Hyperfuzzy subsets and subgroupoids

Liu, Yong Lin; Kim, Hee Sik; Neggers, J.

doi:10.3233/jifs-17104

Cited by 4 publications

(1 citation statement)

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“…Boruvka [2] stated the theory of decompositions of sets and its application to binary systems. Recently, some interesting results in groupoids were investigated by several researchers [3][4][5][6]. Semigroups are in fact the first and simplest type of algebra to which the methods of universal algebra must be applied, and any mathematician interested in universal algebra will find semigroup theory a rewarding study [7].…”

Section: Introductionmentioning

confidence: 99%

Some Special Elements and Pseudo Inverse Functions in Groupoids

2019

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In this paper, we consider a theory of elements u of a groupoid ( X , * ) that are associated with certain functions u ^ : X → X , pseudo-inverse functions, which are generalizations of the inverses associated with units of groupoids with identity elements. If classifying the elements u as special of one of twelve types, then it is possible to do a rather detailed analysis of certain cases, leftoids, rightoids and linear groupoids included, which demonstrates that it is possible to develop a successful theory and that a good deal of information has already been obtained with much more possible in the future.

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Section: Introductionmentioning

confidence: 99%

Some Special Elements and Pseudo Inverse Functions in Groupoids

2019

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Independence concepts for groupoids

Rezaei

Kim

Saeid

2023

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset. Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.

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