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Determining Rules in Fuzzy Multiple Heuristic Orderings for Constructing

In the process of examination timetable construction, the order in which exams are assigned to time slots has been shown to have a major effect on the eventual solution [6]. An assessment of how difficult it is to place a given exam into a timetable (in effect, some measure of how hard it is to satisfy the constraints relevant to the particular exam) is often used to guide the order of placement. The usual strategy is to place the most difficult exams first, on the basis that it is better to leave the easier exams until later in the process when there are fewer time slots remaining. There are many different criteria that may be used when assessing this difficulty. A common approach has been to employ graph based heuristics (a heuristic is an approximate rule or a ‘rule-of-thumb’ [5]) to provide a quantitative indication of difficulty. This measure is then used to determine the order in which the exams are assigned into the timetable and, hence, are referred to as ‘heuristic orderings’. Examples of such heuristics are the number of other exams in conflict with the given exam, the number of students enrolled on each exam, etc. For detailed descriptions of these heuristic orderings, please refer to Asmuni et al. [3]. In our previous papers [1, 3], we explored how fuzzy techniques [7] could be employed to combine multiple heuristics within the construction of examination timetables. Particularly, we proposed the use of fuzzy inference systems to combine multiple heuristics simultaneously in order to provide a measure of the difficulty of placing each exam. This measure was then used to order (rank) the exams for assignment. Various combinations of heuristics were investigated in the construction process. In order to investigate the wider applicability of this novel fuzzy approach, the techniques were also applied to the domain of course timetabling [2]. However, to date, we have only been concerned with tuning the membership functions of the fuzzy variables, utilising a set of pre-defined (and fixed) fuzzy rules. This paper presents a series of experiments which were undertaken to explore the influences of tuning the fuzzy rules in fuzzy inference systems for which the membership functions had been fixed.