Multiset Context Research Articles

MULTISET TOPOLOGICAL SPACE AS GENERALIZATION OF THE CLASSICAL TOPOLOGICAL SPACE VIA SUPPORT SET

Multiset as a genelization of the classical set has triggered the definition and introduction of some algebraic structures in classical set theory under multiset context such as multiset topological spaces. In this paper we defined a root (support) set of a multiset topological space and established that multiset topological spaces are a generalizations classical topological spaces via their root sets respectively.

Accuracy measure of rough membership multiset functions with application

In this paper, the notion of rough membership function has been introduced in the multiset context. As a consequence, we introduced the lower and upper approximations in terms of the rough membership multiset functions. Finally, an application about how to select the best possible suppliers of chemicals has been presented.

MORE RESULTS ON MULTIRING

In this paper we extended the study of S. Debnath and A. Debnath(Debnath and Debnath, (2019)) on the study of ring structure from multiset context. We study more of the operations of multiset on the ring theory, where we discover that the raising to an arithmetic power of a multiring is again a multiring. So also is the composition of multirings. We also critically analyze the rootsets of multirings and introduces the concept multiring with unity, multiring and zero divisor among other results.

COMMUTATIVITY AND CANCELLABILITY OF FINITE SEMI-MULTIGROUPS

In this paper, the concept of Semi-group in multiset context is introduced. The condition for a sub multiset of a semi-multigroup to be a sub semi-multigroup is established and a study of the closure of multiset operationson the class of finite semi-multigroups is carried out.Commutative andcancellative properties of multiset operations on semi-multigroups are studied. We also studiedthe closure of multiset operations on the class of finite commutative and cancellative semi-multigroups.

Certain results on metric and norm in fuzzy multiset setting

Fuzzy multiset is an extension of fuzzy set in multiset framework. In this paper, we review the concept of fuzzy multisets and study the notions of metric and norm on fuzzy multiset. Some results on metric and norm are established in fuzzy multiset context.

Associative filters and associative pseudofilters of residuated lattices in multiset context

Abstract There is an open problem in [5] stated as follows: “Is there a suitable and useful definition of associative filter in residuated lattice?” Yes, here the concept is defined as follows: filter F is associative of L if α → (β → ω) ∈ F ⇔ (α → β) → ω ∈ F for any α,β,ω ∈ L. Also this concept is developed in the context of multisets and thus the notions of multiset associative filter, multiset pre-associative filter, multiset associative pseudofilter have been introduced followed by the relationship between multiset associative filter and other multiset filters have been found.

Multiset filters

A multiset is a collection of objects in which repetition of elements is essential. This paper is an attempt to generalize the notion of filters in the multiset context. In addition, many deviations between multiset filters and ordinary filters have been presented. The relation between multiset filter and multiset ideal has been mentioned. Many properties of multiset filters, multiset ultrafilters, and convergence of multiset filters have been introduced. Also, the notions of basis and subbasis have been mentioned in the multiset context. Finally, several examples have been studied.

Implicative and positive implicative filters of residuated lattices in multiset context

In this paper, we introduce the concept of multiset implicative filter and multiset positive implicative filter of residuated lattice. Also, we discuss their characterizations and we show that M is a multiset implicative filter of X if and only if the quotient residuated lattice X/M is a Heyting algebra.

On multiset group

The concept of multiset is a generalization of Cantor set. In this paper we have attempted to generalize the concept of group in the multiset context and define multiset subgroup and studied some of their basic properties.

On relationship between generalized rough multisets and multiset topologies

The purpose of this paper is to investigate the relationship between multiset topology (M-topology) and generalized rough multiset induced by multiset relation. The notion of transitive closure of a relation is proposed in multiset context. The notable results we establish here are (1) any serial multiset relation induce an M-topology (2) any reflexive multiset relation R and its transitive closure t(R) induce the same M-topology, i.e., \(\tau (R)=\tau (t(R))\). The interior and closure operators of the M-topology \(\tau (R)\) is obtained and discuss their relationship with multiset relation R, when R is a reflexive multiset relation. On the other part, we consider the case when R is a tolerance multiset relation.

Multiset proximity spaces

Abstract A multiset is a collection of objects in which repetition of elements is essential. This paper is an attempt to explore the theoretical aspects of multiset by extending the notions of compact, proximity relation and proximal neighborhood to the multiset context. Examples of new multiset topologies, open multiset cover, compact multiset and many identities involving the concept of multiset have been introduced. Further, an integral examples of multiset proximity relations are obtained. A multiset topology induced by a multiset proximity relation on a multiset M has been presented. Also the concept of multiset δ - neighborhood in the multiset proximity space which furnishes an alternative approach to the study of multiset proximity spaces has been mentioned. Finally, some results on this new approach have been obtained and one of the most important results is: every T 4 - multiset space is semi-compatible with multiset proximity relation δ on M ( Theorem 5.10 ).

Symmetric Groups under multiset perspective

A multiset is a collection of objects in which repetition of elements is significant. In this paper an attempt to define a symmetric group under multiset context is presented and the analogous to Cayley's theorem is derived.

Relations and functions in multiset context

A multiset is a collection of objects in which repetition of elements is significant. In this paper an attempt is made to generalize the concepts of relation, function, composition and equivalence in the multiset context. As a pre-requisite a brief survey of the axiomatic approach to the multiset theory is also presented.

Towards a Symbolic Interpretation of Approximate Reasoning

We study knowledge-based systems using symbolic many-valued logic and we focus on the management of knowledge through linguistic concepts characterized by vague terms or labels. In previous papers we have proposed a symbolic representation of nuanced statements. In this representation, we have interpreated some nuances of natural language as linguistic modifiers and we have defined them within a multiset context. In this paper, we continue the presentation of our symbolic model and we propose new deduction rules dealing with nuanced statements. We limit ourself to present new generalizations of the Modus Ponens rules dealing with nuanced statements.