ࡱ> :=789 Ibjbj 3&hh@  OOOOOccc8OcOKJJJJJJJ;MOJOJOO K/!/!/!OOJ/!J/!/!vDHcFF4JK0OKzFPP PhHPOH"$/!<PJJ/!OKP : Decision Tables Abstract. A decision table is a chart graphically showing what actions are performed when the controlling circumstances of an action change and when the actions governing conditions have various values. This lesson presents logical, pedagogical and practical principles for error avoidance in constructing tables, enhancement of traditional tables, systematic construction, and radical simplification of decision tables and thereby the original verbal policy. The purposes of decision tables and the enhancements presented To represent an organizations policy in a more understandable, non-verbal format. Once constructed, the table may be simplified for prospective users by eliminating overlapping and irrelevant items. By constructing the visual table, one can facilitate the coding of conditional statements in a spreadsheet or computer program and increase the chances of this being done correctly. Decision tables are especially suited for representing case-structures in programming languages, e.g., COBOLs EVALUATE verb. To analyze the actions that are needed for all possible sets of condition-values, not just those that seem obvious or may have been indicated verbally and too informally by a policy maker. To call attention to a set of conditions for which no action was specified in the original verbal policy statement, but which might still matter. Use of the techniques presented here helps ensure that no possible set of condition-values escapes consideration, thereby protecting the organization from overlooking what the corresponding appropriate actions are. Rules may be read off from the columns involving condition values. By numbering the statements expressing the policy or situation to be diagrammed, retracing the logic behind determining the actions is facilitated. Basic ideas Consider this policy of a certain department store: POLICY STATEMENT #1: Display small and yellow dresses, on floor #1, and do not display them on floor #2. POLICY STATEMENT #2: If a dress is either large or green, then display it only on the second floor. By way of illustrating how to construct the type of decision table proposed here, consider:  CONDITION NAMES ABBREVIATED CONDITION VALUE NAMES NUMBER OF CONDITION VALUES RULES (WITH RULE NOS.)1234CONDITION VALUE SETS CONDITIONSDRESS-SIZE[L,S](2)LLSSCOLOR[G,Y](2)GYGYACTION VALUE SETS ACTIONSDISPLAY ON FLOOR 1NNNYDISPLAY ON FLOOR 2YYYN This decision table constitutes the basic model for most of the discussion below. Already one might notice that the style and content differ from traditional, familiar tables. Along the way, other changes will be introduced gradually. This table is designed to represent a policy that involves two conditions. One condition is DRESS-SIZE, which here takes on 2 values, namely, LARGE and SMALL, abbreviated as L and S. Additionally there is another condition, COLOR, which takes values GREEN and YELLOW. Moreover, the table specifies certain pairs of actions and/or prohibited actions for each governing pair of condition-values. When an action governed by a set of values in a column is to be performed, that is signified by a Y; if the action is prohibited, by an N. A pair (or any size set) of condition-values governs one or more actions. Such a governing set (like L and G in the table above) always takes one condition-value from each condition/row and treats the corresponding conditions as if they were parts of a grand premise of a rule. To illustrate, consider condition values SMALL and YELLOW, which appear in this statement of a certain department stores stocking policy. This pair determines that small and yellow dresses will be displayed on floor #1, but not on floor #2. To sum up what we have so far, a decision table column on the right side represents a rule. A rule indicates what action or actions are to be performed provided a certain set of condition-values