JAMM is a tool designed to solve multiple-criteria classification problems. This tool can be used in many different areas e.g. finances, medicine, geology, pharmacology and many others. The methodology that is used within JAMM is called Dominance-based Rough Set Approach (DRSA) to multicriteria classification problems, which concern an assignment of objects (actions) evaluated by a set of criteria to some pre-defined and preference-ordered decision classes DRSA extends the Classical Rough Set Approach (CRSA) proposed by Pawlak [10,11].
The input data to JAMM is a set of classification examples given by a decision maker. It constitutes a preferential information necessary to build a preference model of the decision maker. Very often in multiple-criteria decision analysis, this information has to be given in terms of preference model parameters, such as importance weights, substitution ratios and various thresholds. Presenting such information requires significant effort on the part of the decision maker. It is generally acknowledged that people often prefer to make exemplary decisions and cannot always explain them in terms of specific parameters. For this reason, the idea of inferring preference models from exemplary decisions provided by the decision maker is very attractive. Furthermore, the exemplary decisions may be inconsistent because of limited clear discrimination between criteria and because of hesitation on the part of the decision maker. These inconsistencies cannot be considered as a simple error or as noise. They can convey important information that should be taken into account in the construction of the decision makers preference model. The rough set approach is intended to deal with inconsistency and this is a major argument to support its application to multiple-criteria decision analysis. The extension of CRSA, proposed by Greco, Matarazzo and Slowinski, called the Dominance-based Rough Set Approach,enables the analysis of preference-ordered data. This extension, is mainly based on the substitution of the indiscernibility relation by a dominance relation in the lower and upper (rough) approximations of decision classes. An important consequence of this fact is the possibility of inferring (from rough approximations of unions of preference-ordered decision classes) the preference model in terms of decision rules which are logical statements of the type if conditions then decision.
The separation of certain and uncertain knowledge about the decision maker’s preferences is carried out by the distinction of different kinds of decision rules, depending upon whether they are induced from lower approximations of decision classes or from the difference between upper and lower approximations (composed of inconsistent examples). The principle of both, CRSA and DRSA, is to include in lower approximations of approximated sets only non-ambiguous objects. The analysis of large real-life data sets shows, however, that for some multiple-criteria classification problems, the application of DRSA identifies large differences between lower and upper approximations of the unions of decision classes and, moreover, rather weak decision rules, i.e., supported by few objects from lower approximations. For this reason, a variant of DRSA, called Variable Consistency Dominance-based Rough Set Approach (VC-DRSA) has been proposed [3,8,9,14]. This variant enables relaxation of the conditions for assignment of objects to lower approximationsof the unions of decision classes. In VC-DRSA, the range of the allowed ambiguity is controlled by an index called consistency level.
The model of preferences produced by JAMM in terms of decision rules is very convenient for decision support because it is intelligible and speaks the same language as the decision maker. This model explains the past decisions in terms of the circumstances in which they were made and give recommendation how to make a new classificationdecision under specific circumstances. It has several advantages over the classical models, which are a utility function and a system of binary relations:
- the decision rules do not convert ordinal information into numeric one but keep the ordinal character of input data due to the syntax proposed; in this sense, DRSA is concordant with the paradigm of computing with words which are hardly convertible to numerical scales,
- heterogeneous information (qualitative and quantitative, ordered and non-ordered) and scales of preference (ordinal, cardinal) can be processed within the DRSA, while classical methods consider only quantitative ordered evaluations with rare exceptions,
- the decision rule preference model resulting from the DRSA can represent even inconsistent preferences.
Furthermore, the equivalence of preference representation by a general non-additive and non-transitive utility function, by an outranking relation and by decision rules was proved in [7,12]. Some well known multiple-criteria aggregation procedures were represented, moreover, in terms of the decision rule model; in these cases the decision rules decompose the synthetic aggregation formula used by these procedures; the rules involve partial profiles defined for subsets of criteria plus a dominance relation on these profiles.
