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This article discusses the usability of the Art-Risk 3.0 software for research on the conservation of heritage buildings. It is a new and free software based on fuzzy logic, which enables the assessment of preventive conservation and surveillance of the restoration of heritage buildings over a period of time. This artificial intelligence-based tool considers the vulnerability of buildings, their environments, and their management to evaluate the necessity of their restoration or preventive conservation. To validate the Art-Risk 3.0, 500 theoretical case studies were analyzed, and a 14 thcentury Mudejar-Gothic-style Church in Seville, Spain was studied both before and after its restoration to identify post-restoration changes. This proof of concept demonstrates the capability of the Art-Risk 3.0 software to analyze environmental impacts on the vulnerability, risk, and functional service life of buildings, and assess the effectiveness of restoration activities. Additionally, this software identifies the most problematic factors and the necessity of restoration.

In this work we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between the colours of its vertices. These edge colours are ordered in lexicographical increasing ordering and gives rise to a new element of the graph: the contrast vector. We introduce the notion of maximum contrast vector (in the set of contrast vectors of all possible greyscales defined on the graph) as a new invariant for the graph. The relation between finding the maximum contrast vector for the graph and its chromatic number is established. Thus the maximum contrast problem is an NP-complete problem. However, the set of values of any maximum contrast greyscale for any graph is bounded by a finite set which is given. Several methods to compute the maximum contrast vector with some restrictions are collected in this paper.The interest of these new concepts lies in their possible applications for solving problems of engineering, physics and applied mathematics which are modeled according to a network whose nodes have assigned numerical values of a certain parameter delimited by a range of real numbers. The objective is to maximize the differences between each node and its neighbors, from a local and global point of view simultaneously through a vectorial objective function, that is the contrast vector.

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