Fuzzy rules that turn daily market-breadth into a session consensus

Graded conditions, not yes-or-no labels

Technical breadth and valuation readings are treated as partial indications with membership grades between 0 and 1 rather than as strictly true or false facts. A membership-function maps each crisp market-breadth input onto a mu-value between 0 and 1, describing how well that input belongs to a linguistic category.

Editorial reading: those grades keep the session inspectable. A trader can see which market-breadth facts fired, how strongly they fired, and whether the later consensus is bullish or bearish.

A production-rule decision-tree

A production-rule system is an inference engine plus a knowledge base. The engine tests the left-hand-side of each rule against incoming observations, and only rules whose conditions hold become candidates for execution.

The knowledge base is a decision-tree of if-then rules that can be joined as alternatives or as joint conditions. The max-operator keeps the largest membership grade when rules are joined as alternatives. The min-operator keeps the smallest membership grade when conditions must hold together. The combined left-hand-side membership grade becomes the rule's strength.

Choosing a rule and applying its conclusion

When a rule is chosen by the largest-membership method, the selected right-hand-side is applied in full. The membership grade is used only to choose the rule, not to scale the action.

Rule selection and output construction can follow one of three procedures: keep the single strongest rule, average conclusions scaled by their membership grades, or take the centroid of the scaled membership areas. The selected conclusions are then converted into a session reading.

A daily-exchange demonstration

A worked daily-exchange example fuzzifies published session statistics, evaluates each rule's left-hand-side membership, assigns that grade to the right-hand-side conclusion, then converts the selected conclusions into a session reading.

The demonstration program reads date, new highs, new lows, advances, declines, advancing volume, and declining volume. From those fields it computes a standard Arms-style breadth ratio, the trin, as advancing issues times declining volume divided by declining issues times advancing volume. Values of trin below 1 accompany rising sessions and values above 1 accompany falling sessions.

Derived series, updn, and add1es

Two derived breadth series recast that ratio so large positive values describe rising sessions and large negative values describe falling sessions. The updn statistic is constructed in that signed way: large positive values describe bullish sessions and large negative values describe bearish sessions.

A third series, add1es, is an exponentially smoothed reading of the slope of the advance-decline line. Exponential-smoothing is a recursively updated average that weights the latest observation more heavily than earlier ones. The demonstration uses a 0.4 update constant.

Twenty weighted rules and a session consensus

The knowledge base contains 20 weighted production rules whose signed weights run from +1 to -1. Each fired rule contributes a degree-of-fulfilment equal to membership grade times weight. Those contributions are summed into a session consensus, the signed sum of degrees of fulfilment across all rules that fired, used as a compact bullish-or-bearish reading of the session.

Linguistic grades without a stored table

Inputs are mapped computationally onto linguistic grades such as positive-big through negative-big, then onto compound grades such as any, positive, negative, and not-extreme. The mapping does not rely on a stored membership table.