Lipski's approach to incomplete information data bases restated and generalized in the setting of Zadeh's possibility theory
Information SystemsPublished 1 January 1984
Henri Prade
Citations129
SJR quartileQ1
SJR score0.89
SNIP1.96
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
The main purpose of this paper is to make clear the connection between Lipski's approach to incomplete information databases and Zadeh's possibility theory, which both appeared recently, quite simultaneously, but in different contexts.
Abstract
An earlier and partial version[1] of this paper was presented at the Symposium on Methodology of Fuzzy Systems held at the International Conference on Systems Methodology, Washington, D.C., January 1982
Keywords
Computer Science
Information SciencesThe concept of a linguistic variable and its application to approximate reasoning-III
12,148 Citations1975L. A. Zadeh
Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
Information SciencesThe concept of a linguistic variable and its application to approximate reasoning—I
12,036 Citations1975Lotfi A. Zadeh
It is shown that probabilities, too, can be treated as linguistic variables with values such as likely, very likely, unlikely, etc.
Fuzzy Sets and SystemsFuzzy sets as a basis for a theory of possibility
7,964 Citations1978Lotfi A. Zadeh
Fuzzy Sets and SystemsFuzzy sets as a basis for a theory of possibility
7,280 Citations1999Lotfi A. Zadeh
The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
Mathematics in Science and Engineering/Mathematics in science and engineeringFuzzy Sets and Systems - Theory and Applications
6,430 Citations1980Didier Dubois, Henri Prade
The Annals of Mathematical StatisticsUpper and Lower Probabilities Induced by a Multivalued Mapping
5,972 Citations1967A. P. Dempster
Studies in fuzziness and soft computingUpper and Lower Probabilities Induced by a Multivalued Mapping
5,299 Citations2008Arthur P. Dempster
A distinctive feature of the present approach is a rule for conditioning, or more generally, arule for combining sources of information, as discussed in Sects.
Information SciencesThe concept of a linguistic variable and its application to approximate reasoning—II
2,509 Citations1975Lotfi A. Zadeh
The nonrestricted nonfuzzy variable u constitutes the base variable for X and R(X;u) is a fuzzy subset of U which represents a fuzzy restriction on the values of u imposed by X.
ACM Transactions on Database SystemsExtending the database relational model to capture more meaning
1,555 Citations1979E. F. Codd
This paper proposes extensions to the relational model to support certain atomic and molecular semantics, a synthesis of many ideas from the published work in semantic modeling plus the introduction of new rules for insertion, update, and deletion, as well as new algebraic operators.
Information SciencesRanking fuzzy numbers in the setting of possibility theory
936 Citations1983Didier Dubois, Henri Prade
A complete set of comparison indices is proposed in the framework of Zadeh's possibility theory and it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers.
International Journal of Man-Machine StudiesPRUF—a meaning representation language for natural languages
724 Citations1978Lotfi A. Zadeh
In addition to serving as a foundation for approximate reasoning, PRUF may be employed as a language for the representation of imprecise knowledge and as a means of precisiation of fuzzy propositions expressed in a natural language.
Fuzzy Sets and SystemsA fuzzy representation of data for relational databases
613 Citations1982Bill P. Buckles, Frederick E. Petry
Two critical properties possessed by ordinary relational databases are proven to exist in the fuzzy relational structure, which means no two tuples have identical interpretations, and each relational operation has a unique result.
ACM Transactions on Database SystemsOn semantic issues connected with incomplete information databases
513 Citations1979Witold Lipski
This work emphasizes the distinction between two different interpretations of the query language—the external one, which refers the queries directly to the real world modeled in an incomplete way by the system, and the internal one, under which the queries refer to the system's information about this world, rather than to the world itself.
International Journal of General SystemsA CLASS OF FUZZY MEASURES BASED ON TRIANGULAR NORMS A general framework for the combination of uncertain information
330 Citations1982Didier Dubois, Henri Prade
An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short), which encompasses probability measures, Zadeh's possibility measures and the dual notion of necessity measures.
Journal of the ACMOn Databases with Incomplete Information
277 Citations1981Witold Lipski
The internal interpretation of a simple query language is shown to lead in a natural way to the notions of a topological Boolean algebra and a modal logic related to $4 in the same way as referring queries directly to reality (external interpretation) leads to Boolean algebras and classical logic.
Fuzzy Sets and SystemsUnfair coins and necessity measures: Towards a possibilistic interpretation of histograms
255 Citations1983Didier Dubois, Henri Prade
A bijective mapping is defined which turns a probability measure into a possibility measure and corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available.
KybernetesFUZZY PATTERN MATCHING
180 Citations1982Michel Cayrol, Henri Farreny del Bosque +1 more
Pattern‐directed inference systems are among the most largely used tools in A.I. to‐day in order to represent and exploit knowledge, but the lack of flexibility in the matching remains a drawback in this kind of system.
Information SciencesThe degree of belief in a fuzzy event
152 Citations1981Philippe Smets
Epistemic probabilities are better described by belief functions and their definition is extended in order to apply them to fuzzy events.
A Formal Approach to Null Values in Database Relations
102 Citations1981Joachim Biskup
The view that tuples denote statements of predicate logic about database relations is adopted, which means that a null value of the first kind and the second kind corresponds to an existentially quantified variable, respectively universally quantified variables.
ACM Transactions on Database SystemsA statistical approach to incomplete information in database systems
87 Citations1982Eugene Wong
Boston studies in the philosophy of scienceThe Problem of Vague Predicates
51 Citations1983Rohit Parikh
Defense Technical Information Center (DTIC)A Fuzzy Relational Inference Language for Expert Systems,
32 Citations1983Baldwin,J. F.
Artificial Intelligence
25 Citations2021Ishita Singh, Joy Gupta +1 more
Computer-Aided DesignAESOP: an architectural relational database
10 Citations1979Robert Phillips, M.J. Beaumont +1 more
It is concluded that AESOP could provide a useful framework for a CAAD system and that further work is required in two areas, the user interface, and operations involving geometrical relations.
Information SystemsInformation systems: On queries involving cardinalities
5 Citations1979Witold Lipski, Wiktor Marek
A precise semantics of a query language is described, and a complete axiom system for equivalent transformations of queries is given, able to transform any query into a normal form which makes the retrieval process more efficient.