In this paper, we reintroduce the class of pogroupoids as another class of groupoids (binary systems) associated with posets having minimal elements in a categorical/functorial fashion. Having done we investigate several of its resulting properties. Finally, we introduce results of an associated fuzzy nature and we also develop a method of fixing many scalar fields as fuzzy fields/spaces using a parameter system described below in a simple manner. Moreover, we discuss and analyze fuzzy structure mappings in posets and pogroupoids, and its extension of fuzzy sets and fuzzy spaces.

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, with Professor J. Neggers, and published 240 research papers in several journals. His mathematical research areas are BCK-algebras, fuzzy theory, poset theory and theory of semirings, and Fibonacci functions. He is reviewing many papers in these areas also. He is working as (managing) editors in 5 journals such as Advances in Theoretical and Applied Mathematics, International Reviews of Fuzzy Mathematics, JP J. Algebra, Number Theory and Applications, The World Scientific Journal. He has concerned on martial arts, photography and poetry also.