Decision Support System Driven by Thermo-Complexity: Algorithms and Data Manipulation

Today, making decisions in multi-parameter contexts requires long computational times and increasingly powerful computers. In addition, we are often interested not only in the final decision to be made, but above all in the decision-making path to follow, i.e. the set of subsequent steps to reach a final goal. The originality of this work lies in the design and development of a computational engine that can be integrated into many different operational contexts, capable of providing not only decisions but also decision paths in highly complex multi-parameter environments: here the parameters take on integer values in order to be mapped with objective assessments by the operator, consisting of linguistic steps such as: low, medium-low, medium, medium-high, high. This requires the creation of a specific environment where integer-valued equations are solved, which, as is well known, significantly increases the complexity of the computational solution. After the realisation of a new methodology to connect the original space of the problem and a space with a reduced number of dimensions, in this paper we present the algorithms to build the decision path in a reduced space with a level of complexity less than that of the original space of the problem. Indeed, starting from a n-dimensional space represented by problem variables (referred to as CSF - Critical Success Factors as fixed by the expert), a dimensional embedding procedure is used to move to a two-dimensional space. In the 2-dimensional space thanks to new lattice motion algorithms, the decision support system can quickly determine the optimal solution with lower computational cost based on the decision-maker's preferences. Then, thanks to an algorithm that takes into account the hierarchical order of importance of the 7 CSFs as per the expert's liking or according to his optimization logics, the results are restored to the n-dimensional space from the 2-dimensional one and the final solution in the original space is shown. As we will see, the starting and ending states in the n-dimensional space (referred to as micro-states) when projected into the two-dimensional space generate states (referred to as macro-states) which are degenerate. In other words, the correspondence between micro-states and macro-states is not one-to-one, as multiple microstates correspond to one macro-state. As result, following the decision-maker's preferences, the DSS will provide the decision-maker with the micro-state of interest in the n-dimensional space (dimensional emergence procedure) starting from the obtained optimal macro-state. The target of the present paper is the definition and the implementation of the algorithms to obtain optimal solution in 2-dimensional space. The optimisation is realising by reducing the information disorder and by increasing the dynamics of the system subjected to DSS for studying its evolution: this is made with some specific algorithms able to suggest the state transitions of the system as movements on a discrete 2-dimensional lattice. Moreover, some specific algorithms are developed to emerge from the 2-dimensional space to n-dimensional original space, where the original semantics of the problem takes place.