相关论文: Approximating approximate reasoning: Fuzzy sets an…
The fuzzy or soft $k$-means objective is a popular generalization of the well-known $k$-means problem, extending the clustering capability of the $k$-means to datasets that are uncertain, vague, and otherwise hard to cluster. In this paper,…
Discrete fuzzy numbers, and in particular those defined over a finite chain $L_n = \{0, \ldots, n\}$, have been effectively employed to represent linguistic information within the framework of fuzzy systems. Research on total (admissible)…
Most fuzzy systems including fuzzy decision support and fuzzy control systems provide out-puts in the form of fuzzy sets that represent the inferred conclusions. Linguistic interpretation of such outputs often involves the use of linguistic…
The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh's…
We analyze the behavior of the first few cumulant in an array with a small number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf 19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global coupling and…
Syllogism is a type of deductive reasoning involving quantified statements. The syllogistic reasoning scheme in the classical Aristotelian framework involves three crisp term sets and four linguistic quantifiers, for which the main support…
The approach described here allows to use the fuzzy Object Based Representation of imprecise and uncertain knowledge. This representation has a great practical interest due to the possibility to realize reasoning on classification with a…
Preferential equality is an equivalence relation on fuzzy subsets of finite sets and is a generalization of classical equality of subsets. In this paper we introduce a tightened version of the preferential equality on fuzzy subsets and…
Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a…
We consider the problem where a set of individuals has to classify $m$ objects into $p$ categories and does so by aggregating the individual classifications. We show that if $m\geq 3$, $m\geq p\geq 2$, and classifications are fuzzy, that…
This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation…
This paper introduces the concept of kernels on fuzzy sets as a similarity measure for $[0,1]$-valued functions, a.k.a. \emph{membership functions of fuzzy sets}. We defined the following classes of kernels: the cross product, the…
Spectral clustering uses the global information embedded in eigenvectors of an inter-item similarity matrix to correctly identify clusters of irregular shape, an ability lacking in commonly used approaches such as k-means and agglomerative…
Closure operators are very useful tools in several areas of classical mathematics and in general category theory. In fuzzy set theory, fuzzy closure operators have been studied by G. Gerla (1966). These works generally define a fuzzy subset…
A fuzzy opinion is a Gaussian fuzzy set with the center representing the opinion and the standard deviation representing the uncertainty about the opinion, and a fuzzy opinion network is a connection of a number of fuzzy opinions in a…
The involvement of uncertainty of varying degrees when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate. For the past two or more decades, Fuzzy…
In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough) equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notions were…
Subsethood, which is to measure the degree of set inclusion relation, is predominant in fuzzy set theory. This paper introduces some basic concepts of spatial granules, coarse-fine relation, and operations like meet, join, quotient meet and…
This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the…
We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably, Schnorr,…