# Convex combination and its application to fuzzy sets and interval-valued fuzzy sets I

Omar Salazar, Jairo Soriano

Research output: Contribution to journalArticle

### 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.

Original language English 1061-1068 8 Applied Mathematical Sciences 9 21-24 10.12988/ams.2015.411981 Published - 2015

### Fingerprint

Interval-valued Fuzzy Set
Fuzzy Intervals
Convex Combination
Fuzzy sets
Fuzzy Sets
Closed interval
Existence and Uniqueness Results
Injective
Straight Line
Convex Sets

### 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

In: Applied Mathematical Sciences, Vol. 9, No. 21-24, 2015, p. 1061-1068.

Research output: Contribution to journalArticle

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