A Fuzzy Vector Space On Consensus Space And Category Of Consensus Set

The dif initions of Consensus Space and Consensus Set are given by Hisakichi Suzuki. The discussions surrounding the above-mentioned difinitions are given in this paper.There are two main contents in this paper. The first part is about a fuzzy vetor space on Consensus Space. Firstly, the preliminaries are given. Secondly, concept of C-fuzzy subspace is given in the paper. It is proved thata ∧-fuzzy subspace is a C-fuzzy subspace and a C-fuzzy subspace is a fuzzysubspace based on t-norm. Each C-fuzzy subspace is isomorphic to a special C-fuzzy subspace.These discussions have built up a new theoretical foundation of fuzzy subspace.The second part is about category of Consensus Set. Firstly, the preliminaries are given. Secondly,according to objects and morphisms satisfying the specificcondition, category C(Ω) is built. We prove that it is a topos. Then we buildcategory CS(Ω) and obtain some qualities about it.