The Problem. Sustainability is an abstract concept that cannot be directly measured.
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1 Measurement, Interpretation, and Assessment Applied Ecosystem Services, Inc. (Copyright c 2005 Applied Ecosystem Services, Inc.)
2 The Problem is an abstract concept that cannot be directly measured. There is large political and social pressure to measure and assess sustainability. Indicators are being developed that are believed to reflect various aspects of sustainability. Interpreting and combining indicators is a frustrating exercise.
3 The Problem is an abstract concept that cannot be directly measured. There is large political and social pressure to measure and assess sustainability. Indicators are being developed that are believed to reflect various aspects of sustainability. Interpreting and combining indicators is a frustrating exercise.
4 The Problem is an abstract concept that cannot be directly measured. There is large political and social pressure to measure and assess sustainability. Indicators are being developed that are believed to reflect various aspects of sustainability. Interpreting and combining indicators is a frustrating exercise.
5 The Problem is an abstract concept that cannot be directly measured. There is large political and social pressure to measure and assess sustainability. Indicators are being developed that are believed to reflect various aspects of sustainability. Interpreting and combining indicators is a frustrating exercise.
6 What This Presentation Includes 1 to fuzzy sets and fuzzy logic. 2 Why fuzzy system models solve problems. 3 How an approximate reasoning model assesses forest sustainability.
7 Outline 1 Reasoning Models 2 3
8 History Fuzzy set theory developed 40 years ago by Lotfi Zadeh to express the concept of partial truth characterized by uncertainty. Results are more accurate mathematical representations of truth perception than can be expressed by crisp sets. Perception refers to how the human brain observes and expresses reality. Perception also refers to natural and artificial languages. Applying fuzzy set theory to move from crisp (true/false) mathematics to fuzzy mathematics allows us to express natural language mathematically.
9 History Fuzzy set theory developed 40 years ago by Lotfi Zadeh to express the concept of partial truth characterized by uncertainty. Results are more accurate mathematical representations of truth perception than can be expressed by crisp sets. Perception refers to how the human brain observes and expresses reality. Perception also refers to natural and artificial languages. Applying fuzzy set theory to move from crisp (true/false) mathematics to fuzzy mathematics allows us to express natural language mathematically.
10 History Fuzzy set theory developed 40 years ago by Lotfi Zadeh to express the concept of partial truth characterized by uncertainty. Results are more accurate mathematical representations of truth perception than can be expressed by crisp sets. Perception refers to how the human brain observes and expresses reality. Perception also refers to natural and artificial languages. Applying fuzzy set theory to move from crisp (true/false) mathematics to fuzzy mathematics allows us to express natural language mathematically.
11 History Fuzzy set theory developed 40 years ago by Lotfi Zadeh to express the concept of partial truth characterized by uncertainty. Results are more accurate mathematical representations of truth perception than can be expressed by crisp sets. Perception refers to how the human brain observes and expresses reality. Perception also refers to natural and artificial languages. Applying fuzzy set theory to move from crisp (true/false) mathematics to fuzzy mathematics allows us to express natural language mathematically.
12 History Fuzzy set theory developed 40 years ago by Lotfi Zadeh to express the concept of partial truth characterized by uncertainty. Results are more accurate mathematical representations of truth perception than can be expressed by crisp sets. Perception refers to how the human brain observes and expresses reality. Perception also refers to natural and artificial languages. Applying fuzzy set theory to move from crisp (true/false) mathematics to fuzzy mathematics allows us to express natural language mathematically.
13 Definitions I Definition Fuzzy set A collection of similar items which allow partial memberships across a continuous range of membership values. Examples: Plants There are two sets, Peach and Plum. However, the Nectarine is a member of both sets to some degree as it is a hybrid of both pure fruits. Animals There are two sets, Horse and Donkey. They can be mated to produce a Mule, which is a partial member of both sets.
14 Definitions II Definition Fuzzy logic The formal methods embodied in fuzzy set theory in which the conventional binary logic based on choices yes and no is replaced with a continuum of possibilities that effectively embody the alternatives maybe or somewhat. reasoning The application of fuzzy set theory and fuzzy logic in fuzzy systems that mimic the way humans make decisions based on expertise and common sense. reasoning models use IF-THEN rules to express the consequences of antecedent conditions.
15 Definitions III Example The expression, that forest is big, can now be mathematically described by a fuzzy set, Big, in which the forest belongs to some degree. That is, how true is it that the forest is big? A major element of the transition from crisp to fuzzy is possibility theory. These possibilities are distributed in a membership function. Membership function concept completes the mathematical formulation of that forest is big, and of more complex concepts in daily language.
