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Home  >  Transactions of NAMP VOL 6

38. The theorems of Radon and Helly on convex fuzzy sets by T. O. Sangodapoa and D.O. Ajayi Transactions Vol. 6 (Jan., 2018), pp. 382{ 389
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The theorems of Radon and Helly on convex fuzzy sets

T. O. Sangodapoa and D.O. Ajayi

Department of Mathematics, University of Ibadan, Ibadan, Nigeria

Abstract. 

In Convex Geometry, the study of theorems of Radon, Helly and Caratheodory have played

important roles and their generalizations have been studied from di erent points of view such as Convex

Analysis, Optimization, Discrete Geometry. These theorems give excellent introduction to the theory of

convexity. In this paper, we consider Radon's theorem and Helly's theorem; and extend them to the fuzzy

case. In particular, we shall state and prove the fuzzy version of Radon's theorem and Helly's theorem.

Keywords: Fuzzy points, affinely independent sets, convex fuzzy sets, Radon's theorem, Helly's theorem

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