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The 2000s and Onward
Published in Sidney Dekker, Foundations of Safety Science, 2019
A substantial part of people’s construction of safety, says the interpretivist approach, is reflexive. Reflexive is a term that comes originally from grammar, meaning that what is said refers back to the subject of the clause (e.g., I hurt myself). In the social sciences, reflexive means that our understanding of something has to take into account the effect we ourselves have on what is being investigated. Safety, then, is also something that people relate to themselves. If safety is reflexive, or a ‘reflexive project,’ then people constantly assess their own competence or skill in maintaining safety across different situations.
Vectorial Ekeland variational principle for cyclically antimonotone vector equilibrium problems
Published in Optimization, 2020
Chuang-liang Zhang, Nan-jing Huang
Let be a proper convex cone, that is, , and for every . Clearly, for all , and . Moreover, if D is algebraically solid with , by Proposition 2.3 in [14], we know that vcl = vclD. Recall that is a quasi order (a reflexive and transitive relation) induced by D on Y if, for all , Given , we define a quasi order on Y as follows: for any , Moreover, if D is algebraically solid, we define an order on Y as follows: for any ,
The class of states of the world as an
Published in International Journal of General Systems, 2018
Fernando Tohmé, Gianluca Caterina, Rocco Gangle
Proof We can check this for since the argument for is strictly analogous. By our definition is a partially ordered set. In fact, it is easy to check that is a reflexive (when K is infinite) and transitive relation.The chains of elements ordered by inclusion are understood as simplexes corresponding to [k] and each subchain with one element eliminated (a chain of length k) is a face.This construction is the nerve of . The nerve of any poset (and actually of any small category) is a simplicial set (see Section 1.4 in Joyal and Tierney (2008)).
Convex-cone-based comparisons of and difference evaluations for fuzzy sets
Published in Optimization, 2018
Unless otherwise stated, let V be a real topological vector space. The power set of V is denoted by . The interior, closure, convex hull, and complement of a set A are denoted by , , , and , respectively. A set is a cone if for all and . The transitive relation is induced by a convex cone C as follows: for , , if . If the zero vector belongs to C, then is reflexive and hence a preorder (that is, a reflexive, transitive relation). If not, then is irreflexive and hence a strict order (that is, an irreflexive, transitive relation).