A multiset is a set containing repeated elements. The objective of this paper is to combine the innovative concept of multisets and polygroups. In particular, we use multisets and fuzzy multisets to ...introduce the concepts of multi-polygroups and fuzzy multi-polygroups respectively and we discuss their properties. Moreover, we construct fuzzy multi-polygroups from multi-polygroups.
Polygroups are a special subclass of hypergroups that satisfies group-like axioms. A polygroup is a multigroup that is completely regular and reversible in itself. A topological polygroup is a ...polygroup P with a topology on P that satisfies certain conditions. Moreover, the concept of soft sets is a general mathematical tool for dealing with uncertainty. In this study, we investigate soft topological polygroups over a polygroup. The ideas presented in this article can be used to build more polygroups and soft topological polygroups. KCI Citation Count: 0
Recently, fuzzy
n
-ary sub-polygroups were introduced and studied by Davvaz, Corsini and Leoreanu-Fotea B. Davvaz, P. Corsini, V. Leoreanu-Fotea, Fuzzy
n
-ary sub-polygroups, Comput. Math. Appl. 57 ...(2008) 141–152. Now, in this paper, the concept of
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∈
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-fuzzy
n
-ary sub-polygroups,
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,
∈
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∨
q
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-fuzzy
n
-ary sub-polygroups and fuzzy
n
-ary sub-polygroup with thresholds of an
n
-ary polygroup are introduced and some characterizations are described. Also, we give the definition of implication-based fuzzy
n
-ary sub-polygroups in an
n
-ary polygroup, in particular, the implication operators in Łukasiewicz system of continuous-valued logic are discussed.
Studies on fuzzy topological polygroups Abbasizadeh, N.; Davvaz, B.; Leoreanu-Fotea, V.
Journal of intelligent & fuzzy systems,
01/2017, Volume:
32, Issue:
1
Journal Article
Peer reviewed
In this paper, we study fuzzy topological polygroups and prove some results in this respect. Denote by FC (Y, Z) the set of all fuzzy continuous functions from a fuzzy topological space Y into a ...fuzzy topological space Z. Our aim in this paper is to study a polygroup, fuzzy polygroup, topological polygroup and fuzzy topological polygroup structure on the (fuzzy) function space FC (Y, Z). Also, we study induced fuzzy topological polygroups. It is shown that if ( P , T ) is a usual topological polygroup, then the induced fuzzy topology ω ( T ) on IP makes ( P , ω ( T ) ) a fuzzy topologiccal polygroup.
The purpose of this paper is to provide a detailed structure description of derived subpolygroups of polygroups. We introduce the concept of perfect and solvable polygroups and we give some results ...in this respect. Finally, we discuss on τ-multi-semi-direct hyperproduct of polygroups.
The combination of two elements in a group structure is an element, while, in a hypergroup, the combination of two elements is a non-empty set. The use of hypergroups appears mainly in certain ...subclasses. For instance, polygroups, which are a special subcategory of hypergroups, are used in many branches of mathematics and basic sciences. On the other hand, in a multi-fuzzy set, an element of a universal set may occur more than once with possibly the same or different membership values. A soft set over a universal set is a mapping from parameters to the family of subsets of the universal set. If we substitute the set of all fuzzy subsets of the universal set instead of crisp subsets, then we obtain fuzzy soft sets. Similarly, multi-fuzzy soft sets can be obtained. In this paper, we combine the multi-fuzzy soft set and polygroup structure, from which we obtain a new soft structure called the multi-fuzzy soft polygroup. We analyze the relation between multi-fuzzy soft sets and polygroups. Some algebraic properties of fuzzy soft polygroups and soft polygroups are extended to multi-fuzzy soft polygroups. Some new operations on a multi-fuzzy soft set are defined. In addition to this, we investigate normal multi-fuzzy soft polygroups and present some of their algebraic properties.
This paper provides a new connection between algebraic hyperstructures and fuzzy sets. We present the concept of I-fuzzy topological polygroups and prove some properties. The concept of I-fuzzy ...topological polygroups is a generalization of the concept of I-fuzzy topological groups. By considering the relative fuzzy topology on fuzzy subpolygroups we prove some related properties.
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