Abstract
This paper showed a short characterization of the convex combi- nation operation introduced by Zadeh to fuzzy sets. We proved some properties and established two basic results (existence and uniqueness) in the representation of a fuzzy set as a convex combination. Our the- ory was based on the fact that a closed interval [a, b] of real numbers is a convex set, and the fact that a straight-line function from [0, 1] into [a, b] is surjective always, and additionally, it is injective if a <b. We showed some examples in order to illustrate our ideas.
| Language | English |
|---|---|
| Pages | 1061-1068 |
| Number of pages | 8 |
| Journal | Applied Mathematical Sciences |
| Volume | 9 |
| Issue number | 21-24 |
| DOIs | |
| Publication status | Published - 2015 |
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Keywords
- Convex combination
- Embedded fuzzy set
- Fuzzy set
- In-terval 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 I. / Salazar, Omar; Soriano, Jairo.
In: Applied Mathematical Sciences, Vol. 9, No. 21-24, 2015, p. 1061-1068.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Convex combination and its application to fuzzy sets and interval-valued fuzzy sets I
AU - Salazar, Omar
AU - Soriano, Jairo
PY - 2015
Y1 - 2015
N2 - This paper showed a short characterization of the convex combi- nation operation introduced by Zadeh to fuzzy sets. We proved some properties and established two basic results (existence and uniqueness) in the representation of a fuzzy set as a convex combination. Our the- ory was based on the fact that a closed interval [a, b] of real numbers is a convex set, and the fact that a straight-line function from [0, 1] into [a, b] is surjective always, and additionally, it is injective if a
AB - This paper showed a short characterization of the convex combi- nation operation introduced by Zadeh to fuzzy sets. We proved some properties and established two basic results (existence and uniqueness) in the representation of a fuzzy set as a convex combination. Our the- ory was based on the fact that a closed interval [a, b] of real numbers is a convex set, and the fact that a straight-line function from [0, 1] into [a, b] is surjective always, and additionally, it is injective if a
KW - Convex combination
KW - Embedded fuzzy set
KW - Fuzzy set
KW - In-terval type-2 fuzzy set
KW - Interval-valued fuzzy set
KW - Membership function
UR - http://www.scopus.com/inward/record.url?scp=84929692643&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84929692643&partnerID=8YFLogxK
U2 - 10.12988/ams.2015.411981
DO - 10.12988/ams.2015.411981
M3 - Article
VL - 9
SP - 1061
EP - 1068
JO - Applied Mathematical Sciences
T2 - Applied Mathematical Sciences
JF - Applied Mathematical Sciences
SN - 1312-885X
IS - 21-24
ER -