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This paper presents the results concerning a space of invariants for second type almost geodesic mappings. After discussing the general formulas of invariants for mappings of symmetric affine connection spaces, based on these formulas, invariants for second type almost geodesic mappings of symmetric affine connection spaces and Riemannian spaces are obtained, as well as their mutual connection. Also, one invariant of Thomas type and two invariants of Weyl type for almost geodesic mappings of the second type were attained. [ABSTRACT FROM AUTHOR]

For the past four decades, the methodology of fuzzy analytic hierarchy process based on fuzzy trapezoidal or triangular numbers with the linear type of membership functions has witnessed an expanding development with applicability to a wide variety of areas, such as industry, environment, education, government, economics, engineering, health, and smart city leadership. On the other hand, the interval gray analytic hierarchy process is a more practical method when a significant number of professionals have large variations in preferences and interests in complex decisions. The paper examines the management of architectural heritage in smart cities, using methods of multi-criteria decision making. Two appropriate methods generally recommended by the scientific literature have been applied: fuzzy and interval grey analytic hierarchy process. By using both techniques, there is an opportunity to analyze the consensual results from the aspect of two different stakeholder groups: architectural heritage experts and smart city development experts. Trapezoidal fuzzy analytical hierarchical process shows better stability than a triangular one. Both approaches assign priority to the strategy, but the interval approach gives a more significant rank to architectural heritage factors. The similarity of the proposed methods has been tested, and the similarity factor in the ranking indicates a high degree of similarity in comparing the reference rankings. [ABSTRACT FROM AUTHOR]

With rapid economic development and restructuring, the number of old or obsolete buildings is growing in large cities. Construction practice has actively focused in recent decades on the regeneration of brownfield areas and creating opportunities for their cost-effective and sustainable reuse. Some of the buildings could be identified as-built industrial heritage whose purpose could be modified and used differently. Adaptive reuse can make a major contribution to sustainable development by reducing construction waste and saving natural resources. In the reuse management process, the problem is how to deal with multiple criteria that are imposed as factors in assessing the reuse of a building. Using the adjusted fuzzy analytical hierarchy process (FAHP), we explore the potential for the adaptation and new use of industrial buildings in the former area of Electronic Industry Nis (EI Nis) in Serbia. The standard FAHP, in which we determine the weights of each sub-criterion based on the expert's evaluation, we adjusted for use when no pairwise comparison of existing alternatives was available. Multiple criteria evaluation was performed by applying many criteria and sub-criteria, taking into account the different spatial and physical performance of buildings, as well as their locational indicators. A case study is used to demonstrate the application of the method and show its effectiveness. [ABSTRACT FROM AUTHOR]