# Presentation: 037064

## Applications of Approximate Reasoning in Decision Analysis

**Terry Bott and Steve Eisenhawer**
**Probabilistic Risk and Hazard Analysis, D-11**
**Decision Applications Division**
**Los Alamos National Laboratory**
***Workshop on Novel Approaches to Uncertainty Quantification***
***Los Alamos, New Mexico***
***February 28, 2002***

***LA-UR-02-1628***

## Sample of Problems Addressed During Development of Methodology

******  ****State of Knowledge for Paths to Inadvertent ****	****          ****	****Nuclear Detonation**
******  ****Rank HE Aging Paths Requiring HE Replacement**
******  ****Risk of Information Loss During Foreign Visits**
******  ****Prioritize Spare Parts Procurement**
******  ****Likelihood Ranking of Item Loss Scenarios (2002)**

**Sample of Problems Addressed During Development of Methodology**

**LANL:**
- Better descriptions, title

## Elements of the Decision Process

**Determine possibilities**
**Select metric to rank the possibilities**
**Design an inferential model for the metric**
**Rank the possibilities**
**Express uncertainty in the results**
**Make results useful to the customer**

***Our approach is based upon the theory of approximate reasoning. We call our version of AR “Logic-evolved Decision Models” – LED***

## LANL:

**LANL:**
***Check colors, look at animation, mention uncertainty***

## Identifying Possibilities

**	********  ****Well understood problem**
**	********  ****Limited Scope of Interest**

**Identifying Possibilities**

***Logically Evolved***
**	********  ****Possibilities developed deductively**
**	********  ****Process aided by Visual interface with ****	****	****     equations **
**	********  ****Simlutaneous Set of Logic Equations Produced**
**	********  ****Solution is a Disjoint Set of Paths, Implicants, ****	****      etc. **
**	**** **

**LANL:**
***Can just say this one***

## Problem Statement

**Problem**** ****Statement**

**An item turns up missing in an inventory.  Initial investigation produces conflicting and confusing evidence.  Management wishes to narrow down the possible loss scenarios if possible, identify actions to reduce the likelihood of future events and conduct a damage assessment.**

## We interpreted these needs as: What can be inferred in a short time and with limited effort about the relative likelihood of possible loss scenarios given a limited amount and quality of evidence ?

***We interpreted these needs as: What can be inferred in a short time and with limited effort about the relative likelihood of possible loss scenarios given a limited amount and quality of evidence ?***
***	***

## LANL:

**LANL:**
***Check colors, look at animation, mention uncertainty***

## Something is missing...

***Something is missing...***

***It’s somebody else’s***
***It’s the one without***
*** ******a barcode***
***It’s lost but there’s nothing ***
***important on it***

***What is it?***

***There’s something ***
***important on it....***
***It’s compromised***

## Thrown out and retrieved

***Thrown out and retrieved***
***Targeted collection***
***Opportunistic collection***

***No Compromise of information***

## The underlying logical equation that describes the possibilities...

***The underlying logical equation that describes the possibilities...***

***The tree is a GUI to deduce this equation...***

## Solution of the logical equation yields multiple paths. These paths are the loss scenarios....

- BARCODEASSIGNEDbe, BARCODEMISSINGog, BARCODECAMEOFFbe}

- {UNACCOUNTEDFCeog, CLASSIFIEDLOSSca, CLASSIFIEDFCag, FLASHCARDCLASSog, OWNERCLASSIFIEDbe, PROVENANCEog, OLYMPUSFLASHCARDog, LEGACYog, UAPLACEDINSAFEbe, LOSSPROCESSog, WITHCOMPROMISEog, LLWASTERETREIVALag, INWASTEog, SWEPTUPBYCLEANERag, DROPPEDONFLOORbe, UNMARKEDbe, BARCODEINEFFECTog, BARCODEMISSINGog, BCNOTATTACHEDbe, PUTINTRASHbe, THROWNOUTINLOCbe, LLWASTEACCESSbe, LLWASTERETREIVEDbe}

***Solution of the logical equation yields multiple paths. These paths are the loss scenarios....***

***How should we rank order them?***

## Solution of the logical equation yields multiple paths. These paths are the loss scenarios....

- BARCODEASSIGNEDbe, BARCODEMISSINGog, BARCODECAMEOFFbe}

- {UNACCOUNTEDFCeog, CLASSIFIEDLOSSca, CLASSIFIEDFCag, FLASHCARDCLASSog, OWNERCLASSIFIEDbe, PROVENANCEog, OLYMPUSFLASHCARDog, LEGACYog, UAPLACEDINSAFEbe, LOSSPROCESSog, WITHCOMPROMISEog, LLWASTERETREIVALag, INWASTEog, SWEPTUPBYCLEANERag, DROPPEDONFLOORbe, UNMARKEDbe, BARCODEINEFFECTog, BARCODEMISSINGog, BCNOTATTACHEDbe, PUTINTRASHbe, THROWNOUTINLOCbe, LLWASTEACCESSbe, LLWASTERETREIVEDbe}

***Solution of the logical equation yields multiple paths. These paths are the loss scenarios....***

**Top Event        Connective Element      Active Element**

***We use the active elements as the primary inputs to our inferential model....***

## LANL:

**LANL:**
***Check colors, look at animation, mention uncertainty***

## Determining Precision

**	********  ****Customer’s Needs**
**	********  ****Available Knowledge**
**	********  ****Available time and resources**

