Structure of Rough Approximations Based on Molecular Lattices p. 69 Rough Approximations under Level Fuzzy Sets p. 78 Fuzzy-Rough Modus Ponens and Modus Tollens as a Basis for Approximate Reasoning p. 84 Logic and Rough Sets Rough Truth, Consequence, Consistency and Belief Revision p. 95 A Note on Ziarko's Variable Precision Rough Set Model and Nonmonotonic Reasoning p. 103 Fuzzy Reasoning Base...

This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp antecedents; in case of fuzzy booleans this set contains only two rules. It is shown that Zadeh's ext...

Ontologies have been employed in several applications regarding knowledge representation, aiming to represent data semantics and support reasoning tasks. However, traditional ontologies are less suitable to represent some domains that require the representation of vague or imprecise information, which often occurs in human language. In order to handle such restriction, it is necessary to extend...

We present a unified logical framework for representing and reasoning about both quantitative and qualitative preferences in fuzzy answer set programming [Saad, 2010; Saad, 2009; Subrahmanian, 1994], called fuzzy answer set optimization programs. The proposed framework is vital to allow defining quantitative preferences over the possible outcomes of qualitative preferences. We show the applicat...

This paper examines two interval based uncertain reasoning methods, one is based on interval fuzzy sets, and the other is based on rough sets. The notion of interval triangular norms is introduced. Basic issues on the use of t-norms for approximate reasoning with interval fuzzy sets are addressed. Inference rules are given for using both numeric intervals and lattice based intervals. The theory...

The success and proliferation of the Semantic Web depends heavily on construction of Web ontologies. However, classical ontology construction approaches are not sufficient for handling imprecise and uncertain information that is commonly found in many application domains. Therefore, great efforts on construction of fuzzy ontologies have been made in recent years. In this paper, we propose a for...

The most important part of a Case-Based Reasoning system is the retrieval stage, where the system must find in a sometimes-huge case base, the best matching case or cases from which to produce the prediction for the outcome of a given situation. In this paper we propose a fuzzy logic based approach for identifying cases for the similarity measuring stage of case based reasoning systems. We comb...

The successful application of fuzzy reasoning models to fuzzy control systems depends on a number of parameters, such as fuzzy membership functions, that are usually decided upon subjectively. It is shown in this paper that the performance of fuzzy control systems may be improved if the fuzzy reasoning model is supplemented by a genetic-based learning mechanism. The genetic algorithm enables us...

In the last few years, the complexity of reasoning in fuzzy description logics has been studied in depth. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy description logics using the Gödel t-norm. It was recently shown that in the logic G-IALC under witnessed model semantics, all standard reasoning problems ...