Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ježková, L. Cordero, P. and Enciso, M. 2016. Fuzzy functional dependencies: A comparative survey. Fuzzy Sets and Systems,

    HAJDINJAK, MELITA and BAUER, ANDREJ 2012. SIMILARITY-BASED RELATIONS IN DATALOG PROGRAMS. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 20, Issue. 05, p. 673.

  • Mathematical Structures in Computer Science, Volume 22, Issue 4
  • August 2012, pp. 686-718

Extending relational algebra with similarities

  • DOI:
  • Published online: 25 April 2012

In this paper we propose various extensions to the relational model to support similarity-based querying. We build upon the -relation model, where tuples are assigned values from an arbitrary semiring , and its associated positive relational algebra . We consider a recently proposed extension to using a monus operation on the semiring to support negative queries, and show how, surprisingly, it fails for important ‘fuzzy’ semirings. Instead, we suggest using a negation operator. We also consider the identities satisfied by the relational algebra . We show that moving from a semiring to a particular form of lattice (a De Morgan frame) yields a relational algebra that satisfies all the classical (positive) relational algebra identities. We claim that to support real-world similarity queries realistically, one must move from tuple-level annotations to attribute-level annotations. We show in detail how our De Morgan frame-based model can be extended to support attribute-level annotations and give worked examples of similarity queries in this setting.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

S. Adali , P. Bonatti , M. L. Sapino and V. S. Subrahmanian (1998) A multi-similarity algebra. In: A. Tiwary and M. Franklin (eds.) SIGMOD '98: Proceedings of the 1998 ACM SIGMOD international conference on Management of data. ACM SIGMOD Record 27 402413.

K. Amer (1984) Equationally complete classes of commutative monoids with monus. Algebra Universalis 18 (1) 129131.

B. Bosbach (1965) Komplementäre halbgruppen: Ein beitrag zur instruktiven idealtheorie kommutativer halbgruppen. Mathematische Annalen 161 (4) 279295.

E. Codd (1970) A relational model of data for large shared data banks. Communications of the ACM 13 (6) 377387.

Y. Cui , J. Widom and J. Wiener (2000) Tracing the lineage of view data in a warehousing environment. ACM Transactions on Database Systems 25 179227.

B. Davey and H. Priestley (1990) Introduction to Lattices and Order, Cambridge University Press.

F. Geerts and A. Poggi (2010) On database query languages for k-relations. Journal of Applied Logic 8 173185.

M. Hajdinjak and F. Mihelič (2006) The PARADISE evaluation framework: Issues and findings. Computational Linguistics 32 (2) 263272.

B. Hutton (1975) Normality in fuzzy topological spaces. Journal of Mathematical Analysis and Applications 50 7479.

I. Ilyas , G. Beskales and M. Soliman (2008) A survey of top-k query processing techniques in relational database systems. ACM Computing Surveys 40 (4).

T. Imielinski and W. Lipski (1984) Incomplete information in relational databases. Journal of the ACM 31 (4).

G. Kuper , L. Libkin and J. Paredaens (2000) Constraint Databases, Springer-Verlag.

D. Papadias , Y. Tao , G. Fu and B. Seeger (2005) Progressive skyline computation in database systems. ACM Transactions on Database Systems 30 (1) 4182.

W. Penzo (2005) Rewriting rules to permeate complex similarity and fuzzy queries within a relational database system. IEEE Transactions on Knowledge and Data Engineering 17 (2) 255270.

A. Rosado , R. A. Ribeiro , S. Zadrozny and J. Kacprzyk (2006) Flexible query languages for relational databases: An overview. In: G. Bordogna and G. Psaila (eds.) Flexible databases supporting imprecision and uncertainty, Springer-Verlag353.

S. Shenoi and A. Melton (1989) Proximity relations in the fuzzy relational database model. Fuzzy Sets and Systems 31 (3) 285296.

D. Suciu (2008) Probabilistic databases. SIGACT News 39 (2) 111124.

L. Zadeh (1965) Fuzzy sets. Information and Control 8 338353.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *