Topic
Hyperoperation
About: Hyperoperation is a research topic. Over the lifetime, 61 publications have been published within this topic receiving 522 citations. The topic is also known as: hyperoperation sequence & hyperoperations.
Papers published on a yearly basis
Papers
TL;DR: It is shown that (X, *p), the family of join spaces on a generalized deMorgan lattice, is aL-fuzzy hypergroup (in the sense of Corsini) and can be considered as a lFuzzy join space.
Abstract: On a generalized deMorgan lattice (X, ≤, ∨, ∧,′) we introduce a family of join hyperoperations *
p
, parametrized by a parameterp eX. As a result we obtain a family of join spaces (X, *
p
). We show that: for everya,b eX the family {a*pb}
peX
can be considered as thep-cuts of aL-fuzzy seta*b; in this manner we synthesize aL-fuzzy hyperoperation * which takes pairs fromX toL-fuzzy subsets ofX. We then show that (X, *
p
) is aL-fuzzy hypergroup (in the sense of Corsini) and can be considered as aL-fuzzy join space. Furthermore,a*b is aL-fuzzy interval for alla,b eX.
40 citations
TL;DR: The set of all Hv-groups with a scalar unit, defined on a set with three elements is determined using the property of weak associative hyperoperation.
39 citations
27 May 1998
TL;DR: This work embeds hyperoperations on A into the set Q of all /spl sube/-isotone operations on P and reduces the case of equivalence relations and shows that two types of maximal clones on P produce no maximal subclone of Q.
Abstract: An n-ary hyperoperation on A is a map from A/sup n/ into the set P of nonvoid subsets of A. A hyperclone on A is a set of hyperoperations on A containing all projections and closed with respect to a natural composition. Although special hyperalgebras, like hypergroups, hyperrings etc., have been studied for 6 decades there is no universal-algebra type theory for hyperalgebras. We try to close this gap by embedding hyperoperations on A into the set Q of all /spl sube/-isotone operations on P. The very crucial compatible relations are introduced through this embedding. For A finite we search for a general completeness criterion and the related maximal hyperclones via the maximal subclones of Q. For this we determine the position of Q in the lattice of clones on P and initiate the study of such meet-reducible clones. We find all such clones of the form Q/spl cap/Pol /spl rho/ where /spl rho/ is a proper unary relation on P, toe reduce the case of equivalence relations and show that two types of maximal clones on P produce no maximal subclone of Q.
29 citations
TL;DR: A family of crisp hyperoperations ⊔p (one hyperoperation for each p∈X) is defined and it is shown that, for every p, the hyperalgebra (X, ⊢p) is a join space and thehyperalgebra(X,⊔ p, ∧) is very similar to a hyperlattice.
27 citations
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TL;DR: It is proved that with every fuzzy hyperalgebra the authors can associate a uniquehyperalgebra via a regular (resp., strongly regular) relation.
Abstract: We introduce and study the notion of fuzzy multialgebras on the basis of a new definition of a fuzzy hyperoperation. We introduce the notion of fuzzy regular (resp., fuzzy strongly regular) relations of hyperalgebras and obtain their basic properties. Finally, we prove that with every fuzzy hyperalgebra we can associate a unique hyperalgebra via a regular (resp., strongly regular) relation.
20 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 5 |
| 2019 | 3 |
| 2017 | 5 |
| 2016 | 4 |
| 2015 | 9 |