16 Outline 1 Reasoning Models 2 3
17 Fuzzy Multi-Expert and Multi-Criteria Decision Making Major advantage of approximate reasoning systems is ability to assimilate and use knowledge from multiple experts. These experts can be conflicting, cooperating, or collaborative. Conflicting expert opinions can be incorporated into the results. Disagreements over the meaning of social, environmental, and economic numbers common among experts. Defining and assessing sustainable is the type of complex system resolved only with approximate reasoning techniques.
18 Fuzzy Multi-Expert and Multi-Criteria Decision Making Major advantage of approximate reasoning systems is ability to assimilate and use knowledge from multiple experts. These experts can be conflicting, cooperating, or collaborative. Conflicting expert opinions can be incorporated into the results. Disagreements over the meaning of social, environmental, and economic numbers common among experts. Defining and assessing sustainable is the type of complex system resolved only with approximate reasoning techniques.
19 Fuzzy Multi-Expert and Multi-Criteria Decision Making Major advantage of approximate reasoning systems is ability to assimilate and use knowledge from multiple experts. These experts can be conflicting, cooperating, or collaborative. Conflicting expert opinions can be incorporated into the results. Disagreements over the meaning of social, environmental, and economic numbers common among experts. Defining and assessing sustainable is the type of complex system resolved only with approximate reasoning techniques.
20 Fuzzy Multi-Expert and Multi-Criteria Decision Making Major advantage of approximate reasoning systems is ability to assimilate and use knowledge from multiple experts. These experts can be conflicting, cooperating, or collaborative. Conflicting expert opinions can be incorporated into the results. Disagreements over the meaning of social, environmental, and economic numbers common among experts. Defining and assessing sustainable is the type of complex system resolved only with approximate reasoning techniques.
21 Fuzzy Multi-Expert and Multi-Criteria Decision Making Major advantage of approximate reasoning systems is ability to assimilate and use knowledge from multiple experts. These experts can be conflicting, cooperating, or collaborative. Conflicting expert opinions can be incorporated into the results. Disagreements over the meaning of social, environmental, and economic numbers common among experts. Defining and assessing sustainable is the type of complex system resolved only with approximate reasoning techniques.
22 Fuzzy Expert Systems I Example Prime Rate Movement Model 1 [Expert A]: IF PrimeRate[t-1] is greater than PrimeRate[t] THEN InvestmentPolicy is Aggressive; [Expert B]: IF PrimeRate[t-1] is greater than PrimeRate[t] THEN InvestmentPolicy is Conservative
23 Fuzzy Expert Systems Example Prime Rate Movement Model 2 [Expert A]: IF PrimeRate is MovingDOWN THEN InvestmentPolicy is Aggressive; [Expert B]: IF PrimeRate is MovingDOWN THEN InvestmentPolicy is Conservative;
24 Fuzzy Expert Systems Example New Product Pricing Model [R1] [R2] [R3] [R4] our Price must be High; our Price must be Low; our Price must be Around 2*MfgCost; if the CompetitionPrice is not Very_high then our Price must be Near CompetitionPrice;
25 Distinguishing Among Experts Important Point: Experts can have relative weights assigned to them: Adaptive Peer Ranking Parameter: P truth = (1 + R peer ) P truth Peer Ranking by Membership Modification: µ A [x] = µ 1 R i A [x]
26 Complex Modeling Use fewer rules than do conventional numeric or expert models. Use natural language of experts, decision makers, and the public. Uncertainty and imprecision are what are modeled. Tuning, sensitivity analyses, and testing done quickly and easily. Possibilities more representative of the real world than are probabilities. Components beyond human control (e.g., fire, wind throw) incorporated into the model.
27 Complex Modeling Use fewer rules than do conventional numeric or expert models. Use natural language of experts, decision makers, and the public. Uncertainty and imprecision are what are modeled. Tuning, sensitivity analyses, and testing done quickly and easily. Possibilities more representative of the real world than are probabilities. Components beyond human control (e.g., fire, wind throw) incorporated into the model.
28 Complex Modeling Use fewer rules than do conventional numeric or expert models. Use natural language of experts, decision makers, and the public. Uncertainty and imprecision are what are modeled. Tuning, sensitivity analyses, and testing done quickly and easily. Possibilities more representative of the real world than are probabilities. Components beyond human control (e.g., fire, wind throw) incorporated into the model.
29 Complex Modeling Use fewer rules than do conventional numeric or expert models. Use natural language of experts, decision makers, and the public. Uncertainty and imprecision are what are modeled. Tuning, sensitivity analyses, and testing done quickly and easily. Possibilities more representative of the real world than are probabilities. Components beyond human control (e.g., fire, wind throw) incorporated into the model.
