Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0, 1]. The logic is known to be axiomatizable, but no deduction system amenable to prooftheoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work o...

An important notion of inconsistency occurring in the theory of IF-THEN rules is discussed. We propose a definition of it in the frame of fuzzy logic deduction and show some properties.

This paper presents a new approach to show the validity of the chaining syllogism for fuzzy IF-THEN rules and rule bases. Based on this approach new conditions are given on which the deduction scheme holds.

In this paper, an Integrated C-Object Tool, namely ICOT, is proposed for knowledge-based programming. A major drawback of current rule-based expert system languages is that they have difficulty in handling composite objects as a unit of inference. An object-oriented model is a powerful alternative to complement the drawback. Each of these alone cannot capture all the semantics of knowledge, par...

In accordance with Tarski point of view, in this chapter the theory of closure operators is proposed as a unifying tool for fuzzy logics. Indeed, let F be the set of formulas of a given language. Then an abstract fuzzy logic is defined by a fuzzy semantics (i.e. a class of valuations of the formulas in F) and by a closure operator in the lattice of the fuzzy subsets of F (we call deduction oper...

This paper proposes a new fuzzy approach for automatic segmentation of normal and pathological brain MRI volumetric data sets. MRI is generally useful for brain tumor deduction because it provide more detailed information about its type, position, size. Brain tumor segmentation is the separation of different tumor tissues from normal brain tissue. In automatic brain segmentation MRI is a sophis...

When applying rules induced from training examples to a test example, there are three possible cases which demand different actions: (1) no match, (2) single match, and (3) multiple match. Existing techniques for dealing with the fist and third cases are exclusively based on probability estimation. However, when there are continuous attributes in the example space, and if these attrihrrtnn hilv...

In this paper, extension of the EQ-logic by the ∆connective is introduced. The former is a new kind of many-valued logic which based on EQ-algebra of truth values, i.e. the algebra in which fuzzy equality is the fundamental operation and implication is derived from it. First, we extend the EQ-algebra by the ∆ operation and then introduce axioms and inference rules of EQ∆-logic. We also prove th...