Computing generalized belief functions for continuous fuzzy sets

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

Intelligent systems often need to deal with various kinds of uncertain information. It is thus essential to develop evidential reasoning models that (1) can cope with different kinds of uncertain information in a theoretically sound manner and (2) can be implemented efficiently in a computer system. Generalizing the Dempster-Shafer theory to fuzzy sets has been suggested as a promising approach for dealing with probabilistic data, vague concepts, and incomplete information in a uniform framework. However, previous efforts in this area do not preserve an important principle of D-S theory-that belief and plausibility measures are the lower and upper bounds on belief measures. Recently, Yen proposed an alternative approach in which the degree of belief and the degree of plausibility of a fuzzy set are interpreted as its lower and upper belief measure, respectively. This paper briefly describes his generalized D-S reasoning model and discusses the computational aspects of the model. In particular, efficient algorithms are presented for computing the generalized belief function and plausibility functions for strong convex fuzzy sets, which are a wide class of fuzzy sets used most frequently in existing fuzzy intelligent systems. The algorithm not only facilitates the application of the generalized D-S model but also provides the basis for developing efficient algorithms for more general cases.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalInternational Journal of Approximate Reasoning
Volume6
Issue number1
DOIs
StatePublished - Jan 1 1992

Fingerprint

Belief Functions
Fuzzy sets
Generalized Functions
Fuzzy Sets
Computing
Intelligent systems
Intelligent Systems
Efficient Algorithms
Convex Fuzzy Sets
Evidential Reasoning
Dempster-Shafer Theory
Incomplete Information
Model
Fuzzy Systems
Upper and Lower Bounds
Computer systems
Reasoning
Acoustic waves
Beliefs
Alternatives

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Artificial Intelligence
  • Applied Mathematics

Cite this

@article{5a7b47e1d31e4a1698da53485c19eda7,
title = "Computing generalized belief functions for continuous fuzzy sets",
abstract = "Intelligent systems often need to deal with various kinds of uncertain information. It is thus essential to develop evidential reasoning models that (1) can cope with different kinds of uncertain information in a theoretically sound manner and (2) can be implemented efficiently in a computer system. Generalizing the Dempster-Shafer theory to fuzzy sets has been suggested as a promising approach for dealing with probabilistic data, vague concepts, and incomplete information in a uniform framework. However, previous efforts in this area do not preserve an important principle of D-S theory-that belief and plausibility measures are the lower and upper bounds on belief measures. Recently, Yen proposed an alternative approach in which the degree of belief and the degree of plausibility of a fuzzy set are interpreted as its lower and upper belief measure, respectively. This paper briefly describes his generalized D-S reasoning model and discusses the computational aspects of the model. In particular, efficient algorithms are presented for computing the generalized belief function and plausibility functions for strong convex fuzzy sets, which are a wide class of fuzzy sets used most frequently in existing fuzzy intelligent systems. The algorithm not only facilitates the application of the generalized D-S model but also provides the basis for developing efficient algorithms for more general cases.",
author = "John Yen",
year = "1992",
month = "1",
day = "1",
doi = "10.1016/0888-613X(92)90037-Z",
language = "English (US)",
volume = "6",
pages = "1--31",
journal = "International Journal of Approximate Reasoning",
issn = "0888-613X",
publisher = "Elsevier Inc.",
number = "1",

}

Computing generalized belief functions for continuous fuzzy sets. / Yen, John.

In: International Journal of Approximate Reasoning, Vol. 6, No. 1, 01.01.1992, p. 1-31.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Computing generalized belief functions for continuous fuzzy sets

AU - Yen, John

PY - 1992/1/1

Y1 - 1992/1/1

N2 - Intelligent systems often need to deal with various kinds of uncertain information. It is thus essential to develop evidential reasoning models that (1) can cope with different kinds of uncertain information in a theoretically sound manner and (2) can be implemented efficiently in a computer system. Generalizing the Dempster-Shafer theory to fuzzy sets has been suggested as a promising approach for dealing with probabilistic data, vague concepts, and incomplete information in a uniform framework. However, previous efforts in this area do not preserve an important principle of D-S theory-that belief and plausibility measures are the lower and upper bounds on belief measures. Recently, Yen proposed an alternative approach in which the degree of belief and the degree of plausibility of a fuzzy set are interpreted as its lower and upper belief measure, respectively. This paper briefly describes his generalized D-S reasoning model and discusses the computational aspects of the model. In particular, efficient algorithms are presented for computing the generalized belief function and plausibility functions for strong convex fuzzy sets, which are a wide class of fuzzy sets used most frequently in existing fuzzy intelligent systems. The algorithm not only facilitates the application of the generalized D-S model but also provides the basis for developing efficient algorithms for more general cases.

AB - Intelligent systems often need to deal with various kinds of uncertain information. It is thus essential to develop evidential reasoning models that (1) can cope with different kinds of uncertain information in a theoretically sound manner and (2) can be implemented efficiently in a computer system. Generalizing the Dempster-Shafer theory to fuzzy sets has been suggested as a promising approach for dealing with probabilistic data, vague concepts, and incomplete information in a uniform framework. However, previous efforts in this area do not preserve an important principle of D-S theory-that belief and plausibility measures are the lower and upper bounds on belief measures. Recently, Yen proposed an alternative approach in which the degree of belief and the degree of plausibility of a fuzzy set are interpreted as its lower and upper belief measure, respectively. This paper briefly describes his generalized D-S reasoning model and discusses the computational aspects of the model. In particular, efficient algorithms are presented for computing the generalized belief function and plausibility functions for strong convex fuzzy sets, which are a wide class of fuzzy sets used most frequently in existing fuzzy intelligent systems. The algorithm not only facilitates the application of the generalized D-S model but also provides the basis for developing efficient algorithms for more general cases.

UR - http://www.scopus.com/inward/record.url?scp=38249015332&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249015332&partnerID=8YFLogxK

U2 - 10.1016/0888-613X(92)90037-Z

DO - 10.1016/0888-613X(92)90037-Z

M3 - Article

AN - SCOPUS:38249015332

VL - 6

SP - 1

EP - 31

JO - International Journal of Approximate Reasoning

JF - International Journal of Approximate Reasoning

SN - 0888-613X

IS - 1

ER -