Convex combination and its application to fuzzy sets and interval-valued fuzzy sets II

Omar Salazar, Jairo Soriano

Research output: Contribution to journalArticle

  • 5 Citations

Abstract

This paper showed a short characterization of embedded fuzzy sets of an interval-valued fuzzy set. We proved that any embedded fuzzy set can be expressed as a convex combination of three fuzzy sets always. We established two basic results (existence and uniqueness) in the rep- resentation as a convex combination. We showed three examples from the literature, and we showed they can be deduced by using the theory presented herein.

LanguageEnglish
Pages1069-1076
Number of pages8
JournalApplied Mathematical Sciences
Volume9
Issue number21-24
DOIs
Publication statusPublished - 2015

Fingerprint

Interval-valued Fuzzy Set
Fuzzy Intervals
Convex Combination
Fuzzy sets
Fuzzy Sets
Existence and Uniqueness Results

Keywords

  • Convex combination
  • Embedded fuzzy set
  • Fuzzy set
  • Interval type-2 fuzzy set
  • Interval-valued fuzzy set
  • Membership function

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Convex combination and its application to fuzzy sets and interval-valued fuzzy sets II. / Salazar, Omar; Soriano, Jairo.

In: Applied Mathematical Sciences, Vol. 9, No. 21-24, 2015, p. 1069-1076.

Research output: Contribution to journalArticle

@article{b390b2bab5fc461997c7c25df6ce0bbe,
title = "Convex combination and its application to fuzzy sets and interval-valued fuzzy sets II",
abstract = "This paper showed a short characterization of embedded fuzzy sets of an interval-valued fuzzy set. We proved that any embedded fuzzy set can be expressed as a convex combination of three fuzzy sets always. We established two basic results (existence and uniqueness) in the rep- resentation as a convex combination. We showed three examples from the literature, and we showed they can be deduced by using the theory presented herein.",
keywords = "Convex combination, Embedded fuzzy set, Fuzzy set, Interval type-2 fuzzy set, Interval-valued fuzzy set, Membership function",
author = "Omar Salazar and Jairo Soriano",
year = "2015",
doi = "10.12988/ams.2015.411982",
language = "English",
volume = "9",
pages = "1069--1076",
journal = "Applied Mathematical Sciences",
issn = "1312-885X",
publisher = "Hikari Ltd.",
number = "21-24",

}

TY - JOUR

T1 - Convex combination and its application to fuzzy sets and interval-valued fuzzy sets II

AU - Salazar, Omar

AU - Soriano, Jairo

PY - 2015

Y1 - 2015

N2 - This paper showed a short characterization of embedded fuzzy sets of an interval-valued fuzzy set. We proved that any embedded fuzzy set can be expressed as a convex combination of three fuzzy sets always. We established two basic results (existence and uniqueness) in the rep- resentation as a convex combination. We showed three examples from the literature, and we showed they can be deduced by using the theory presented herein.

AB - This paper showed a short characterization of embedded fuzzy sets of an interval-valued fuzzy set. We proved that any embedded fuzzy set can be expressed as a convex combination of three fuzzy sets always. We established two basic results (existence and uniqueness) in the rep- resentation as a convex combination. We showed three examples from the literature, and we showed they can be deduced by using the theory presented herein.

KW - Convex combination

KW - Embedded fuzzy set

KW - Fuzzy set

KW - Interval type-2 fuzzy set

KW - Interval-valued fuzzy set

KW - Membership function

UR - http://www.scopus.com/inward/record.url?scp=84929670650&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929670650&partnerID=8YFLogxK

U2 - 10.12988/ams.2015.411982

DO - 10.12988/ams.2015.411982

M3 - Article

VL - 9

SP - 1069

EP - 1076

JO - Applied Mathematical Sciences

T2 - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

SN - 1312-885X

IS - 21-24

ER -