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Functions
Published in Janet Woodcock, Software Engineering Mathematics, 1988
A surjective function from A to B is one where the range is the whole of B. Recalling what we said about functionality and injectivity, it is worth noting here that totality and surjectivity are dual notions: a function / is surjective whenever f~l is total. We define the set of all partial surjections from A to £ as
Scaled group consensus in multi-agent networks with high-order continuous dynamics
Published in International Journal of Systems Science, 2020
Junyan Yu, Qiongyan Yu, Mei Yu, Yanping Gao
We assume that all agents in the network is divided into q groups with . Denote with , for all , and . For any l satisfying , the set of neighbours in group l of node is denoted by . For designing a scaled group consensus protocol, we define a surjective function with two finite sets and Q containing q nonzero real numbers , and satisfying for any .
RPMInter-work: a multi-agent approach for planning the task-role assignments in inter-organisational workflow
Published in Enterprise Information Systems, 2020
Meriam Jemel, Nadia Ben Azzouna, Khaled Ghedira
Using the notions presented above, we define a valid role plan as follows: Definition 3.8. (Valid role plan)Let be a constrained inter-organisational workflow schema, a role plan is a function .● is authorised in if .● satisfies if () where .● is valid if it is authorised in and it satisfies all the constraints in . is a surjective function since a role can be assigned to multiple tasks.
The implications obtained by two given implications on bounded lattices
Published in International Journal of General Systems, 2021
Funda Karaçal, M. Nesibe Kesicioğlu, Ümit Ertuğrul
If or , then the function on , defined by for any x, y, is surjective. Indeed, for all , there exists an element such that Also, there exists such that Thus, α is a surjective function on .