Functions provably total in
Functions provably total in
Functorial bounds for cut elimination in L... .I.
Functorial bounds for cut elimination in L.. .II.
Functorial polymorphism and semantic parametricity
Functorial uniform reducibility
Fundamentals of a mathematical theory of fuzzy sets
Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.
Further applications of ultra-conservative ...-rules.
Further development of Chebyshev type inequalities for Sugeno integrals and T-(S-)evaluators
In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function and a scale transformation is given. Consequences for T-(S-)evaluators are established.
Fuzziness and fuzzy equality
Fuzzy BCI-subalgebras with interval-valued membership functions.
Fuzzy Boolean algebras and Łukasiewicz logic.
Fuzzy clustering of fuzzy data considering the shape of the membership functions using a novel representation learning technique
Most existing distance measures for fuzzy data do not capture differences in the shapes of the left and right tails of membership functions. As a result, they may calculate a distance of zero between fuzzy data even when these differences exist. Additionally, some distance measures cannot compute distances between fuzzy data when their membership functions differ in type. In this paper, inspired by human visual perception, we propose a fuzzy clustering method for fuzzy data using a novel representation...
Fuzzy concepts defined via residuated maps
Fuzzy data in statistics
The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data...
Fuzzy decision trees to help flexible querying
Fuzzy data mining by means of the fuzzy decision tree method enables the construction of a set of fuzzy rules. Such a rule set can be associated with a database as a knowledge base that can be used to help answering frequent queries. In this paper, a study is done that enables us to show that classification by means of a fuzzy decision tree is equivalent to the generalized modus ponens. Moreover, it is shown that the decision taken by means of a fuzzy decision tree is more stable when observation...
Fuzzy diagnostic reasoning that takes into account the uncertainty of the relation between faults and symptoms
Knowledge about the relation between faults and the observed symptoms is necessary for fault isolation. Such a relation can be expressed in various forms, including binary diagnostic matrices or information systems. The paper presents the use of fuzzy logic for diagnostic reasoning. This method enables us to take into account various kinds of uncertainties connected with diagnostic reasoning, including the uncertainty of the faults-symptoms relation. The presented methods allow us to determine the...
Fuzzy distances
In the paper, three different ways of constructing distances between vaguely described objects are shown: a generalization of the classic distance between subsets of a metric space, distance between membership functions of fuzzy sets and a fuzzy metric introduced by generalizing a metric space to fuzzy-metric one. Fuzzy metric spaces defined by Zadeh’s extension principle, particularly to are dealt with in detail.
Fuzzy equality and convergences for -observables in -quantum spaces
We introduce a fuzzy equality for -observables on an -quantum space which enables us to characterize different kinds of convergences, and to represent them by pointwise functions on an appropriate measurable space.
Fuzzy functions in fuzzy logic with fuzzy equality