Fuzzy logic adds to bivalent logic an important capability—a capability to reason precisely with imperfect information. Imperfect information is information which in one or more respects is imprecise, uncertain, incomplete, unreliable, vague or partially true. In fuzzy logic, results of reasoning are expected to be provably valid, or p-valid for short. Extended fuzzy logic adds an equally impor...

Our reasoning is clearly fuzzy, so why is crisp logic so often adequate? We explain this phenomenon by showing that in the presence of noise, an arbitrary continuous (e.g., fuzzy) system can be well described by its discrete analog. However, as the description gets more accurate, the continuous description becomes necessary. 1 Formulation of the Problem Fuzzy logic is needed. Our reasoning is c...

In this paper, we incorporate fuzzy reasoning in fractional-order PD controllers. The resulting fuzzy fractional PD controller is investigated in terms of its digital implementation and robustness. The combined features of both algorithms will result in a better control system performance. Also, the effectiveness and robustness of the new methodology is illustrated through an application exampl...

In this paper, we present the interval neutrosophic logics which generalizes the fuzzy logic, paraconsistent logic, intuitionistic fuzzy logic and many other non-classical and non-standard logics. We will give the formal definition of interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. Then we give one application of interval neutrosophic logics to do appr...

As a generalization of the triple I method, the universal triple Imethod is investigated from the viewpoints of both fuzzy reasoningand fuzzy controller. The universal triple I principle is putforward, which improves the previous triple I principle. Then,unified form of universal triple I method is established based onthe (0,1)-implication or R-implication. Moreover, the reversibilityproperty o...

If the given fact for an antecedent in a fuzzy production rule (FPR) does not match exactly with the antecedent of the rule, the consequent can still be drawn by technique such as fuzzy reasoning. Many existing fuzzy reasoning methods are based on Zadeh’s Compositional rule of Inference (CRI) which requires setting up a fuzzy relation between the antecedent and the consequent part. There are so...

Case-based reasoning (CBR) attempts to solve new problems by using previous experiences. However traditional CBR systems are restricted by the similarity requirement, i.e., the availability of similar cases to new problems. This paper proposes a novel CBR approach that exploits dissimilarity information in problem solving. A fuzzy dissimilarity model consisting of fuzzy rules has been developed...

Fuzzy Description Logics (DLs) generalize crisp ones by providing membership degree semantics for concepts and roles. A popular technique for reasoning in fuzzy DL ontologies is by providing a reduction to crisp DLs and then employ reasoning in the crisp DL. In this paper we adopt this approach to solve conjunctive query (CQ) answering problems for fuzzy DLs. We give reductions for Gödel, and Ł...

In this contribution we carry out an analysis of the rule weights and Fuzzy Reasoning Methods for Fuzzy Rule Based Classification Systems in the framework of imbalanced data-sets with a high imbalance degree. We analyze the behaviour of the Fuzzy Rule Based Classification Systems searching for the best configuration of rule weight and Fuzzy Reasoning Method also studying the cooperation of some...

This paper proposs a systematic methodology of fuzzy logic modeling as a generic tool for modeling of complex systems. The methodology conveys three distinct features: 1) a unified parameterized reasoning formulation; 2) an improved fuzzy clustering algorithm; and 3) an efficient strategy of selecting significant system inputs and their membership functions. The reasoning mechanism introduces f...