| Biography | |
|---|---|
 Prof. Hee Sik Kim Hanyang University, Korea, Republic of Korea |
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| Title: Probability functions on partially ordered sets | |
| Abstract: In this talk, we define a probability function on a poset which is similar to the probability function on $d/BCK$-algebras, and obtain several probability functions on posets. Moreover, we discuss probability functions on an order geometry.
We obtain the following: Theorem 1. If π is a probability function on a poset (P, ≤), then y<z implies π(z,x)≤π(y,x) for all x,y,z.
Theorem 2. Let (P,≤) be a finite poset. If we define a mapping Π: P^2 →[0,1] by Π(x,y) : = |L(P; x≤y)|/|L(P) For all x, y ∈P, then Π is a probability function on P.
Theorem 3. Let (P, ≤) be a poset and ∧be a linear extension of (P, ≤). Then Π is a probability function on P. | |
| Biography:
Hee Sik Kim is working at Department of Mathematics, Hanyang University as a professor. He has received his Ph.D. at Yonsei University. He has published a book, `Basic Posets, World Scientific Publ. Co., Singapore, 1988’ with Professor J. Neggers, and published 250 research papers in several journals. His mathematical research areas are BCK-algebras, graph theory, poset theory and theory of semirings, fuzzy algebra, theory of groupoids and Fibonacci numbers. He is reviewing many papers in these areas also. He is working as (managing) editors in 6 journals such as Advances in Theoretical and Applied Mathematics, International Reviews of Fuzzy Mathematics, JP J. Algebra, Number Theory and Applications, World Scientific Journal. He is engaged in martial arts, photography and poetry also.
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