These notes are concerned with recent developments in multivalued logic, particularly in fuzzy logic and its status as a model for human linguistic reasoning. This first section discusses the status of formal logic and the need for logics of approximate reasoning with vague data. The following sections present a hasic account of fuzzy sets theory; fuzzy logics; Zadeh's model of linguistic hedge...

In this paper we consider Description Logics (DLs), which are logics for managing structured knowledge, with a well-known fuzzy extension to deal with vague information. While for fuzzy DLs ad-hoc, tableaux-like reasoning procedures have been given in the literature, the topic of this paper is to present a reasoning preserving transformation of fuzzy DLs into classical DLs. This has the conside...

Fuzzy Description Logics (f-DLs) are extensions of classic DLs that are capable of representing and reasoning about imprecise and vague knowledge. Though reasoning algorithms for very expressive fuzzy DLs have been explored, an open issue in the fuzzy DL community is the study of tractable systems. In this paper we introduce the fuzzy extension of EL, we provide its syntax and semantics togethe...

In this contribution we carry out an analysis of the Fuzzy Reasoning Methods for Fuzzy Rule Based Classification Systems in the framework of balanced and imbalanced data-sets with different degrees of imbalance. We analyze the behaviour of the Fuzzy Rule Based Classification Systems searching for the best type of Fuzzy Reasoning Method in each case, also studying the cooperation of some pre-pro...

In this paper, advanced interval type-2 fuzzy sliding mode control (AIT2FSMC) for robot manipulator is proposed. The proposed AIT2FSMC is a combination of interval type-2 fuzzy system and sliding mode control. For resembling a feedback linearization (FL) control law, interval type-2 fuzzy system is designed. For compensating the approximation error between the FL control law and interval type-2...

For any correct argument in scientific reasoning as well as our everyday reasoning, the premises of the argument must be in some way relevant to the conclusion of that argument, and vice versa. On the other hand, in scientific reasoning as well as our everyday reasoning, many arguments may be correct to some degree, and therefore, a reasoning consisting of such fuzzy arguments is approximate. A...

Fuzzy qualitative reasoning (FQR) is a form of approximate reasoning that can be defined loosely as the fusion of Fuzzy Reasoning (FR) with Qualitative Reasoning (QR). Both these research areas have as one of their goals the construction of computational reasoning tools that can predict and explain the behaviour of, often dynamic, systems whose analytic relations are incompletely specified. Whe...

Due to the enormous success of fuzzy control, there has been a great interest in fuzzy reasoning, i.e. the formalization and application of human rule based knowledge. But when we take a closer look at the practical success of fuzzy reasoning, we nd that there are only simple rule bases involved. So far, we are not able to cope with complex fuzzy rule bases. Despite lots of theoretical investig...