In this paper, we have generalized the definition of vector space by considering the group as a canonical $m$-ary hypergroup, the field as a krasner $(m,n)$-hyperfield and considering the multiplication structure of a vector by a scalar as hyperstructure. Also we will be consider a normed $m$-ary hypervector space and introduce the concept of convergence of sequence on $m$-ary hypernormed space...

We have enhanced the fuzzy set model by replacing MIN and MAX operators with binary positively compensatory operators. Though the binary operators provide higher retrieval eeectiveness, they can give diierent document values for logically equivalent queries, e.g. t1 AND (t2 AND t3) and (t1 AND t2) AND t3. This is because they do not satisfy the basic boolean processing laws such as distributive...

We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary operators. Then we generalize them to n-ary fuzzy logic and neutrosophic logic operators using the smarandache codification of the Venn diagram and a defined vector neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built. Introduction. For the beginning let’s con...