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Applications of Fuzzy Logic: Evolution and Case Study

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Overview

• Commercial Applications of Fuzzy Logic

• Evolution in Growth of Fuzzy Applications

• Fuzzy Logic and the World

• Example: Sendai Subway Control

• Case Study: Fuzzy-based Path Ordering

• Limitations

• Probability vs. Possibility

• Conclusions

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Commercial Fuzzy Applications

• Two broad categories of commercial applications:– Industrial process control: Used for modeling and

controlling complex industrial systems– Modeling human intelligence: Development of

fuzzy expert systems using the representation and inference techniques of fuzzy logic able to model imprecise processes of human experts.

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Fuzzy Statistics

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Fuzzy Logic and the World

• Most important players in Asia are China and Japan with India and Singapore playing minor roles

• All major Japanese companies involved in integrating fuzzy technology ($2-3 B)

• Fuzzy logic technology largely ignored in USA (NASA, Otis)

• France and Germany among European nation conducting fuzzy logic research (Peugeot, VW)

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Fuzzy Logic in JapanHitachi Automatic control for subway trains in Sendai yielding smoother,

more efficient ride with higher stopping precision

Nippon Electric Controlling temperatures in glass fusion at the Notogawa and Takatsuki factories

Nissan Anti-skid brake systems and automatic transmissions for cars

Canon, Minolta, Ricoh Auto-focusing in cameras by choosing the right subject in the picture frame to focus

Panasonic Jitter removal in video camcoders by distinguishing between jitters and actual movement of subjects

Matshushita, Toshiba, Sanyo, Hitachi

Vacuum cleaners that use sensors to gather information about floor and dirt conditions and then use a fuzzy expert system to choose the right program

Yamaichi Computerized trading programs which mimic the approximate reasoning processes of experienced fund managers

Matshushita A/C that make judgments based on factors such as number of persons in room and optimum degree of comfort

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Sendai Subway Control

• Research on automation of train operations in Japan begins in 1960

• Conventional automatic train operation (ATO) based on PID control

• Preset target speed which the ATO tries to achieve by powering and braking

• In practice, many changes in running conditions such as gradient of track and the braking force of rolling stock

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Sendai Subway Control (2)

• PID works best with linear systems

• Train is a complex non-linear system and all ATO use simplified linear representations of the train’s operation to apply to PID

• Fuzzy rules attempts to emulate the reasoning and control decisions of an experience subway driver

• Minimize difference between desired speed and actual speed

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Sendai Subway Control (3)

ATO by conventional control ATO with fuzzy control

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Sendai Subway Control (4)

• Satisfy goals like good riding comfort and accurate stopping

• Sendai subway operational since July 1987.

• Hitachi engineers compared fuzzy and conventional controllers in 300,000 simulations and 3,000 rider less test runs.

• Reduced stop-gap distance 2.5 times, doubled the comfort index, reduced power consumption by 10%

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Case Study

• Fuzzy-based method for path selection under additive quality of service constraints (delay), where the information available for making routing decisions is inaccurate.

• Identify a feasible path while minimizing the overall setup time.

• Performance evaluation compare between the fuzzy approach, the optimal solution, and greedy approach.

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Basics of Networks

local ISP

companynetwork

regional ISP

router workstation

servermobile

• millions of connected computing devices: hosts, end-systems– PCs workstations, servers– PDAs phones, toastersrunning network apps

• communication links– fiber, copper, radio,

satellite– Links have different bandwidth

• routers: forward packets • Packet: a piece of message

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ATM Networks

• ATM is a connection-oriented low-layer networking concept

• An end-to-end path called a virtual channel must be set up in advance, using an ATM signaling (control) protocol, before any data cells can be sent

• All cells of a virtual channel travel on the same path• Cells arrive in the order that they were sent• Switches must maintain state about the virtual

channels passing through them

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QoS and ATM

• Quality of Service (QOS)

– a specification of the desired (or acceptable) grade of service required for a traffic flow

– some traffic is delay-sensitive (e.g., voice)

– some traffic is loss-sensitive (e.g., data)

– some traffic is both (e.g., compressed video)

– QoS requested at time of call setup

– ATM network tries to provide requested QoS

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Introduction

• Modern networks define parameters that represent QoS they expect to receive from the network.