obtains. The action-values appear in the lower section of the same rule-column (just below the governing combination of condition-values). Thus, Rule/Column #1 asserts that IF THE SIZE OF A DRESS IS LARGE AND GREEN, THEN DO NOT DISPLAY THE DRESS ON FLOOR 1, BUT DISPLAY THE DRESS ON FLOOR 2. Constructing a table The first step is to determine the condition, actions, and their respective possible values by analyzing the verbal policy. List all possible permutations of condition values in a systematic way following the information next to the condition-name. Next, one calculates the number of columns to allow for all possible rules by taking the product of the numbers of condition values. In the table above, there are two values in the each of the two conditions; hence, there are four columns for rules. Each such column potentially constitutes a rule for action. In the table below, the string of condition-values along the rows for each condition are obtained as follows: MULTIPLY ALL THE NUMBERS GIVING THE NUMBER OF VALUES IN EACH CONDITION TOGETHER. THAT PRODUCT GIVES THE NUMBER OF RULES/COLUMNS. [Note: These are the numbers in parentheses after the condition-name abbreviations.] DIVIDE THE NUMBER IN ROW 1 INTO THIS PRODUCT, GIVING THE LENGTH OF A STREAK. A STREAK IS THE LENGTH OF REPEATED CONDITION VALUES IN THE ROW TO THE RIGHT OF THE CONDITION. [Note: In the table above, the streak is the result of four divided by 2 (which is 2). There is one streak of two Ts followed by a streak of 2 Fs. One alternates streaks all the way across. FOR EACH SUCCESSIVE ROW, DIVIDE ITS NUMBER OF CONDITION VALUES (ALWAYS THE NUMBER IN PARENTHESES) INTO THE PREVIOUS ROWS STREAK LENGTH. IN THE TABLE BELOW, DIVIDE 2 INTO 2 GIVING 1. Here, alternate a streak of one T with one F all the way across. RULES1234COND-1 [T,F](2)TTFFCOND-2 [T,F](2)TFTFACTION-1 YXNYACTION-2 NXUY The four quadrants with bold, black borders, are sometimes called stubs. These will be referred to by location: UL (UPPER LEFT), UR (UPPER RIGHT), LL (LOWER LEFT), LR (LOWER RIGHT). The columns intersecting UR and LR now represent IF-THEN rules. The IF-conditions are derived from the UR part of a column and the THEN-actions are indicated by the LR part of a column. UL: lists the conditions. A number in parentheses indicates how many values each condition will have in the table; finally, all the condition-values to be used are shown in brackets. Planning just this quadrant often sharpens thinking for the entire decision making process. In this example, the condition-values are T and F, but not always--they could, in case of a SIZE condition be given in the presently proposed notation as (3) [S, M, L], for Small, Medium, Large. When it is later discovered that the values of a condition do not have any influence on whether a certain action is performed, one can place a dash in the relevant cells. UR: gives all permutations of the condition-values for each set of conditions. LL: simply lists the relevant actions. An enhancement is possible here by listing the actions in the sequence in which they will be performedif that is important. Decision tables have been criticized for lacking that capability (Rademacher et al. 1982). Sequence could be represented most simply by the action listing order or else by a numeral attached to the action name. If the sequence of actions were to vary from column to column, one could numerically subscript the action values within each column to reflect this. For example, we could indicate that a lower action must precede an upper action by T2 over T1 in LR. LR: Symbols in each cell indicate whether or not the associated row action is to be performed, given the condition-values of the column. Y = the action should be done; N = the action is definitely not done. X = impossible (i.e., the combination of condition-values in the UR part of the column could never occur simultaneously)i.e., the rule never applies. If there is even one X in the LR part of a