Search

In this paper we introduce RL-instances as a way to represent and manipulate gradual conjunctive collections of tuples. Our proposal, based on the theory of Representation by Levels, overcomes the limitations of fuzzy instances in keeping all the properties of conventional Relational Algebra operations. We provide a proof of concept implementation in a conventional relational database management system, where flexible queries can be performed on crisp tables using the same patterns that are used in conventional querying. [ABSTRACT FROM AUTHOR]

Although there have been many fuzzy or probabilistic relational database models proposed for representing and handling imprecise and uncertain information of objects in real-world applications, models combining the relevance and strength of both fuzzy set theory and probability theory appear sporadic. In this paper, we propose a new fuzzy and probabilistic relational database model where the imprecision of an attribute value is represented by a fuzzy set and the uncertainty of a relational tuple is represented by a probability interval. The mass assignment theory is employed to deal with the challenge of integration and computation of both fuzzy sets and probabilities in the same model. The conjunction and disjunction strategies to combine imprecise and uncertain information are introduced. Then the fundamental concepts of the classical relational database model are extended and generalized in this new model. The syntax and semantics of the selection operation are formally defined. Finally, the other important algebraic operations on imprecise attributes and uncertain tuples are developed. [ABSTRACT FROM AUTHOR]

The concept of universal integral, recently proposed, generalizes the Choquet, Shilkret and Sugeno integrals. Those integrals admit a discrete bipolar formulation, useful in those situations where the underlying scale is bipolar. In this paper we propose the concept of discrete bipolar universal integral, in order to provide a common framework for bipolar discrete integrals, including as special cases the discrete Choquet, Shilkret and Sugeno bipolar integrals. Moreover we provide two different axiomatic characterizations of the proposed discrete bipolar universal integral. [ABSTRACT FROM AUTHOR]

Abstract: Dedekind categories provide a suitable categorical framework for lattice-valued binary relations. It is known that the notion of crispness cannot be described by the basic tools of this theory only. In this paper we will study Dedekind categories with a cutoff operator in order to circumvent this shortage. We will introduce and investigate the properties of the operator and its relationship with other tools previously used for the same purpose. The main result of this paper is a representation theorem for Dedekind categories with a cutoff operator satisfying the point axiom. [Copyright &y& Elsevier]

Abstract: Let be a residuated complete lattice with the underlying lattice L a meet continuous lattice. This paper presents a systematic investigation of the interrelationship between the categories of limit spaces, L-topological spaces, and L-preorders. The results exhibit a close connection between these different mathematical structures. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to introduce monadic -fuzzy quantifiers of the type and investigate some of their semantic properties that are well-known in generalized quantifier theory. Relationships between the properties of generalized quantifiers are also studied for monadic -fuzzy quantifiers. Finally, a property “to be extensional with respect to a given -permutation equivalence” is proposed and some properties are shown. [Copyright &y& Elsevier]

Abstract: Relational algebra serves as the theoretical basis for database design and queries. This paper extends our efforts on fuzzy relational algebraic operations under a fuzzy relational data model, namely, extended-possibility-based model. With a more general setting of fuzzy relational algebraic operators, some properties of the operators are investigated including equivalent definitions and transformation rules of the operators. These properties are important and desirable for processing queries in an effective and efficient manner. [Copyright &y& Elsevier]

Goguen categories constitute a suitable algebraic formalisation for L-fuzzy relations. It is well-known that an L-fuzzy relation may be represented by the set of all its α-cuts. The aim of this paper is to show a similar result for Goguen categories. Furthermore, given an algebraic structure of relations, a Dedekind category R, and a complete Brouwerian lattice L, the idea above allows us to define a Goguen category G such that the underlying structures are R and L. Using our pseudo-representation theorem we show that the representation theory of Goguen categories is equivalent to the representation theory of simple Dedekind categories. This result allows us to transfer known representation results for Dedekind categories to the theory of Goguen categories. [Copyright &y& Elsevier]