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Following the development of fuzzy logic theory by Lotfi Zadeh, its applications were investigated by researchers in different fields. Presenting and working with uncertain data is a complex problem. To solve for such a complex problem, the…

Fuzziness in databases is used to denote uncertain or incomplete data. Relational Databases stress on the nature of the data to be certain. This certainty based data is used as the basis of the normalization approach designed for…

This paper examines attribute dependencies in data that involve grades, such as a grade to which an object is red or a grade to which two objects are similar. We thus extend the classical agenda by allowing graded, or fuzzy, attributes…

This book gives the basic notions of fuzzy matrix theory and its applications to simple fuzzy models. The approach is non-traditional in order to attract many students to use this methodology in their research. The traditional approach of…

Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of…

This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…

This tutorial overviews the state of the art in learning models over relational databases and makes the case for a first-principles approach that exploits recent developments in database research. The input to learning classification and…

In an automated search system, similarity is a key concept in solving a human task. Indeed, human process is usually a natural categorization that underlies many natural abilities such as image recovery, language comprehension, decision…

Reynolds' original theory of relational parametricity was intended to capture the idea that polymorphically typed System F programs preserve all relations between inputs. But as Reynolds himself later showed, his theory can only be…

Representation learning is a fundamental building block for analyzing entities in a database. While the existing embedding learning methods are effective in various data mining problems, their applicability is often limited because these…

It is known that fuzzy set theory can be viewed as taking place within a topos. There are several equivalent ways to construct this topos, one is as the topos of \'{e}tal\'{e} spaces over the topological space $Y=[0,1)$ with lower topology.…

We prove The Equivalence Theorem: structurally complete knowledge representation requires exactly four mutually entailing capabilities -- n-ary relationships with attributes, temporal validity, uncertainty quantification, and causal…

Modeling of relation pattern is the core focus of previous Knowledge Graph Embedding works, which represents how one entity is related to another semantically by some explicit relation. However, there is a more natural and intuitive…

Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…

A model to represent spatial information is presented in this paper. It is based on fuzzy constraints represented as fuzzy geometric relations that can be hierarchically structured. The concept of spatial template is introduced to capture…

The increasing rise in artificial intelligence has made the use of imprecise language in computer programs like ChatGPT more prominent. Fuzzy logic addresses this form of imprecise language by introducing the concept of fuzzy sets, where…

The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient…

The transitivity of fuzzy relations plays an important role in fuzzy set theory, artificial intelligence, clustering and decision-making. However, it is often difficult for fuzzy relations to satisfy the transitivity property in many…

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…

This paper introduces techniques to integrate WordNet into a Fuzzy Logic Programming system. Since WordNet relates words but does not give graded information on the relation between them, we have implemented standard similarity measures and…