Fuzzy sets as a basis for a theory of possibility

@article{Zadeh1999FuzzySA,
  title={Fuzzy sets as a basis for a theory of possibility},
  author={L. Zadeh},
  journal={Fuzzy Sets and Systems},
  year={1999},
  volume={100},
  pages={9-34}
}
  • L. Zadeh
  • Published 1999
  • Mathematics
  • Fuzzy Sets and Systems
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. More specifically, if F is a fuzzy subset of a universe of discourse U = {u} which is characterized by its membership function μF, then a proposition of the form “X is F”, where X is a variable taking values in U, induces a possibility… Expand

Figures and Tables from this paper

A note on the conditional probability of fuzzy subsets of a continuous domain
TLDR
The notion of a mass assignment corresponding to a discrete fuzzy set is generalised to include all fuzzy sets and it is shown that in the case, where the probability distribution on the domain has a density function then the conditional probability can be expressed as the probability of f calculated relative to a conditional density function dependent on g. Expand
Approximation techniques for the transformation of fuzzy sets into random sets
TLDR
In this paper, three approximation techniques are proposed and compared to classical approximations techniques used in evidence theory and the quality of the approxIMations is quantified using a distance between two random sets. Expand
Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities
TLDR
New properties of this transformation of a probability distribution into a possibility distribution are described, by relating it with the well-known probability inequalities of Bienaymé-Chebychev and Camp-Meidel. Expand
On the normalization of subnormal possibility distributions: New investigations
  • M. Oussalah
  • Mathematics, Computer Science
  • Int. J. Gen. Syst.
  • 2002
TLDR
The two approaches to the handling of subnormal possibility distributions are investigated with respect to some appealing criteria like preference preservation, distance minimization, entropy, minimum/maximum specificity, and, further, particular interest is focused on information based uncertainty preservation. Expand
Fuzzy Possibility Space and Type-2 Fuzzy Variable
TLDR
An axiomatic approach to developing the theory of type-2 (T2) fuzziness, called fuzzy possibility theory is presented, which defines a T2 fuzzy vector as a measurable map from a fuzzy possibility space (FPS) to the space of real vectors. Expand
On the Variability of the Concept of Variance for Fuzzy Random Variables
  • I. Couso, D. Dubois
  • Mathematics, Computer Science
  • IEEE Transactions on Fuzzy Systems
  • 2009
TLDR
This paper discusses another view of fuzzy random variables, which comes down to a set of random variables induced by a fuzzy relation describing an ill-known conditional probability that leads to yet another definition of the variance of a fuzzy random variable in the context of the theory of imprecise probabilities. Expand
The application of level-2 fuzzy sets in fuzzy and uncertain data modeling
A formal framework for the uniform representation and manipulation of fuzzy and/or uncertain data is presented. This framework can be used within the context of (the formal definition of) e.g. fuzzyExpand
A new approach to specificity in possibility theory: Decision-making point of view
  • A. V. Zubyuk
  • Mathematics, Computer Science
  • Fuzzy Sets Syst.
  • 2019
TLDR
The paper investigates the problem of defining a specificity relation in Pyt'ev possibility theory and states that the specificity relation definition has to be consistent with the possibilistic decision-making approaches. Expand
Type-2 fuzzy variables and their arithmetic
TLDR
An axiomatic framework from which the theory of type-2 (T2) fuzziness is developed is proposed, and the T2 possibility distribution function is obtained as the transformation of a fuzzy possibility measure from a universe to the space $$Re^m$$ via T2 fuzzy vector. Expand
Possibility Theory, Probability and Fuzzy Sets Misunderstandings, Bridges and Gaps
Possibility theory was coined by L.A. Zadeh in the late seventies as an approach to model flexible restrictions constructed from vague pieces of information, described by means of fuzzy sets.Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 44 REFERENCES
Calculus of fuzzy restrictions
ABSTRACT A fuzzy restriction may be visualized as an elastic constraint on the values that may be assigned to a variable. In terms of such restrictions, the meaning of a proposition of the form “x isExpand
Similarity relations and fuzzy orderings
  • L. Zadeh
  • Mathematics, Computer Science
  • Inf. Sci.
  • 1971
TLDR
An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric. Expand
A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges
Abstract A basic idea suggested in this paper is that a linguistic hedge such as very, more or less, much, essentially. slightly, etc. may be viewed as an operator which acts on the fuzzy setExpand
Fuzzy sets and their applications to cognitive and decision processes
TLDR
By providing a basis for a systematic approach to approximate reasoning, the theory of fuzzy sets may well have a substantial impact on scientific methodology in the years ahead, particularly in the realms of psychology, economics, law, medicine, decision analysis, information retrieval, and artificial intelligence. Expand
Probability measures of Fuzzy events
In probability theory [I], an event, A, is a member of a a-field, CY, of subsets of a sample space ~2. A probability measure, P, is a normed measure over a measurable space (Q, GY); that is, P is aExpand
A fuzzy set approach to modifiers and vagueness in natural language.
SUMMARY Recent developments in semantic theory, such as the work of Labov (1973) and Lakoff (1973), have brought into question the assumption that meanings are precise. It has been proposed that theExpand
CONDITIONAL FUZZY MEASURES AND THEIR APPLICATIONS
Publisher Summary This chapter introduces a set function, that is, conditional fuzzy measure and a relation between a priori and a posteriori fuzzy measures. These are very useful for describing anyExpand
Applications of Fuzzy Sets to Systems Analysis
TLDR
One of the objects of this book was to facilitate communication by bringing toge- ther different viewpoints and coloring them from a common viewpoint. Expand
Probability Theory I
These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law ofExpand
Deductive verbal models of organizations
TLDR
It is generally concluded that the present approach towards modelling the behavior of complex organizations is not without interesting potentialities, and that verbal models may, under certain circumstances, be superior to corresponding conventional simulation models. Expand
...
1
2
3
4
5
...