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Creating hypothesis combination operators is possible; in this figure hypothesis ha and hb are combined using a conjunction operator to produce hab.
This means that, unlike merging, combination operators cannot take into account cardinality considerations.
Two combination operators sum and product are used to produce two separate spatial likelihood functions (SLFs).
Another difference is that when combination operators are used, the information about the source of the knowledge bases is ignored.
The logical properties of such combination operators have been investigated in (Konieczny 2000) and compared to merging operators as defined in (Konieczny and Pino Pérez 1998, 1999).
Figure 2 Three common likelihood combination operators, normalized sum ( -norm), product ( -norm), and Hamacher -norm are illustrated along their resulting likelihoods.
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Criterion maps were combined using the fuzzy weighted linear combination operator.
In site selection for artificial recharge, the fuzzy algebraic product operator can be an appropriate combination operator, because at each location, the combined fuzzy membership value of the thematic maps to illustrate water depth, slope, drainage, soil, infiltration, lithology and landuse, and their characteristics is obtained.
The combining notion ⊕ here refers to the Dempster's combination operator, which is defined as the orthogonal sum (commutative and associative) as follows m = m 1 ⊕ m 2 ⊕ ⋅ ⋅ ⋅ ⊕ m m, where the aggregation m is expressed as m A = ∑ A 1, ⋯, A m ∈ Θ A 1 ∩ ⋯ ∩ A m ≠ ϕ m 1 A 1 ⋯ m m A m - 1 ⋅ ∑ A 1, ⋯, A m ∈ Θ A 1 ∩ ⋯ ∩ A m = A m 1 A 1 ⋅ ⋅ ⋅ m m A m.
The proposed algorithm integrates a distance-and-quality based solution combination operator and a tabu search procedure based on neighborhood combination of one-flip and constrained exchange moves.
Analysis indicates that the neighborhood combination and the solution combination operator play key roles to the effectiveness of the proposed algorithm.
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