A New Similarity Measure of Fuzzy Signatures with a Case Study Based on the Statistical Evaluation of Questionnaires Comparing the Influential Factors of Hungarian and Lithuanian Employee Engagement

Similarity between two fuzzy values, sets, etc., may be defined in various ways. The authors here attempt introducing a general similarity measure based on the direct extension of the Boolean minimal form of equivalence operation. It is further extended to hierarchically structured multicomponent fuzzy signatures. Two versions of this measure, one based on the classic min-max operations and one based on the strictly monotonic algebraic norms, are proposed for practical application. A real example from management science is chosen, namely the comparison of employee attitudes in two different populations. This example has application possibilities in the evaluation and analysis of employee behaviour in companies as, due to the complex aspects in analysing multifaceted behavioural paradigms in organizational management, it is difficult for companies to make reliable decisions in creating processes for better social interactions between employees. In the paper, the authors go through the steps of building a model for exploring a set of different features, where a statistical pre-processing step enables the identification of the interdependency and thus the setup of the fuzzy signature structure suitable to describe the partially redundant answers given to a standard questionnaire and the comparison of them with help of the (pair of the) new similarity measures. As a side result in management science, by using an internationally applied standard questionnaire for exploring the factors of employee engagement and using a sample of data obtained from Hungarian and Lithuanian firms, it was found that responses in Hungary and Lithuania were partially different, and the employee attitude was thus in general different although in some questions an unambiguous similarity could be also discovered.