Starting from the primary representation of neutrosophic information, namely the degree of truth, degree of indeterminacy and degree of falsity, we define a nuanced representation in a penta valued fuzzy space, described by the index of truth, index of falsity, index of ignorance, index of contradiction and index of hesitation. Also, it was constructed an associated penta valued logic and then ...

We study the Liar paradox and related systems of self-referential sentences. Specifically, we consider the problem of assigning consistent fuzzy truth values to systems of self-referential sentences. We show that this problem can be reduced to the solution of a system of nonlinear equations and we prove that, under certain conditions, a solution (i.e. a consistent truth value assignment) always...

In this paper, we extend the domains of affirmation and negation operators, and more important, of triangular (semi)norms and (semi)conorms from the unit interval to bounded partially ordered sets. The fundamental properties of the original operators are proven to be conserved under this extension. This clearly shows that they are essentially based upon order-theoretic notions. Consequently, a ...

A dozen papers have considered the concept of negation probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point functions defined on a set values and called here negators. Recently class pd-independent linear negators has been characterized using Yager’s negator. The open problem was how to introduce involutive generating pd. To solve this problem...

We introduce nearly Frank t-norms as t-norms which are generated from Frank t-norms by means of a negation-preserving automorphism. We state basic properties of nearly Frank t-norms and we show their speci c role in the characterization of T -measures. 1 Basic facts about T -norms A t-norm (fuzzy conjunction) is a binary operation T : [0; 1]2 ! [0; 1] which is commutative, associative, nondecre...

—Experts are often not 100% con dent in their statements. In traditional fuzzy logic, the expert's degree of con dence in each of his or her statements is described by a number from the interval [0, 1]. However, due to similar uncertainty, an expert often cannot describe his or her degree by a single number. It is therefore reasonable to describe this degree by, e.g., a set of numbers. In this ...

Negation operation is important in intelligent information processing. Different existing arithmetic negation, an exponential negation presented this paper. The new can be seen as a kind of geometry negation. Some basic properties the proposed are investigated, and we find that fix point uniform probability distribution, which reaches maximum entropy. entropy increase operation, all distributio...

Recently we proposed the linguistic Copenhagen interpretation (or, quantum language, measurement theory), which has a great power to describe both classical and systems. Thus think that language can be viewed as of science. Further, showed certain logic (called fuzzy logic) works in language. In general, it is said time do not go well together. Then, purpose this paper show with time. That is, ...