A t-tautology (triangular tautology) is a propositional formula which is a tautology in all fuzzy logics deened by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.

Recent development of mathematical fuzzy logic is brieey surveyed. The set of all formulas of predicate logic that are tautologies with respect to all continuous t-norms is shown to be heavily non-recursive ((2-hard).

all practical digital circuits are usually a mixture of combinational and sequential logic. flip–flops are essential to sequential logic therefore fuzzy flip–flops are considered to be among the most essential topics of fuzzy digital circuit. the concept of fuzzy digital circuit is among the most interesting applications of fuzzy sets and logic due to the fact that if there has to be an ultimat...

Triangular norms (t-norms for short) play a crucial role in several fields of mathematics and AI. For an exhaustive overview on t-norms we refer to [20]. Recently an increasing interest of left-continuous t-norm based theories can be observed (see e.g. [3, 5, 6, 7, 18]). In this paper we discuss in detail the presently existing construction methods which result in left-continuous triangular nor...

and Applied Analysis 3 Example 1.4. Let X, ‖ · ‖ be a normed space, a ∗ b ab, and a b min{a b, 1} for all a, b ∈ 0, 1 . For all x ∈ X and every t > 0, consider μ x, t ⎧ ⎪⎨ ⎪⎩ t t ‖x‖ if t > 0, 0 if t ≤ 0; ν x, t ⎧ ⎪⎨ ⎪⎩ ‖x‖ t |x| if t > 0, 1 if t ≤ 0. 1.1 Then X, μ, ν, ∗, is an IFNS. Remark 1.5 see 3 . Let X, μ, ν, ∗, be an IFNS with the condition μ x, t > 0, ν x, t < 1 implies x 0 ∀t ∈ . 1.2 L...

In some knowledge domains, a correct handling of vagueness and imprecision is fundamental for adequate knowledge representation and reasoning. For example, when trying to diagnose a disease, medical experts need to confront symptoms described by the patient, which are by definition subjective, and hence vague. Moreover, a single malady may present a diversity of clinical manifestations in diffe...

In fuzzy logic in wider sense, i.e. in the field of fuzzy sets applications, t-norms got a prominent rôle in recent times. In many-valued logic, the Lukasiewicz systems, the Gödel sytems, and also the product logic all are t-norm based systems. The present paper discusses the more general problem of the adequate axiomatizability for such t-norm based logical systems in general, surveying result...

Genetic programming (GP) is applied to automatic discovery of full knowledge bases for use in fuzzy logic control applications. An extension to a rule learning GP system is presented that achieves this objective. In addition, GP is employed to handle selection of fuzzy set intersection operators (t-norms). The new GP system is applied to design a mobile robot path tracking controller and perfor...