Operator intersection

The final degree-of-satisfaction resulting from certain variable set, nv(xy) can be determined by aggregating the degree-of-satisfaction for all objectives, /ijs (xv), s e S. via specific fuzzy intersection operator, T. 

Using the fuzzy intersection operator, the original multiobjective optimization problem, Eq. (11), is converted into a single objective problem, Eq. (17). Several operators for implementing fuzzy intersection can be selected for T, therein two most popular ones are shown below. 

There are three reference operators the range operator (colon), the union operator (comma) and the intersection operator (space). The range operator produces a reference that includes all the cells between and including the two references, e.g., G3 L3. The union operator produces a reference that includes the... 

Figure 3-1. A single cell reference (F5) produced by the intersection operator.

The first character of a name must be a letter. Subsequent characters can be letters or numbers or the period or underline character. Spaces are not allowed (the space character is the intersection operator) Excel will substitute an underline character for a space in any name that it proposes based on text in worksheet cells. 

If the data table is a two-dimensional one, as in Figure 3-7, cells are referenced both by row and by column. Excel proposes the row and column titles as names, as shown in the Create Names dialog box of Figure 3-8. Excel will apply the name max to the range F5 I5, the name band1 to the range F5 F7, etc. The intersection operator (the space character) can then be used to identify the named variables. For example, bands A 0 refers to cell H6. 

NULL is displayed if you have used the intersection operator to specify an intersection of two references that do not intersect. 

VBA can create references by using methods that are the equivalents of the union operator or intersection operator described in Chapter 3. The Union method creates a reference that includes multiple selections, e.g., A1,B5 or G3 L3,G5 L5. The syntax of the Union method is Un on range1, range2). The intersect method creates a reference that is common to two references (e.g.. 

Equation (2.2-56) is most easily solved graphically by determining the mutual intersection (= operating point) of the S-shaped curve and the straight line as... 

In our example of a hyperstructure covering 4 individual structures, the question of the justification of its introduction and use boils down to comparing the computational effort required for performing the four separate substructure searches in the four individual structures, with the summary computational effort required for performing one such search in the hyperstructure, combined with the set intersection operations following each separate bond matching step in the atom-by-atom substructure procedure. 

The level curve model represents the geometric object by its intersections with a number of parallel, equidistant planes. The resulting curves define levels of equal height and thus are very similar to the depiction of landscape surveys in maps. To intersect the represented workpiece with a tool, it is sufficient to determine the section of the tool in the respective plane and to intersect the resulting section line with the respective level curve. This operation can be carried out much more easily than with the general polyhedron model since it is a two-dimensional intersection operation (Fig. 3). 

In reliability analyses of lane group operation it is key to determine boundary traffic conditions at which a transition from reliability to failure occurs. Reliability status covers the period of time in which the intersection operates without problems, i.e. when traffic intensity Q is less than capacity C (usually between peak periods or in night-time conditions). During traffic peak periods entries to intersections can also function reliably when traffic intensity is low and delays are accepted by all drivers. Where traffic intensity Q is close to or exceeds capacity C the conditions at entries to the intersection are characterized by failure and long and unacceptable queues and delays. On the lane in question unreliability occurred both in morning and afternoon peaks (Table 1). 

Ostrowski, K. 2010. Reliability of signalized intersection operation at variable saturation flows (in polish). PhD. Thesis. Cracow University of Technology. Poland. 

Commonly, within the arithmetic interval approach, judgments combination is performed by the classical mean, union or intersection operators. The mean and the intersection operators lead to a reduction of the aggregated interval, namely some values that sources of information consider as possible are ignored. Otherwise, by the union operator the aggregated interval expresses the highest level of uncertainty of the aggregated judgments. In the classic fuzzy approach, each interval information... 

Furthermore, one believes that the suggested aggregation rule is able to adequately synthesize the available information. In fact, the intersection operator allows at taking into account the concordance among expert judgments and results into the crisp part of the FuBI, whereas the uncertainty associated with the discordance is expressed by means of fuzzy numbers. Furthermore, the totally available information is saved and results into the support of the FuBI associated with each basic event. 

This relation expresses the fact that the points referenced by the results attribute have been produced in the sending CAD system by intersecting the two-dimensional wireframe model referenced by the geometry attribute with the test line. The CAD system user in the receiving environment may use this information to test the accuracy of the transmitted geometry by repeating this intersection operation. 

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