**4. Discussion**

The result of the study is technology providing decision support for the managers of smart cities for the estimation of the competencies of experts and their selection for special or innovative tasks. For this purpose, a fuzzy model for assessing the competencies of specialists, a hybrid fuzzy model, and a neuro-fuzzy network were developed. The models are able to assess the levels of competencies of specialists and derive their ranking based on many subjects of managemen<sup>t</sup> (specialists) of a subject area in the system of a smart city, information models of criteria (groups of criteria) for assessing the competencies of specialists that take into account human impact on the controllability of the smart city system, and a kind of competency assessment model. At the same time, the tools of intellectual analysis of knowledge, a system approach, processing of fuzzy data, and a neuro-fuzzy network are used. The models developed in the work reveal the vagueness of the input estimates and increase the degree of validity of further managemen<sup>t</sup> decisions by the managers of the municipality regarding the selection of specialists to perform innovative tasks. The output of the models is an assessment of the competencies of specialists and their rating.

Depending on the requirements for the choice of specialists, information methods are proposed that allow to obtain a set of input data for the work of the developed models, namely evaluation of ways of thinking; assessment of theoretical knowledge; assessment of practical knowledge; assessment of knowledge in the theory of pedagogy, psychology and communicative competence; and assessment of narrowly specialized skills. For the proposed information methods, it is necessary to define a set of evaluation criteria for specialists, which will allow assessing their competencies depending on the tasks assigned to them.

The paper proposes an information model for evaluation and selection of an expert group as members of the Transport and Construction Commission. Innovative software support in the form of a web platform has been constructed, which implements the developed methods, algorithms, and information models for application by smart city managers in the evaluation and selection of specialists. The toolkit allows smart city analysts to change decision-making levels, synaptic weights, and the degree of suitability of the specialist to perform tasks in the context of reasoning by municipal managers and to set different sets of criteria for evaluating specialists within the proposed information methods. All of this allows for maximizing the adaptation process and supports decision-making for specific professionals within the functioning of the smart city system. In addition, the study was tested on the example of the evaluation of experts for smart city and green transportation and mobility as members of the Transport and Construction Commission of the city of Košice, using a neuro-fuzzy network.

The advantages of technology to support decision-making by smart city managers in the selection of specialists (management entities) stem from the advantages of the developed models in particular. The model of assessing the competence of specialists is based on different methods of competence assessment of specialists, which uses not only the skills of specialists but also different qualitative properties, and can be used for different inputs and different methods of competencies and criteria, taking into account the wishes of the manager and importance assessment competency methods. The advantage of the fuzzy hybrid model is its ability to take into account the own opinions of municipal managers regarding the specialists in question—if necessary, taking into account other additional indicators. The advantages of a neuro-fuzzy assessment network are the objectivity of expert assessments using input linguistic variables and the "coefficient of confidence" of the specialist's reasoning regarding their assignment; it is based on a neuro-fuzzy network, which has the ability to change the settings of synaptic scales; upon receipt of experimental data, it is possible to conduct training of the neural network.

The disadvantages of this technology for supporting decision-making include the fact that it is necessary to adequately select membership functions for the criteria of competency models. The membership function in a fuzzy network corresponds to the stage of rough debugging, and this process depends on the partitioning of the interval [*a*1; *<sup>a</sup>*5], which requires the sampling of reliable experimental data. Additionally, the use of different types of convolutions can lead to ambiguity of the final results.

The mathematical substantiation of the models has already been described in more detail by the authors in [24,25,37,38]. Determining the effectiveness of the developed models *M*1—fuzzy model, for assessment of the competence of specialists, and *M*2—hybrid fuzzy model, was performed by the number of comparison operations. The number of operations of comparison of alternatives decreases, in comparison with methods using the technology of pairwise comparisons (analytic hierarchy process), by 100\*(n − 3)/(n − 1) percent or in (n − 1)/2 times (n—number of evaluation specialists) [22,23]. Thus, at n = 4 by 33.3%, at n = 5 by 50%, at n = 11 by 80%, etc.

The proposed model *M*3—neuro-fuzzy network was tested for different data sets [24,25] and compared with known, widely used artificial neural networks and teaching methods, forming a knowledge base by generating new production rules that do not contradict the rules of the knowledge base of the system, based on the analysis of experimental data. The method of teaching corresponds to a simplified method of fuzzy inference, but it differs in that the knowledge base is not fixed, but supplemented by the receipt of experimental data [24]. The consistency of the new production rule is guaranteed by the procedure of replenishment of the knowledge base.

The rationality of the research results is proved by the advantages of the developed technology. The reliability of the obtained results is ensured by the correct use of the apparatus of fuzzy sets, system approach, and neural-fuzzy networks, which is confirmed by the research results.