**Determining Precision**

***Our rule is to ultimately convert precise into imprecise knowledge in mixed precision situations.***

**LANL:**
***Just say it***

## Inference Precision

***Precision describes how knowledge is expressed.  Numerical knowledge is precise, linguistic knowledge is imprecise.***

## Inferential Evaluation

**Inferential Evaluation**

***Descriptors*****:  Linguistic values for each factor**

***Factors*****:  Linguistic variables that influence an inference**

***Implicant Equations*****:  Rules for combining linguistic values to infer resultant linguistic values.  This includes simple Modus Ponens as well as more complex rules.**

## Linked Inferences

**D****x********E****y********F****z**

**(F****z********C****n****)**

**(A****i********B****j****) ********C****p**

**J********M********N**

**G********N********O**

**Linked**** ****Inferences**

******G****a**

****** ****(F****z********C****p****)**

## Types of Uncertainty We Consider

**LANL:**
***This needs to be clarified***

**LANL:*****We’re setup to discuss inference and uncertainty together in the rest of the example***

**Outcome Uncertainty**
***Probability*****: appropriate for describing uncertainty in precise knowledge**
***Possibility*****: appropriate for describing uncertainty in imprecise knowledge**

**Set Assignment Uncertainty**
***Ambiguity*****:  Linguistic variables are not precise**
***Set Assignment*****:  Informant is uncertain which linguistic value is best**

## Supporting Evidence

**Supporting Evidence**

**Contradictory Evidence**

**Prior Likelihood**

**Posterior Likelihood**

**Aggregate Evidence**

- Rule 2

- Rule 1

**LANL:**
***Likelihood- imprecise outcome :possibility***
***Evidence - imprecise assignment  and more...***

## Individual Element Likelihood

**Individual Element Likelihood**

**Scenario Likelihood**

## Scenario Prior Likelihood

**Scenario Prior Likelihood**

**Scenario Posterior Likelihood**

**Scenario Likelihood Change**

## LANL:

**LANL:**
***Intro to look in more detail***

## Aggregate Evidence

**Aggregate**** ****Evidence**

- Rule 2

## IF ESmax is Weakly Supporting and ECmax is Strongly Contradictory THEN Eagg is Weakly Contradictory  

- Rule 2

**E****Smax**** : {None, Weakly Supporting,Strongly Supporting}**
**E****Cmax**** : {None, Weakly Contradictory,Strongly Contradictory}**
**E****agg**** : {None, Strongly Contradictory, Weakly Contradictory, Conflicting,**
**           ****Weakly Supporting,Strongly Supporting}**

**IF E****Smax**** is *****Weakly Supporting***** and E****Cmax**** is *****Strongly***** *****Contradictory***** THEN E****agg**** is *****Weakly Contradictory*****  **

**LANL:**
***Evaluation with min-max, more on this later***

## The rule base shifts the posterior based upon the specific, forensic evidence available

**L ****E****(Pr) : {Very Low, Low, High}**
**E****agg**** : {None, Strongly Contradictory, Weakly Contradictory, Conflicting,**
**           ****Weakly Supporting,Strongly Supporting}**
**L ****E****(Po) : {Very Low, Low, High, Very High}**

***The rule base shifts the posterior based upon the specific, forensic evidence available***

**LANL:**
***Rulebase here***

## LANL:

**LANL:**
***How do we deduce the model form?***

## Slide 28

## All of the information in the inferential model is represented in this logical equation...

**Element Posterior  Likelihood:**
***High***

**A single entry in the rulebase**

***All of the information in the inferential model is represented in this logical equation...***

## How does this work in practice?

## Inferring Element Posterior Likelihood

- BARCODEASSIGNEDbe, BARCODEMISSINGog, BARCODECAMEOFFbe}

**LANL:**
***Add the actual data and discuss for one element***

***Inferring Element Posterior Likelihood***

## Inferring Scenario Posterior Likelihood

***Do the scenario likelihood the same way Show the posterior results Mention or slide on defuzzification***

***Inferring Scenario Posterior Likelihood***

## Inferring Likelihood Change

***Results here***

***Inferring Likelihood Change***

## LANL:

**LANL:**
***How do we deduce the model form?***

## Solving AR Inference Models Quickly – The Fast Min-Max Procedure

**LANL:**
***FMM here***

***Solving AR Inference Models Quickly – The Fast Min-Max Procedure***

***Digraph of the Inferential logical equation***

## Aggregate

**LANL:**
***FMM here***

***Aggregate***
***Evidence***

***Prior***
***Likelihood***

***Rule 2***

***Subsets for ***
***Element***
***Likelihood***
***In Rule 1***

***To Rule 1***

## The FMM Algorithm

**Solve the inference equation for the implicant chains linking the active elements and the output metric linguistic subsets**
**For each subset do the min on each of the associated implicant chains**
**Do the max over all of the results of the min operation**

***This procedure is of O[10] times faster per node relative to the SMM. Since it is only performed once per evaluation it is of O[10*N] times faster per scenario evaluation. This is typically of O[100] - O[1000]***

## Conclusions

******  ****Identifying an exhaustive set of possibilities**
******  ****Ranking the possibilities according to some metric(s)**
** **
**When**
******  ****All or critical parts of knowledge base are imprecise**
******  ****Uncertainty is imprecise as well**
******  ****Knowledge base is scattered among informants**

**Conclusions**

***Using a logic model to generate possibilities and an inference engine, capturing uncertainty  using AR has proven to be a flexible and ffficient analysis technique***