert scale, r is the number of items and n is equal to the sample size (number of respondents). For example, in the safety climate questionnaire, the dimension of management commitment for safety and priority of safety matters has 10 questions and the neglecting dangers dimension has 2 questions. Given that the sum of the scores for each dimension is calculated on a Likert basis, naturally, the dimension with the fewer questions receives the lower percentage of points compared to the part with the more questions. So by fuzzy scaling, the effect of the number of questions omitted and the score of each dimension will be calculated from zero to 100.
Unsafe behaviors measurement
Direct observation was used to record unsafe behaviors while workers performing the task. For this purpose, a checklist of unsafe behaviors was prepared based on the risk factors of accidents and near-miss that have taken place on the oil platforms over the past 10 years and then approved by experts and university professors to gain the capability for using as a tool for measuring unsafe behaviors. The checklist consisted of 15 questions and was completed by 10 certified safety experts who worked on five oil platforms. In this step, each worker was being monitored in an intangible way for 30 to 45 minutes to record their unsafe behaviors during working time. The range of unsafe behavior score was between 0 and 100%.
In the present study, descriptive statistics such as mean, standard deviation and frequency were presented. Kolmogorov-Smirnov statistical test was used to evaluate the normality/non-normality of the data distribution. By confirming the normality of the data distribution (P-value> 0.05), data were analyzed using One-way analysis of variance (ANOVA) and Pearson's correlation coefficient. All tests were performed at the significant level of 0.05 and the data were analyzed by SPSS software version 25.
Design of fuzzy logarithmic model
In this study, based on research literature and fuzzy sets, fuzzy inference system was designed to evaluate safety performance based on organizational factors. In the present study, the triangular function was used for fuzzy modeling. The fuzzy inference method was used by the Mamdani method. All mathematical operations were performed in MATLAB software (version 2018a). After model development and assurance of model accuracy, the developed system was used for a case study to evaluate safety performance. Initially, input and output variables were determined. According to the calculations performed in the previous steps in SPSS software, only the components that had a significant relationship with the occurrence of unsafe behaviors and were statistically significant (accounted for the highest frequency) were considered as input variables in MATLAB software. After obtaining the statistical information, the dominant dimensions of organizational leadership style and occupational safety climate were considered as system inputs and unsafe behaviors were identified as the only dependent variable and system output. Figure 1 shows a schematic view of how the fuzzy inference system works in this study.
The fuzzy logic system is actually the path and rules for studying the output variable changes according to input variable changes. This logic expresses the degree of membership of each variable in a set. Formula 1 illustrates how to investigate the triangular variable in fuzzy logic.
Figure 2 also shows an image of a triangular function.
Fuzzification of input and output variables
Fuzzification is a step to determine the degree to which an input data belongs to each of the appropriate fuzzy sets via the membership functions. Using the data collected from the statistical sample of research in each dimensions of leadership style, safety climate and unsafe behaviors, significant components of leadership style (transformational and transactional leadership) and safety climate (neglecting danger and safety of workplace) were considered as input variables. Each of the variables was placed in fuzzy intervals with appropriate distances.
The inference rules (fuzzy inference system) were formulated considering four input variables, each of variables is divided into three linguistic variables. In an ideal condition 81 (four 3× 3 matrices) law can be explained. After preparation, the fuzzy inference system was approved by academic professors and experts and then entered into the inference system.