The concept of entropy is one the most important notions information theory. Entropy quantifies amount uncertainty involved in value a random variable or outcome process. Shannon’s useful types. notion enthalpy energy expressed by complement entropy. In this paper, we propose interval-valued hybrid fuzzy set modifying single and multisets. context, an contains about both data their We also prov...

Markov categories, having tensors with copying and discarding, provide a setting for categorical probability. This paper uses finite colimits what we call uniform states in such categories to define (fixed size) multiset functor, basic operations sums zips of multisets, graded monad structure. Multisets can be used represent both urns filled coloured balls also draws multiple from urns. The mai...

In this work we discuss a parameter $\sigma$ on weighted $k$-element multisets of $[n]= \{1,\dots ,n\}$. The sums $k$-multisets are related to $k$-subsets, $k$-multisets, as well special instances truncated interpolated multiple zeta values. We study properties using symbolic combinatorics. (re)derive and extend certain identities for $\zeta^{t}_n(\{m\}_k)$. Moreover, introduce random variables...

Membrane computing is a formal computational paradigm, invented in 1998 by Gh. Păun [5], that rewrites multisets of objects within a spatial structure inspired by the membrane structure of living cells and according to evolution rules that are reminiscent of the processes that take place inside cells. In this paper we use techniques based on fuzzy sets to develop a general membrane computing mo...

The paper presents an axiomatisation for functional dependencies on trees that are defined using constructors for records, lists, sets and multisets. A simple form of restructuring permitting lists to be mapped onto multisets and multisets onto sets is added to the theory. Furthermore, the theory handles dependencies on sets treated as multisets. This adds the possibility to use the count of el...

In this paper, we have investigated single valued neutrosophic multisets in detail. Several operations have been defined on them and their important algebraic properties are studied.We have further introduced the notion of distance and similarity measures between two single valued neutrosophic multisets. An application of single valued neutrosophic multisets in medical diagnosis has been discus...

This paper proposes a novel way of introducing multisets into declarative programming languages. Starting from a standard deenition of a multiset, suitable operations on multisets are deened and implemented in a declarative programming language, and a variety of programming examples are given to illustrate the utility of the ideas. This approach to multisets is compared with their treatment in ...