This paper is concerned with the foundations of fuzzy reasoning and its relationships with other logics of uncertainty. The definitions of fuzzy logics are first examined and the role of fuzzification discussed. It is shown that fuzzification of PC gives a known multivalued logic but with inappropriate semantics of implication and various alternative forms of implication are discussed. In the m...

Fuzzy cellular automata (FCA) are continuous cellular automata where the local rule is defined as the “fuzzification" of the local rule of a corresponding Boolean cellular automaton in disjunctive normal form. In this paper, we are interested in the relationship between Boolean and fuzzy models and, for the first time, we analytically show the existence of a strong connection between them by fo...

In this paper, a classification method based on fuzzy linguistic rules is exposed. It is applied for the recognition of the gradual color of wood in an industrial context. The wood, which is a natural material, implies uncertainty in the definition of its color. Moreover, the timber context leads obtaining imprecise data. Several factors can have an impact on the sensors (ageing of the acquisit...

Inclusion for fuzzy sets was &rst introduced by Zadeh in his seminal 1965 paper. Since it was found that the de&nition of inclusion was not in the true spirit of fuzzy logic, various researchers have set out to de&ne alternative indicators of the inclusion of one fuzzy set into another. Among these alternatives, the indicator proposed by Sinha and Dougherty stands out as an intuitively appealin...

If-then rules are one of the most common forms of knowledge discovered by data mining methods. The number and the length of extracted rules tend to increase with the size of a database, making the rulesets less interpretable and useful. Existing methods of extracting fuzzy rules from numerical data improve the interpretability aspect, but the dimensionality of fuzzy rulesets remains high. In th...

We present a new information architecture based on one recently introduced to structure categorized but otherwise unstructured information. The new architecture is based on fuzzy set theory subset operations that define graph theory nodes. Two types of graph edges are defined such that a user interface based on this architecture can logically minimize the number of visible navigable edges and a...

Complexities of geological processes portrayed as certain feature in a map (e.g., faults) are natural sources of uncertainties in decision-making for exploration of mineral deposits. Besides natural sources of uncertainties, knowledge-driven (e.g., fuzzy logic) mineral prospectivity mapping (MPM) is also plagued and incurs further uncertainty in subjective judgment of analyst when there is no r...

In this paper, we first extend the concept of arity in crisp convex spaces to case fuzzification and give some related properties. From view hull operator, study relations between disjoint sum M-fuzzifying its factor spaces. We also examine additivity degree separability (S0,S1,S2,S3,S4). Finally, show that every space is JHC iff corresponding JHC.

The role and significance of adaptive neuro-fuzzy systems as well the theory fuzzy sets are considered in article. method for determination truth rules is interrogated, iterative feature algorithm under study put on focus. practical implementation calculation fuzzification layer function functional mathematical apparatus network presented. importance used perception creation a inference digital...