This paper is an attempt to summarize most things that are related to multiset theory. We begin by describing multisets and the operations between them. Then we present hybrid sets and their operations. We continue with a categorical approach to multisets. Next, we present fuzzy multisets and their operations. Finally, we present partially ordered multisets.

This introduction to the R package sets is a (slightly) modified version of Meyer and Hornik (2009a), published in the Journal of Statistical Software. We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Fu...

To study the various algebraic structures of intuitionistic fuzzy multisets, in this paper the concept of intuitionistic fuzzy multi groups are introduced and its various properties are discussed

an orthogonal approach to the fuzzification of both multisets and hybridsets is presented. in particular, we introduce $l$-multi-fuzzy and$l$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. in addition, we study the properties ofthese structures. also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...

The content of a membrane in a configuration of an ‘exact’ P system is described by a multiset. Recall that a (crisp) multiset over a set of types X is simply a mapping d : X → N. The usual interpretation of a multiset d : X → N is that it describes a set consisting of d(x) “exact” copies of each type x ∈ X. In particular, it is assumed that the set described by the multiset does not contain an...

This paper proposes a generalized distance measure and its similarity measures between single valued neutrosophic multisets (SVNMs). Then, the similarity measures are applied to a medical diagnosis problem with incomplete, indeterminate and inconsistent information. This diagnosis method can deal with the diagnosis problem with indeterminate and inconsistent information which cannot be handled ...