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

Omar Salazar, Jairo Soriano

Research output: Contribution to journalArticle

6 Citations (Scopus)

### 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.

Original language English 1069-1076 8 Applied Mathematical Sciences 9 21-24 10.12988/ams.2015.411982 Published - 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

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

Research output: Contribution to journalArticle

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