The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0,1]; the inclusion measure proposed here takes values in a Boolean lattice. In other words, inclusion is viewed as an Lfuzzy valued relation between fuzzy sets. This relation is reflexive, antisymmetric and transitive,...

We present an axiomatic approach to conditional measures of fuzzy events which is inspired by the Dupré–Tipler argument for Bayesianism. Unlike there or in the older and related Cox argument, although we are able to derive additive probabilities other non-additive solutions exist. Our motivation is to show that Bayesian foundational arguments are based on Boolean logic but they do not require i...

The discovery of association rule acquire an imperative role in data mining since its inception, which tries to find correlation among the attributes in a database. Classical algorithms/procedures meant for Boolean data and they suffer from sharp boundary problem in handling quantitative data. Thereby fuzzy association rule (i.e., association rule based on fuzzy sets) with fuzzy minimum support...

Bounded residuated lattice ordered monoids (R -monoids) are a common generalization of pseudo-BL-algebras and Heyting algebras, i.e. algebras of the non-commutative basic fuzzy logic (and consequently of the basic fuzzy logic, the Łukasiewicz logic and the non-commutative Łukasiewicz logic) and the intuitionistic logic, respectively. In the paper we introduce and study classes of filters of bou...

Boolean logic is frequently applied in order tomap landscape patterns. Nonetheless this implies to divide the gradual variability of the earth’s surface into a finite number of non-overlapping classes, which are considered exhaustive and mutually exclusive. On the contrary, landscapes are expected to be spatially continuous. Fuzzymembership seems to better fit such an issue, by associating for ...

(1) Elkan’s proof uses too strong a notion of logical equivalence. The particular equivalence he considers, while valid in Boolean algebra, has nothing to do with fuzzy logic. (2) Elkan claims that De Morgan’s algebra “allows very little reasoning about collections of fuzzy assertions,” although he correctly states that when logical equivalence is restricted to De Morgan algebra equalities’ “co...

In this paper, first we will find the solution of the system A ∗ X ≤ b, where A, b are the known suitable matrices and X is the unknown matrix over a pseudoBoolean lattice. Then its application to find the solution of some fuzzy linear systems as well as finding the solution of the optimization problem Z = max{C∗X|A∗ X ≤ b} is discussed. Key-words: pseudo-Boolean lattice, linear programming, fu...

The paper is devoted to the development of methods of ontology supported knowledge discovery in the field of mobile network subscribers. We develop the ontological model of the domain of mobile networks. This ontological model is intended to describe the behavior of mobile network subscribers. The ontological model is based on the four-level model of knowledge representation. In the paper, spec...

Markov Logic Networks (MLN) and Probabilistic Soft Logic (PSL) are widely applied formalisms in Statistical Relational Learning, an emerging area in Artificial Intelligence that is concerned with combining logical and statistical AI. Despite their resemblance, the relationship has not been formally stated. In this paper, we describe the precise semantic relationship between them from a logical ...

Starting from the idea that the closer the query terms in a document are to each other the more relevant the document, we propose an information retrieval method that uses the degree of fuzzy proximity of key terms in a document to compute the relevance of the document to the query. Our model handles Boolean queries but, contrary to the traditional extensions of the basic Boolean information re...