30 Complex Modeling Use fewer rules than do conventional numeric or expert models. Use natural language of experts, decision makers, and the public. Uncertainty and imprecision are what are modeled. Tuning, sensitivity analyses, and testing done quickly and easily. Possibilities more representative of the real world than are probabilities. Components beyond human control (e.g., fire, wind throw) incorporated into the model.
31 Complex Modeling Use fewer rules than do conventional numeric or expert models. Use natural language of experts, decision makers, and the public. Uncertainty and imprecision are what are modeled. Tuning, sensitivity analyses, and testing done quickly and easily. Possibilities more representative of the real world than are probabilities. Components beyond human control (e.g., fire, wind throw) incorporated into the model.
32 Outline 1 Reasoning Models 2 3
33 General Business Examples I Corporations Using Fuzzy Logic Solutions Shearson-Lehman (portfolio safety and suitability) Boeing Corporation (manufacturing optimization) BP Corporation (petroleum refining and transportation) Dow Chemical (project risk analysis) IBM (managed health care fraud detection) American Express (credit capacity and stress prediction)
34 General Business Examples II Fuzzy Logic Business Risk assessment/management (banks, credit card companies) Fraud detection (medical provider, consumer) Project management Scheduling Drug concentrations for maximum therapeutic value Investment portfolio safety and stability Data mining
35 Outline 1 Reasoning Models 2 3
36 Perspective Fuzzy logic theory is very broad and is perhaps the only theory that easily propagates into multiple disciplines such as sociology, biology, psychology, artificial intelligence, linguistics, engineering, medicine, law and so forth. This is due to the capability of computing with words in a manner no other method can cope with. Riza C. Berkan, Univ. of Tennessee These models work because they are based on so what? rather than on what.
37 General Model Properties The model is completely transparent. That is, it is easy to see how it works and to understand it. Input options: 1 Expert knowledge (IF-THEN rules, variables, fuzzy sets, hedges). 2 Existing databases (harvest rates, listed species populations). Output options: 1 Linguistic, with possibilty value. 2 Crisp numeric value. You and the technical work group are the experts who determine how the model is structured and works. No outside experts limiting your options by the way they created the model.
38 Outline 1 Reasoning Models 2 3
39 Model Organization: Policies Definition A policy is a block of similar events or conditions that is treated the same as a sub-model. In a forest sustainability model, each major and minor category can be a separate policy. Each policy is evaluated by itself, then aggregated into the whole result.
40 Input Values I 1 Diverse Plant and Animal Populations: 1 Populations 2 Structure 3 Ecosystem Diversity 2 Legal, Institutional, Economic Framework 1 Monitoring 2 Legal 3 Economic 4 Recreational Some indicators can be measured, others cannot. But, they can all be described with words.
41 IF-THEN Rules Within each policy, indicator variables are interpreted by IF-THEN rules. These rules are expressed by subject matter experts, not by us. We do not set the relationships in the model, you and your experts do. IF-THEN rules can be unconditional or conditional, simple or complex.
42 IF-THEN Rules Within each policy, indicator variables are interpreted by IF-THEN rules. These rules are expressed by subject matter experts, not by us. We do not set the relationships in the model, you and your experts do. IF-THEN rules can be unconditional or conditional, simple or complex.
43 IF-THEN Rules Within each policy, indicator variables are interpreted by IF-THEN rules. These rules are expressed by subject matter experts, not by us. We do not set the relationships in the model, you and your experts do. IF-THEN rules can be unconditional or conditional, simple or complex.
44 IF-THEN Rules Within each policy, indicator variables are interpreted by IF-THEN rules. These rules are expressed by subject matter experts, not by us. We do not set the relationships in the model, you and your experts do. IF-THEN rules can be unconditional or conditional, simple or complex.
