In Abstract Algebraic Logic the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this kind of process one considers the Leibniz relation of indiscernible, i.e. logically equivalent, formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: ...

We present results of situation assessment that: i) uses type 1 fuzzy logic (T1FL) for decision making/fusion in some aviation scenarios, ii) uses modified situation assessment (pilot’s mental-) models, and iii) can have noisy inputs to the situation assessment models. The results indicate that some existing fuzzy logic implication functions in decision making/fusion work very well. This beacon...

Two principal semantics have been assigned to the division of fuzzy relations. In the first one, the weights of the divisor are seen as thresholds and in the other, they act as grades of importance. This paper discusses a third approach in which the weights play the role of ideal values. In this context, the notion of a graded inclusion between (fuzzy) sets moves to that of a graded equality. I...

Fig. 3 Total silicon area versus number of inputs (n), with number of fuzzy sets constant List of Symbols n Number of inputs p Number of fuzzy sets A f Device area for fuzzifier circuit A m Device area for multiplier circuit A tad Total active device area A ts Total silicon area A s Device area for a summer circuit A ic Device area of intersection block A ti Total area for interconnect λ scalea...

Recently, Grzegorzewski [9] introduced two new families of fuzzy implication functions called survival implications and survival S-implications. These two classes of multivalued implications are based on conditional copulas. In the same article the author gave a motivation to his ideas and he analyzed some properties of these classes of fuzzy implications. In this paper the laws of contrapositi...

In this paper we consider algebras of fuzzy truth values equipped with an implication operation. Generalizing the definition of type-1 fuzzy implications, we discuss extended fuzzy S-implications and coimplications and also extended residual implications and coimplications, in particular to the extended residual of minimum. We study the algebraic properties of these operations and their relatio...

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained fr...

Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [12] has introduced two new classes of fuzzy implications called the f -generated and g-generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the h-generated implications. In this article we discuss in detail some properti...

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant 0, namely ¬φ isφ → 0. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which i...