Reasoning about Data - A Rough Set Perspective

The paper contains some considerations concerning the relationship between decision rules and inference rules from the rough set theory perspective. It is shown that decision rules can be interpreted as a generalization of the modus ponens inference rule, however there is an essential difference between these two concepts. Decision rules in the rough set approach are used to describe dependencies in data, whereas modus ponens is used in general to derive conclusions from premises.

[1]  Dov M. Gabbay,et al.  Handbook of philosophical logic. Vol. 1, Elements of classicallogic , 1994 .

[2]  Andrzej Skowron.  Management of Uncertainty in AI: A Rough Set Approach , 1993, SOFTEKS Workshop on Incompleteness and Uncertainty in Information Systems.

[3]  Z. Pawlak.  Granularity of knowledge, indiscernibility and rough sets , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[4]  Andrzej Skowron,et al.  Rough Mereology , 1994, ISMIS.

[5]  Ewa Orlowska,et al.  A logic of indiscernibility relations , 1984, Symposium on Computation Theory.

[6]  E. Trillas,et al.  ON IMPLICATION AND INDISTINGUISHABILITY IN THE SETTING OF FUZZY LOGIC , 1993 .

[7]  J. Kacprzyk,et al.  Incomplete Information: Rough Set Analysis , 1997 .

[8]  Helena Rasiowa,et al.  Rough concepts logic , 1984, Symposium on Computation Theory.

[9]  Ewa Orlowska,et al.  Modal Logics in the Theory of Information Systems , 1984, Math. Log. Q..

[10]  L. Zadeh.  The role of fuzzy logic in the management of uncertainty in expert systems , 1983 .

[11]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[12]  H. Rasiowa,et al.  Approximating sets with equivalence relations , 1986, ISMIS '86.

[13]  Dimiter Vakarelov,et al.  A model logic for similarity relations in pawlak knowledge representation systems , 1991, Fundam. Informaticae.

[14]  P. Pagliani.  Rough Set Theory and Logic-Algebraic Structures , 1998 .

[15]  Philippe Smets,et al.  Fuzzy modus ponens: A new model suitable for applications in knowledge‐based systems , 1989, Int. J. Intell. Syst..

[16]  Stéphane Demri,et al.  Logical Analysis of Indiscernibility , 1998 .

[17]  Dov M. Gabbay,et al.  Elements of classical logic , 1994 .

[18]  Victor W. Marek,et al.  Approximating Sets with Equivalence Relations , 1986, Theor. Comput. Sci..

[19]  Zdzislaw Pawlak,et al.  Rough Set Theory and its Applications to Data Analysis , 1998, Cybern. Syst..

[20]  W Ziarko,et al.  On learning and evaluation of decision rules in the context of rough sets , 1986, ISMIS '86.

[21]  L. Kohout,et al.  FUZZY POWER SETS AND FUZZY IMPLICATION OPERATORS , 1980 .

[22]  Andrzej Skowron,et al.  Rough mereology: A new paradigm for approximate reasoning , 1996, Int. J. Approx. Reason..

[23]  Zdzisław Pawlak,et al.  Rough modus ponens , 1998 .