We propose a parameterized framework based on a Heyting algebra and Lukasiewicz negation for modeling uncertainty for belief. We adopt a probability theory as mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of information in the form of belief types: as a single probability, as an interval (lower and upper boundary for a p...

The characterization of (S,N)-implications when N is a non-continuous negation has remained one the most significant open problems in fuzzy logic for last decades. This paper constitutes first progress this topic. Namely, general family implication functions presented, which central property existence completion binary function defined on certain subregion [0,1]2 to t-conorm. In paper, dual pro...

Let Gm be the m-valued Gödel-Dummett fuzzy logic. If m ≥ 3 then neither conjunction nor implication is in Gm expressible in terms of the remaining connectives. This fact remains true even if the propositional language is enriched by propositional constants for all truth values. Gödel-Dummett fuzzy propositional logic can be defined as an extension of the intuitionistic propositional logic by th...

This paper proposes a new formalization of the classical probability-possibility relation, which is further confirmed as a much complex, but natural provability – reachability possibility probability fuzzy membership – integrability interconnection. Searching for the right context in which this relation can be consistently expressed for the particular case of experimentally obtained iris recogn...

In this paper, we introduce and study the GD′-operations, which are a hyper class of known D′-operations. GD′-operations in fact D′-operations, that generated not only from same fuzzy negation. Similar with they always implications. Nevertheless, some sufficient, but necessary conditions for GD′-operation to be implication, will proved. A satisfaction, or violation basic properties implications...

Fuzzy Description Logics (FDLs) combine classical Description Logics with the semantics of Fuzzy Logics in order to represent and reason with vague knowledge. Most FDLs using truth values from the interval [0, 1] have been shown to be undecidable in the presence of a negation constructor and general concept inclusions. One exception are those FDLs whose semantics is based on the infinitely valu...

In this paper we show how the concepts of answer set programming and fuzzy logic can be succesfully combined into the single framework of fuzzy answer set programming (FASP). The framework offers the best of both worlds: from the answer set semantics, it inherits the truly declarative non-monotonic reasoning capabilities while, on the other hand, the notions from fuzzy logic in the framework al...

We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary operators. Then we generalize them to n-ary fuzzy logic and neutrosophic logic operators using the smarandache codification of the Venn diagram and a defined vector neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built. Introduction. For the beginning let’s con...