The algorithms for induction of decision rules implemented in JAMM use three different strategies:
- The generation of a minimal set of rules covering all objects from a data set (Minimal Cover Set of Rules).
- The generation of an exhaustive set of rules consisting of all possible rules for a data set (Complete Set of Rules).
- The generation of a set of ‘strong’ decision rules, even partly discriminant, covering relatively many objects from the decision table (but not necessarily all of them).
The set of decision rules is often called classifier and the process of obtaining a recommendation using a set of rules is called classification. JAMM provides this function and, moreover, it permits an assessment of a quality of the classifier in course of a validation test.
For more information concearning CRSA, DRSA and VC-DRSA you may consult the following references:
- Greco, S., Matarazzo, B., Slowinski, R.: The use of rough sets and fuzzy sets in MCDM. Chapter 14 [in]: T.Gal, T.Stewart, T.Hanne (eds.), Advances in Multiple Criteria Decision Making. Kluwer, 1999, pp. 14.1-14.59
- Greco, S., Matarazzo, B., Slowinski, R.: Rough sets theory for multicriteria decision analysis. European J. of Operational Research 129 (2001) 1-47
- Greco, S., Matarazzo, B., Slowinski, R., Stefanowski, J.: Variable consistency model of dominance-based rough set approach. [In]: W.Ziarko, Y.Yao (eds.): Rough Sets and Current Trends in Computing, Lecture Notes in Artificial Intelligence, vol. 2005, Springer-Verlag, Berlin, 2001, pp. 170-181
- Greco, S., Matarazzo, B., Slowinski, R.: Rough sets methodology for sorting problems in presence of multiple attributes and criteria. European J. of Operational Research 138 (2002) 247-259
- Greco, S., Matarazzo, B., Slowinski, R.: Rough approximation by dominance relations. International J. of Intelligent Systems 17 (2002) no.2, 153-171
- Greco, S., Matarazzo, B., Slowinski, R.: Multicriteria classification. [In]: W. Kloesgen, J. Zytkow (eds.), Handbook of Data Mining and Knowledge Discovery. Oxford University Press, New York, 2002, chapter 16.1.9, pp. 318-328
- Greco, S., Matarazzo, B., Slowinski, R.: Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules. European Journal of Operational Research 158 (2004) 271-292
- Greco, S., Matarazzo, B., Slowinski, R.: Dominance-Based Rough Set Approach to Knowledge Discovery (I) General Perspective. Chapter 20 [in]: N.Zhong, J.Liu, Intelligent Technologies for Information Analysis Springer-Verlag, Berlin, 2004
- Greco, S., Matarazzo, B., Slowinski, R.: Dominance-Based Rough Set Approach to Knowledge Discovery (II) Extensions and Applications. Chapter 21 [in]: N.Zhong, J.Liu, Intelligent Technologies for Information Analysis Springer-Verlag, Berlin, 2004
- Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer, 1991
- Pawlak, Z., Grzymala-Busse, J.W., Slowinski, R., Ziarko, W.: Rough sets. Communications of the ACM 38 (1995) 89-95
- Slowinski, R., Greco, S., Matarazzo, B.: Axiomatization of utility, outranking and decision-rule preference models for multiple-criteria classification problems under partial inconsistency with the dominance principle. Control and Cybernetics 31 (2002) 1005-1035
- Slowinski, R., Greco, S., Matarazzo, B.: Rough set analysis of preference-ordered data. [In]: J.J. Alpigini, J.F. Peters, A. Skowron, N. Zhong (eds.), Rough Sets and Current Trends in Computing. Springer LNAI 2475, 2002a, pp. 44-59
- Slowinski, R., Greco, S., Matarazzo, B.: Rough set based decision support. Chapter 15 [in]: E. Burke and G. Kendall (eds.), Introductory Tutorials on Optimization, Search and Decision Support Methodologies, Springer-Verlag, Boston, 2004