A MULTICRITERIA BASED METHODOLOGICAL APPROACH FOR QUALITY CONTROL IN HISTORICAL BUILDINGS

1. A MULTICRITERIA BASED METHODOLOGICAL APPROACH FOR QUALITY CONTROL IN HISTORICAL BUILDINGS The historic preservation works demand a tight organizational structure of supervising and management, in order to increase building’s lifetime, by ensuring that incidents of future failure are avoided (preventive maintenance) (Moropoulou, Chandakas et al.). In the proposed methodology, four Decision Support Systems (DSS’s) are enrolled to asses a quality control index that will indicate whether and to which extend a building needs intervention. For assessing the value of this index for a building, values for three different groups of factors are gathered. The first group, the inspection group, includes criteria responsible for calculating the inspection index for the specific building, i.e. construction year, time and appraisals of previous inspection, building category, etc . The second group of factors involves criteria that affect the diagnosis process, including environment and pollution data, climate, etc., while  the last category, the intervention group of factors is related to parameters such as ISO existence etc .

2. The values of the aforementioned groups of factors serve as input to a multicriteria algorithm that calculates: a) significance weights for every factor, and b) an overall index in each case. Three different indices are calculated at this point, which subsequently act as parameter values for the three criteria (inspection, diagnosis and intervention) and by applying an aggregation function, a quality index is assessed. In flowchart of figure below the overall methodology is presented. All of the four DSS’s exploit the so called disaggregation – aggregation approach of Multiple Criteria Decision Analysis field.

3. In decision-making involving multiple criteria, the basic problem stated by analysts and decision-makers concerns the way that the final decision should be made. Two basic approaches under which numerous methodologies have been developed are • the bottom up approach and • the top-down approach. The first, the most trivial one, includes all methodologies and techniques that aim at building a decision model by aggregating preferential information on criteria. • This means that the criteria aggregation model is known a priori and the analyst guides the decision maker via a process of incrementally declaring preferences to construct his/ her global preference model. This approach is referred to the literature as the aggregation approach and several representatives of it include MAUT, SMART, TOPSIS, MACBETH, or AHP(Figueira, Greco et al. 2005). The second approach, can be though as a reverse process in which the final decision in know a priori and is decomposed to reveal the underlying attributes that led the decision maker to the specific decision and utilize this information to construct a value system that will be used in future decision support cases.

4. The UTA (UTilités Additives) methods are considered the most representative methods of the second approach, also known in the literature as the Disaggregation-Aggregation approach (Jacquet-Lagreze and Siskos 1982 ) or simply the Disaggregation approach. UTA methods refer to the philosophy of assessing a set of value or utility functions, assuming the axiomatic basis of MAUT and adopting the preference disaggregation principle. UTA methodology uses linear programming techniques in order to optimally infer additive value/utility functions, so that these functions are as consistent as possible with the global decision-maker’s preferences (inference principle). More details as well as a historical background on the development of the preference disaggregation philosophy can be found in the review of Jacquet-Lagreze and Siskos (Jacquet-Lagreze and Siskos 2001).

5. In the traditional aggregation paradigm, the criteria aggregation model is known a priori, while the global preference is unknown. On the contrary, the philosophy of disaggregation involves the inference of preference models from given global preferences. The Disaggregation-Aggregation approach aims at analyzing the behavior and the cognitive style of the Decision Maker (DM) (Jacquet-Lagreze and Siskos 2001). Special iterative interactive procedures are used, where the components of the problem and the DM’s global judgment policy are analyzed and then they are aggregated into a value system as shown in figure below. The goal of this approach is to aid the DM to improve his/her knowledge about the decision situation and his/her way of preferring that entails a consistent decision to be achieved.

6. In order to use global preference given data, Jacquet-Lagrèze and Siskos (Jacquet-Lagreze and Siskos 2001) note that the clarification of the DM’s global preference necessitates the use of a set of reference actions AR . • Usually, this set could be: • A set of past decision alternatives (AR: past actions), • A subset of decision actions, especially when A is large (AR⊂A), • A set of fictitious actions, consisting of performances on the criteria, which can be easily judged by the decision-maker to perform global comparisons (AR: fictitious actions). In each of the above cases, the DM is asked to express and/or confirm his/her global preferences on the set AR taking into account the performances of the reference actions on all criteria.

7. Following the Disaggregation- Aggregation methodological schema, the modeling process of level 2 must conclude to a consistent family of criteria {g1,g2,...,gk}. More details on the criterion family requirements can be also found in (Figueira, Greco et al. 2005). We briefly mention here that each criterion must be a non-decreasing, real valued function, defined on A, as follows: is the criterion evaluation scale the worst and the best level of the jth criterion respectively gj(α) is the evaluation or performance of action α on the jth criterion and g(α) is the vector of performances of action α on the k criteria. The multi-criteria data input matrix is processed by the UTA* algorithm through an iterative ordinal regression procedure. Analytical details and an illustrative example of the UTA* algorithm can be found in (Siskos, Grigoroudis et al. 2005) and (Lakiotaki, Matsatsinis et al. 2011).

8. In abstract, the UTA* algorithm, considers as input a weak-order preference structure on a set of actions, together with the performances of the alternatives on all attributes, and returns as output a set of additive value functions based on multiple criteria, in such a way that the resulting structure would be as consistent as possible with the initial structure given by the user. This is accomplished by means of special linear programming techniques. Four basic steps are followed in UTA* according to which, all the necessary parameters to estimate global value functions for each item and user are calculated.

9. The UTA* algorithm aims at estimating additive utilities of the form: subject to the following constrains: where ui(gi) i=1,…,m are non decreasing real valued functions, named marginal utility functions. Τhe UTA* algorithm may be summarized in the following steps:

10. Step 1: Express the global value of reference actions u[g(αk)], k = 1,2,...,m, first in terms of marginal values ui(gi), and then in terms of variables wij according to the formula 4.2.2-4. The transformation of the global value of reference actions into weights values expression is made according to formula:

11. Step 2: Introduce two error functions σ+ and σ- on ARi(reference set of alternatives) by writing for each pair of successive actions in the given ranking the formula: Step 3: Solve the linear program (LP):

12. Step 4 (stability analysis): Check the existence of multiple or near optimal solutions of the linear program. In case of non uniqueness, find the mean additive value function of those (near) optimal solutions which maximize the objective functions, on the polyhedron of the constraints of the LP bounded by the following constraint, where z* is the optimal value of the LP in step 3 and ε a very small positive number.

13. By applying the UTA* algorithm all the necessary parameters to estimate global utility functions U(g(α)) for each alternative are calculated. Thus, a value is assessed quantifying alternative’s utility to each user and ensuring consistency with his/ her value system. In the case of a historical building the quality control index is the actual utility function calculated as a linear combination of the three indices and their respective weights. The three indices are calculated separately as utility functions for each of the three aforementioned DSS’s.