Related papers: Approximating approximate reasoning: Fuzzy sets an…
We present connections between the recent literature on multigroup fairness for prediction algorithms and classical results in computational complexity. Multiaccurate predictors are correct in expectation on each member of an arbitrary…
Fuzzy rough set theory can be used as a tool for dealing with inconsistent data when there is a gradual notion of indiscernibility between objects. It does this by providing lower and upper approximations of concepts. In classical fuzzy…
The mathematical representation of uncertainty has led to a proliferation of preference structures, such as interval-valued fuzzy sets, intuitionistic fuzzy sets, and various granular models. While these extensions are often studied…
In this paper, we present a proof of the consistency of the New Foundations set theory ($\mathit{NF}$). $\mathit{NF}$'s main idea is to permit very large sets (including the Universal Set) by restricting set formation to stratified…
Red and blue galaxies are traditionally classified using some specific cuts in colour or other galaxy properties, which are supported by empirical arguments. The vagueness associated with such cuts are likely to introduce a significant…
Simulations and bisimulations are well-established notions in crisp/fuzzy automata theory and are widely used to compare the behaviors of automata. Their main drawback is that they compare the behaviors of fuzzy automata in a crisp manner.…
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
Hesitant fuzzy sets find extensive application in specific scenarios involving uncertainty and hesitation. In the context of set theory, the concept of inclusion relationship holds significant importance as a fundamental definition.…
We prove the basic trigonometric Korovkin approximation theorem for fuzzy valued functions of two variables and verify the approximation by the help of fuzzy modulus of continuity. Also, we introduce double level Fourier series of fuzzy…
Fuzzy implication functions are a key area of study in fuzzy logic, extending the classical logical conditional to handle truth degrees in the interval $[0,1]$. While existing literature often focuses on a limited number of families, in the…
It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have…
The fuzzy rough approximation operator serves as the cornerstone of fuzzy rough set theory and its practical applications. Axiomatization is a crucial approach in the exploration of fuzzy rough sets, aiming to offer a clear and direct…
Here a novel idea to handle imprecise or vague set viz. Pseudo fuzzy set has been proposed. Pseudo fuzzy set is a triplet of element and its two membership functions. Both the membership functions may or may not be dependent. The hypothesis…
In this work we are analyzing scalability of the heuristic algorithm we used in the past to discover knowledge from multi-valued symbolic attributes in fuzzy databases. The non-atomic descriptors, characterizing a single attribute of a…
By universal formulas we understand parameterized analytic expressions that have a fixed complexity, but nevertheless can approximate any continuous function on a compact set. There exist various examples of such formulas, including some in…
Fuzzy clustering is a famous unsupervised learning method used to collecting similar data elements within cluster according to some similarity measurement. But, clustering algorithms suffer from some drawbacks. Among the main weakness…
Hierarchical clustering seeks to uncover nested structures in data by constructing a tree of clusters, where deeper levels reveal finer-grained relationships. Traditional methods, including linkage approaches, face three major limitations:…
Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL $\mathcal{SROIQ}$ based on finite chains of…
The novelty of this paper is to construct the explicit combinatorial formula for the number of all distinct fuzzy matrices of finite order, which leads us to invent a new sequence. In order to achieve this new sequence, we analyze the…
Several research initiatives have been proposed for computing similarity between two Fuzzy Sets in analysis through Fuzzy Rough Sets. These techniques yield two measures viz. lower similarity and upper similarity. While in most applications…