column, all the other entries there must logically be X's as well. This use of X's can only occur in LR. U = undetermined so far, i.e., there is at the time of table construction no definitive guidance as to whether the action--on that row-- should be executed or not. C = the policy to be represented contains a contradiction that would cause conflicting action-cell entries. For instance in the policy and table below, there is conflicting guidance as to what to do with blue, medium size dresses. These policy statements are represented by the table below: We sell no large dresses, unless they are blue. Medium and large size dresses are to be displayed on the second floor. The first floor is where blue dresses are to be displayed. RULES123456SIZE[S,M,L]3SSMMLLCOLOR[R,B]2RBRBRBDISPLAY ON 1ST FLOORUYNYXNDISPLAY ON 2ND FLOORUNYYXY Notes: We do not have to perform any action pertaining to large red dresses, because there are no such dresses (by policy statement #1); hence, we put Xs in column 5. Nothing is specified about small red dresses, hence one puts Us in column #1. All the Ns appear because a floor is already indicated and a dress cannot be on two different floors. Notice that an anomaly appears in the action cells of column 4: we are directed by the policy to put all medium blue dresses on two different floors simultaneously. One of the main benefits constructing a decision table is noticing such, less than obvious, conflicting guidance; hence, we replace those Ys with Cs as below. C differs from X since X applies to contradiction among condition-values. RULES123456SIZE[S,M,L]3SSMMLLCOLOR[R,B]2RBRBRBDISPLAY ON 1ST FLOORUYNCXNDISPLAY ON 2ND FLOORUNYCXY The above table would have Ps (P = possibly perform) in place of the Cs, if, say, there were a fourth policy statement: Medium blue dresses might possibly go on either floor (thus leaving the decision to the stock person). RULES123456SIZE[S,M,L]3SSMMLLCOLOR[R,B]2RBRBRBDISPLAY ON 1ST FLOORUYNPXNDISPLAY ON 2ND FLOORUNYPXY The role of common sense in non arbitrary policies. Another action-cell indicator is useful to for not having to resort to Us, namely CS (= decided by common sense). In the policy below, common sense dictates that a person who pays one type of admittance fee obviously should not pay either of the two other amounts. Policy statement: 1. Senior citizens pay $3 2. Non-senior adults pay $5. 3. Children are admitted free. STATUS[A, C, S,]3ACSCHARGE $0N-CSY-3N-CSCHARGE $3N-CSN-CSY-2CHARGE $5Y-2N-CSN-CS Only Y, N, X, U, C, P and CS can appear as action values in the LR quadrant. Other enhancements to be explained later will add other symbols. Note: The proposed method of constructing decision tables stipulates that no action cell should be left empty, even for readability, since that procedure (while common) opens the possibility of unnoticed or careless omissions of action-values. In practice, one would regard total uncertainty about an action cell as merely a temporary situation and one should seek to determine an actual action-value to replace U before giving the table to anyone for use. Also, one probably should not present a user with a version of a table showing X's, since he/she would never encounter that (impossible) state of affairs indicated by those Xs. Removing columns and rows. Guidelines for consolidating columns by recognizing unneeded condition values and representing them by a dash RULES1234COND-1 [T,F](2)TTFFCOND-2 [T,F](2)TFTFACTION-1 YYNYACTION-2 NNUY Look in quadrant LR for columns with identical vertical series of action cells. In the table above, columns 1 and 2 both have Y over N. So far, it looks as if columns 1 and 2 can be consolidated. In those same columns (in the UR), see if there is any horizontal row where all possible condition values for the row appear in the columns being examined. Here there is just one such row, the row containing condition-2. This strengthens the case that columns 1 and 2 can be consolidated. In those same columns (in UR), see if each remaining horizontal row contains identical condition values; there could be, say, all Fs in one row and all Ts in another, but each row would have the identical values within the row. When all the above three guidelines are satisfied, the columns can be consolidated; superfluous columns can be dropped in a new version of the table. This maneuver is both feasible and desirable because the values of condition-2 have no effect on which actions are to be performed, and only the values of condition-2 differentiated among the columns involved. Furthermore, the new version of the table will be simpler to understand and use. When condition-values (such as the T and F for condition-2 of columns 1 and 2 above respectively) are immaterial to the action sets they would have determined they can be replaced by dashes, and the columns involved can then be combined into one column, (I suggest choosing the lowest numbered of the columns involved). To indicate table-size reduction took place, the numbers of the original columns (in the first version) can be preserved for historical or rechecking purposes and written above the surviving column, as below. RULES1,234COND-1 [T,F](2)TFFCOND-2 [T,F](2)-TFACTION-1 YNYACTION-2 NUY Guidelines for formal readings of the column rules Each condition along with its value is mentioned in an IF-clause, while each condition-value pair is conjoined to any succeeding pair by AND. The word IS is inserted to connect the condition with its value. For example, the rule for column 4 above would commence: IF COND-1 IS FALSE AND CONDITION-2 IS FALSE, THEN . Each action with its value is mentioned in a THEN-clause, while each action-value pair is conjoined to any succeeding pair by AND (or in the case of an action with value N, perhaps BUT + DO NOT would be more apt). For example, the rule for column 4 above would continue: THEN PERFORM ACTION-1 AND PERFORM ACTION-2. Thus if the last Y in column 4 were N, the rule would continue: THEN PERFORM ACTION-1 BUT DO NOT PERFORM ACTION-2. Consider the table below. RULES1,234COND-1 [T,F](2)TFFCOND-2 [T,F](2)-TFACTION-1 YUXACTION-2 NUX The following maneuvers suppress some information, but will cause no problem for the actual application of the table in everyday use. Since Rule 3 above has no determinate action, one can eliminate it in a table to make it more comprehensible for the person who will use it. Similarly, Rule 4 never has an application and can also be eliminated. Thus, the above table reduces to a more practical version. RULE1,2COND-1 [T,F][T,F](2)TCOND-2 [T,F](2)-ACTION-1 YACTION-2 N One can eliminate a condition if all its table values are -', because the condition makes no difference for any actions in the table. Finally, one can eliminate an action row if the action is never performed, i.e., if its row values are all F. Thus, the previous table reduces to RULECOND-1 [T,F](2)TACTION-1 Y  6. How to indicate which action values are determined by which policy statements. Number the policy statements (or sometimes internal clauses within long sentences) and attach the numerals (by means of a hyphen) to the action values in the action cells of LR to show which statement determines whether to do the action. This enhancement helps avoid errors and enables one to retrace ones reasoning. Furthermore, it indicates if any policy statement has been overlooked. An example follows. Policy: When COND-1 is true, then COND-2 is true. [NOTE: no action is mentioned] When both conditions are true, just do ACTION-1. 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t06    344 lapPyt/FT5$$If!vh5>5555555 #v>#v#v#v :V l t065553pPyt/FT;kd<$$IfTlִ] wog_WO[! t06    344 lapPyt/FT$$If!vh5>55#v>#v#v:V l4 t06+5553pytx TB$$If!vh5>5555555 #v>#v#v#v :V l4 t06+5553pPytx TCkd@$$IfTl4ִ] wog_WO[!  t06    344 lapPytx Tz$$If!v h5l5.5555555 5  #vl#v.#v#v#v #v :V l t065055|55 3pdytx Tkd~D$$IfTl ] wog_WO[!0| t06((((344 lapdytx Tz$$If!v h5l5.5555555 5  #vl#v.