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Relaxed Intersection
The ''relaxed intersection'' of ''m'' sets corresponds to the classical intersection between sets except that it is allowed to relax few sets in order to avoid an empty intersection. This notion can be used to solve Constraint satisfaction problem, constraints satisfaction problems that are inconsistent by Maximum satisfiability problem, relaxing a small number of constraints. When a set estimation, bounded-error approach is considered for parameter estimation, the relaxed intersection makes it possible to be robust with respect to some outliers. Definition The ''q''-relaxed intersection of the ''m'' subsets X_,\dots ,X_ of R^, denoted by X^=\bigcap^X_ is the set of all x \in R^ which belong to all X_ 's, except q at most. This definition is illustrated by Figure 1. Define \lambda (x) =\text \left\. We have X^=\lambda ^([m-q,m]) . Characterizing the q-relaxed intersection is a thus a set inversion problem. Example Consider 8 intervals: X_=[1,4], X_=\ [2,4], ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Satisfaction Problem
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