• QoS requirements for a connection set-up include:– Bandwidth– Loss ratio– Average/Maximum delay– Delay variation

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Introduction (2)

• Finding path that satisfies all QoS requirements is NP-complete where # of additive QoS parameters 2

• Present algorithms depend on deterministic knowledge of availability of resources

• Network resources should be used efficiently

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Introduction (3)

• Fuzzy approach used for the following reasons– Multiple parameters– Intuitive – Advantage over non-fuzzy approach

• Development of a mechanism for solving complex routing problems in communications networks

• Complex routing problems in uncertain environment analyzed in simple rules and decision process modeled by sets of these rules

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Inaccurate Information in Networks

• Unavailable parameters– Information about topology and availability of

resources collected through routing protocols– Existing protocols do not advertise all relevant

parameters necessary for making routing decisions– Network management mechanisms only provide

partial values– Lack of practical tools that provide QoS

information

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Inaccurate Information in Networks (2)

• Inaccurate calculations

– Computation of link state parameters based on traffic measurements and forecasts

– Values usually only averages or bounds, which causes inaccuracies

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Inaccurate Information in Networks (3)

• Obsolete information – Dynamic parameters are significantly affected by

temporal network conditions– Difficult to have the most current view of the

parameters available on the other links and nodes– Requires frequent updates– Trade-off between overhead costs and accuracy of

the network state information that the path selection algorithm depends on

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Inaccurate Information in Networks (4)

• Aggregation in large networks – Sheer growth in information makes it practically

impossible to maintain accurate knowledge about all nodes and links.

– Concept of hierarchical routing used to overcome scalability problem

– Nodes and links of each hierarchy recursively aggregated into higher levels representing collection of lower nodes

– Increase in aggregation, decrease in accuracies

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Inaccurate Information in Networks (5)

• Partial information – Routing information exchanged between nodes

when under same network administration

– Difficult to do so in interconnected networks which include multiple operators and private networks

– Networks only publish partial information

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Impact of Uncertain Parameters

• Connections with only bandwidth demands, impact of inaccuracies relatively minimal

• Connections with end-to-end delay demands inaccuracies cause significant impact on:

– Routing complexity

– Path selection process becomes intractable

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Simple Example

• Not sufficient to consider only probability of failure of selected path, but also connection setup time to successfully establish connection

A

S T

C D EB

Pf = 0.2

Pf = 0.24

Pf = 0.18

S: Source T: Destination

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Proposed Approach

• Algorithm whose target function is to find a feasible path that meets the end-to-end delay requirement, while minimizing the average connection setup time

• Assumptions– Routing environment: ATM or MPLS– Information available to source node is inaccurate– Crankback allowed

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Assumptions

• Connection setup time taken to cross each other node in network is known

• With each link (u,v) E is a toll t(u,v) representing time spent for propagation along (u,v) and the queuing and processing times at v

• Propagation delay constant, queuing and processing times almost constant at each node

• WLOG t(u,v)=1 for each link (u,v) E, thus, the setup time of a given path is directly proportional to the number of hops along this path.

2

2

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Assumptions (2)

• Source node can approximate probability of connection setup failure for each possible given path as a function of its estimated delay to the destination

• Density function of the accumulative delay of P(n0,nk): pdf(e1… ek)=pdf(e1) pdf(e2)… pdf(ek)

• Probability of failure P(n0,nk) Pf(P(n0,nk))= pdf(e1… ek) (x) dx

N N

R1D

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Problem Definition

• Adopting connection setup time as cost function

• Objective: Minimizing the average connection setup time

• Given: – directed graph G=(N,E)– candidate paths L={P(1), P(2)…P(L)}– source (S) and destination (T) node

• Problem: Order L for routing algorithm such that avg connection setup time is minimal

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Routing Algorithm

• Input: An ordered list of L candidate S-T paths

• Output: Feasible path P(i) or a rejection message1. i=1

2. Fwd connection setup request from S to T along P(i)

3. If P(i) satisfies all constrains; path feasible

4. Else if i<L then i=i+1 return to step 2

5. Rejection: No feasible path

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Fuzzy-based Ordering

• Input: – H(i): number of hops in P(i)– Pf(i): failure probability of P(i)

• Output:– Cost(i): Cost of P(i) in terms of connection setup

time

• Inputs used to define fuzzy rules and fuzzy logic membership functions

• Output used to determine preference order of connection paths

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Rule Matrix

• IF H(i) is LOW AND Pf(i) is LOW THEN Cost(i) is VERY LOW

• IF H(i) is LOW AND Pf(i) is MEDIUM THEN Cost(i) is LOW

Very Low

Low Medium

Low Medium High

Medium High Very High

H(i)

Pf(i)

Low Medium High

Low

Medium

High

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Membership Function

40%

1.0

Low Medium High

Degree of Membership

Probability of Failure

1.0

Low Medium High

Degree of Membership

Number of Hops105.5

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Input Degree of Memberhip Low Medium High