#v#v#v #v :V l t065055|55 3pdytx TkdH$$IfTl ] wog_WO[!0| t06((((344 lapdytx T~$$If!v h5l5.5555555 5  #vl#v.#v#v#v #v :V lP t065055|55 3pdytx TkdL$$IfTlP ] wog_WO[!0| t06((((344 lapdytx Tz$$If!v h5l5.5555555 5  #vl#v.#v#v#v #v :V l t065055|55 3pdytx TkdP$$IfTl ] wog_WO[!0| t06((((344 lapdytx Tz$$If!v h5l5.5555555 5  #vl#v.#v#v#v #v :V l t065055|55 3pdytx TkdT$$IfTl ] wog_WO[!0| t06((((344 lapdytx T$$If!vh565555#v6#v#v#v#v:V l t06555X553p2ytx Tu$$If!v h5655555555 5  #v6#v#v#v#v #v :V l t06555X55 3pdytx Tkd3Z$$IfTl ]S !X t06((((344 lapdytx Tu$$If!v h5l5W5555555 5  #vl#vW#v#v#v #v :V l t06505/555 3pdytx TkdG^$$IfTl ] !0/ t06((((344 lapdytx Tu$$If!v h5l5W5555555 5  #vl#vW#v#v#v #v :V l t06505/555 3pdytx Tkd[b$$IfTl ] !0/ t06((((344 lapdytx Ty$$If!v h5l5W5555555 5  #vl#vW#v#v#v #v :V lP t06505/555 3pdytx Tkdof$$IfTlP ] !0/ t06((((344 lapdytx Tu$$If!v h5l5W5555555 5  #vl#vW#v#v#v #v :V l t06505/555 3pdytx Tkdj$$IfTl ] !0/ t06((((344 lapdytx Tu$$If!v h5l5W5555555 5  #vl#vW#v#v#v #v :V l t06505/555 3pdytx Tkdn$$IfTl ] !0/ t06((((344 lapdytx T$$If!vh5c 55b55255#vc #v#vb#v#v2#v:V l t065c 55b5525ayt^$$If!vh5c 55b55255#vc #v#vb#v#v2#v:V l t065c 55b5525ayt^$$If!vh5c 55b55255#vc #v#vb#v#v2#v:V l t065c 55b5525ayt^$$If!vh5c 55b55255#vc #v#vb#v#v2#v:V l t065c 55b5525ayt^$$If!vh5c 55b55255#vc #v#vb#v#v2#v:V l t065c 55b5525ayt^$$If!vh5c 55b55255#vc #v#vb#v#v2#v:V l t065c 55b5525ayt^$$If!vh5s55 #vs#v#v :V l40+5755f 3pytx T4$$If!vh5s5555F5#vs#v#v#v#vF#v:V l40+5755f5553p<ytx Tl$$If!vh5m 5755555F5#vm #v7#v#v#v#v#vF#v:V l051 5555f5553pPytx T2kdz$$IfTlִ] n!g1 f0    344 lapPytx Tl$$If!vh5m 5755555F5#vm #v7#v#v#v#v#vF#v:V l051 5555f5553pPytx T2kd1~$$IfTlִ] n!g1 f0    344 lapPytx Tp$$If!vh5m 5755555F5#vm #v7#v#v#v#v#vF#v:V l051 5555f5553pPytx T6kdӁ$$IfTlִ] n!g1 f0    344 lapPytx Tl$$If!vh5m 5755555F5#vm #v7#v#v#v#v#vF#v:V l051 5555f5553pPytx T2kd}$$IfTlִ] n!g1 f0    344 lapPytx Tl$$If!vh5m 5755555F5#vm #v7#v#v#v#v#vF#v:V l051 5555f5553pPytx T2kd$$IfTlִ] n!g1 f0    344 lapPytx T$$If!vh555550 #v#v#v#v0 :V l40+5I5553p2yt_T8$$If!vh555555F5#v#v#v#vF#v:V l40+5I55553pFyt_Tkdɍ$$IfTl4֞] n I0344 lapFyt_T0$$If!vh555555F5#v#v#v#vF#v:V l05I55553pFyt_Tkd $$IfTl֞] nI0344 lapFyt_T0$$If!vh555555F5#v#v#v#vF#v:V l05I55553pFyt_Tkd@$$IfTl֞] nI0344 lapFyt_T0$$If!vh555555F5#v#v#v#vF#v:V l05I55553pFyt_Tkdv$$IfTl֞] nI0344 lapFyt_T$$If!vh5s555F5#vs#v#vF#v:V l0575553p2yt_T$$If!vh5s555F5#vs#v#vF#v:V l0575553p2yt_T$$If!vh5 55550 #v #v#v#v0 :V l40+55i553p2ytx T8$$If!vh5 55555F5#v #v#v#vF#v:V l40+55i5553pFytx Tkd$$IfTl4֞]p n i0344 lapFytx T0$$If!vh5 55555F5#v #v#v#vF#v:V l055i5553pFytx Tkd$$IfTl֞]p ni0344 lapFytx T0$$If!vh5 55555F5#v #v#v#vF#v:V l055i5553pFytx Tkd+$$IfTl֞]p ni0344 lapFytx T0$$If!vh5 55555F5#v #v#v#vF#v:V l055i5553pFytx Tkda$$IfTl֞]p ni0344 lapFytx T0$$If!vh5 55555F5#v #v#v#vF#v:V l055i5553pFytx Tkd$$IfTl֞]p ni0344 lapFytx T0$$If!vh5 55555F5#v #v#v#vF#v:V l055i5553pFytx Tkdͭ$$IfTl֞]p ni0344 lapFytx T$$If!vh555h5h5F#v#v#vh#vF:V l40+5}5\5@5 3p2ytx T$$If!vh555h5h5F#v#v#vh#vF:V l40+5}5\5@5 3p2ytx T$$If!vh555h5h5F#v#v#vh#vF:V l05}5\5@5 3p2ytx T$$If!vh555h5h5F#v#v#vh#vF:V l05}5\5@5 3p2ytx T$$If!vh555h5h5F#v#v#vh#vF:V l05}5\5@5 3p2ytx T$$If!vh555h5h5F#v#v#vh#vF:V l05}5\5@5 3p2ytx T$$If!vh555h5h5F#v#v#vh#vF:V l05}5\5@5 3p2ytx T$$If!vh555$5?5o#v#v#v$#v?#vo:V l0,5o5\55533p2ytx T$$If!vh555$5?5o#v#v#v$#v?#vo:V l00,5o5\55533p2ytx T$$If!vh555$5?5o#v#v#v$#v?#vo:V l0,5o5\55533p2ytx T$$If!vh555$5?5o#v#v#v$#v?#vo:V l00,5o5\55533p2ytx T $$If!vh5_5E555 #v_#vE#v#v :V l4B0+5#555 3p2yt!lTX$$If!vh5_5E55555F5#v_#vE#v#v#vF#v:V l40+5#555553pPyt!lT5kd$$IfTl4ִ] n!g #0    344 lapPyt!lTP$$If!vh5_5E55555F5#v_#vE#v#v#vF#v:V l05#555553pPyt!lT2kd$$IfTlִ] n!g#0    344 lapPyt!lTP$$If!vh5_5E55555F5#v_#vE#v#v#vF#v:V l05#555553pPyt!lT2kd$$IfTlִ] n!g#0    344 lapPyt!lTT$$If!vh5_5E55555F5#v_#vE#v#v#vF#v:V l05#555553pPytOeT6kd$$IfTlִ] n!g#0    344 lapPytOeTP$$If!vh5_5E55555F5#v_#vE#v#v#vF#v:V l05#555553pPyt!lT2kd$$IfTlִ] n!g#0    344 lapPyt!lTP$$If!vh5_5E55555F5#v_#vE#v#v#vF#v:V l05#555553pPyt!lT2kd0$$IfTlִ] n!g#0    344 lapPyt!lT^