45 Example: New Product Pricing Rules: [R1] [R2] [R3] [R4] our Price must be High; our Price must be Low; our Price must be around 2*MfgCosts; if the CompetitionPrice is not Very_high then our Price must be near the CompetitionPrice;
46 High and Low Prices PRICE Domain [UofD]: 4.00 to FuzzySet: HIGH Description: High for Price FuzzySet: LOW Description: Low for Price
47 Around 2*MfgCost Price PRICE Domain [UofD]: 4.00 to FuzzySet: Around 2*MfgCosts Description: Near [Around] Twice MfgCosts AlphaCut: 0.10
48 Near Competition Price PRICE Domain [UofD]: 4.00 to FuzzySet: Near CompPrice Description: Near [Around] CompetitionPrice AlphaCut: 0.10
49 Rule 1 Fired PRICE Domain [UofD]: 4.00 to FuzzySet: PRICE Description: The estimated product price Rule1: our price must be HIGH
50 Rule 2 Fired PRICE Domain [UofD]: 4.00 to FuzzySet: PRICE Description: The estimated product price Rule2: our price must be LOW
51 Rule 3 Fired PRICE Domain [UofD]: 4.00 to FuzzySet: PRICE Description: The estimated product price Rule3: our price must be AROUND 2*MFGCOSTS
52 Rule 4 Fired PRICE Domain [UofD]: 4.00 to FuzzySet: PRICE Description: The estimated product price Rule4: Premise truth of
53 Defuzzified Results CENTROID defuzzification. Value: , [0.5417] Model Solution: Price = CIX = 0.54 SurfaceHght = 0.71
54 Term Set SUSTAINABILITY Very Low 1.00 Low Moderate High Very High
55 Linguistic Solution SUSTAINABILITY High [0.63]
56 What This Shows The result is an estimate of measured on an arbitrary scale, e.g., The variable,, can be a single fuzzy set or partitioned into several sets such as Very_low, Low, Moderate, High, and Very_high. If a single fuzzy set, the result is defuzzified to a crisp number (and confidence index) that can be compared spatially and temporally. If multiple term sets, the result can be defuzzified or expressed linguistically.
57 What This Shows The result is an estimate of measured on an arbitrary scale, e.g., The variable,, can be a single fuzzy set or partitioned into several sets such as Very_low, Low, Moderate, High, and Very_high. If a single fuzzy set, the result is defuzzified to a crisp number (and confidence index) that can be compared spatially and temporally. If multiple term sets, the result can be defuzzified or expressed linguistically.
58 What This Shows The result is an estimate of measured on an arbitrary scale, e.g., The variable,, can be a single fuzzy set or partitioned into several sets such as Very_low, Low, Moderate, High, and Very_high. If a single fuzzy set, the result is defuzzified to a crisp number (and confidence index) that can be compared spatially and temporally. If multiple term sets, the result can be defuzzified or expressed linguistically.
59 What This Shows The result is an estimate of measured on an arbitrary scale, e.g., The variable,, can be a single fuzzy set or partitioned into several sets such as Very_low, Low, Moderate, High, and Very_high. If a single fuzzy set, the result is defuzzified to a crisp number (and confidence index) that can be compared spatially and temporally. If multiple term sets, the result can be defuzzified or expressed linguistically.
60 Semantic Results I 1 Unsustainable Sustainable 1 Membership Grade (µ[x]) Universe of Discourse S-curve Membership Function Thresholds approached asymptotically. Change is gradual and varies across the Universe of Discourse.
61 Semantic Results II 1 Unsustainable Sustainable Membership Grade (µ[x]) Universe of Discourse Shouldered Membership Function Distinct thresholds when µ[x] = 0.0, 1.0. Sudden transition and constant rate of change between shoulder thresholds.
62 Semantic Results III Unsustainable Sustainable 1 Membership Grade (µ[x]) Universe of Discourse Straight Membership Function No threshold. Constant rate of change in membership grade across the Universe of Discourse.
63 Benefits of The approaches used so far are subjective and unsatisfactory. reasoning models work with words and numbers; focus is on so what?, not what. Subjective values are quantified and modeled with mathematical rigor. Risk assessments of highly complex systems are the strength of fuzzy system models. Multiple, conflicting expert opinions all included in the output values.
64 Benefits of The approaches used so far are subjective and unsatisfactory. reasoning models work with words and numbers; focus is on so what?, not what. Subjective values are quantified and modeled with mathematical rigor. Risk assessments of highly complex systems are the strength of fuzzy system models. Multiple, conflicting expert opinions all included in the output values.
65 Benefits of The approaches used so far are subjective and unsatisfactory. reasoning models work with words and numbers; focus is on so what?, not what. Subjective values are quantified and modeled with mathematical rigor. Risk assessments of highly complex systems are the strength of fuzzy system models. Multiple, conflicting expert opinions all included in the output values.
66 Benefits of The approaches used so far are subjective and unsatisfactory. reasoning models work with words and numbers; focus is on so what?, not what. Subjective values are quantified and modeled with mathematical rigor. Risk assessments of highly complex systems are the strength of fuzzy system models. Multiple, conflicting expert opinions all included in the output values.
67 Benefits of The approaches used so far are subjective and unsatisfactory. reasoning models work with words and numbers; focus is on so what?, not what. Subjective values are quantified and modeled with mathematical rigor. Risk assessments of highly complex systems are the strength of fuzzy system models. Multiple, conflicting expert opinions all included in the output values.
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