Number of Hops

Low Medium High

Probability of Failure

7 hops => 0.667 Medium, 0.33 High

10% Pf => 0.25 Medium, 0.75 Low

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Defuzzification

Rule H(i) Pf(i) Fuzzy Consequent

Output response value

1 L: 0 L: 0.75 VL 0

2 L: 0 M: 0.25 L 0

3 M: 0.667 L: 0.75 L 0.667

4 L: 0 H: 0 M 0

5 H: 0.33 L: 0.75 M 0.33

6 M: 0.667 M: 0.25 M 0.25

7 H: 0.33 M: 0.25 H 0.25

8 M: 0.667 H: 0 H 0

9 H: 0.33 H: 0 VH 0

H(i)=7

Pf(i)=10%

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Defuzzification (2)

• Using the fuzzy output matrix and the output response value:– Very Low = VL = max{rule1}=0– Low = L = max{rule2, rule3}=0.667– Medium = M = max{rule4, rule5, rule6}=0.33– High= H = max{rule7, rule8}=0.25– Very High = VH = max{rule9}=0

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Defuzzification (3)

• The output center points of the defuzzification method are:– Very Low Center = vlc = 0– Low Center = lc = 25– Medium Center = mc = 50– High Center = hc = 75– Very High Center = vhc = 100

• The output center points of the defuzzification method as explained in Fuzzy sets and Fuzzy Logic: Theory and Applications by Klir and Yuan

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Defuzzification (4)

• Path cost calculated using the center of gravity method

• Cost(pi)=

• Calculate the cost of the rest of the paths and sort them in an increasing order

• Requests are forwarded according to routing algorithm

vlc¤V L +lc¤L +mc¤M +hc¤H +vhc¤V HV L +L +M +H +V H = 41:64

Cost(P(1)) · Cost(P (2)) · : : : · Cost(P (L))

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Example Simulation ResultPath Failure

ProbabilitySuccess Probability

# Hops Optimal Greedy Fuzzy

Upper 0.20 0.80 2 2nd 2nd 3rd

Middle 0.24 0.76 1 1st 3rd 1st

Lower 0.18 0.82 5 3rd 1st 2nd

T(Fuzzy) = 0.76 * (1 * 2) + 0.24 * 0.82 * (1 * 2 + 5 * 2) + 0.24 * 0.18 * 0.8 * (1 * 2 + 5 * 2 + 2 * 2) = 4.4

T(Greedy)= 0.82 * (5 * 2) + 0.18 * 0.8 * (5 * 2 + 2 * 2) + 0.8 * 0.2 * 0.76 (1 * 2 + 2 * 2 + 5 * 2) = 10.65

T(Optimal)= 0.76 * (1 * 2) + 0.24 * 0.8 * (1 * 2 + 2 * 2) + 0.24 * 0.2 * 0.82 * (1 * 2 + 2 * 2 + 5 * 2) = 3.3

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Simulation Results

• Fuzzy algorithm higher than optimal by 10% while Greedy algorithm higher than optimal by 90%

Probability of path failure

Average connection setup time

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Simulation Results (2)

• Fuzzy algorithm higher than optimal by 11% while Greedy algorithm higher optimal by 100%

Average number of hops per candidate path

Average connection setup time

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Simulation Results (3)

• No significant gap between the three algorithms

Probability of path failure

Average number of crankbacks per connection

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Case Study Summary

• Average deviation of fuzzy algorithm from optimal is 10%; more than acceptable for practical networks

• Significant advantage over optimal since it does not require the knowledge of the exact pdf for each additive QoS constraint of every link

• Easily implemented in routing protocols of communication networks with minimal computational overhead while significantly improving overall setup time

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Possibility vs. Probability

Sum of possibility distribution does not need to sum to 1

Sum of probability distribution should equal 1

Directed at the uncertainty in the description of an event

Concerned with uncertainty in the outcome of clearly defined and randomly occurring events

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Problems and Limitations

• Stability: No theoretical guarantee that fuzzy system does not go chaotic

• Learning capability: Capability of machine learning, memory, or pattern recognition through hybrid fuzzy-neural systems

• Determining or tuning good membership functions not always easy

• Verification and validation requires extensive testing with hardware in the loop.

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Conclusions

• Long term implications for industry and business due to commercialization of fuzzy logic

• Need to market innovative products at cheaper price

• Can not afford to ignore fuzzy technology

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References

1. S. Dutta, Fuzzy Logic Applications: Technological and Strategic Issues, IEEE Transactions on Engineering Management, Vol 40, No 3, pg 237 – 254, 1993

2. A. Cohen, E. Korach, M. Last, and R. Ohayon, A Fuzzy-based Path Ordering Algorithm for QoS Routing in Non-deterministic Communication Networks, Fuzzy Sets and Systems, Vol 150, pg 401-417, 2005

3. T. Munakata and Y. Jani, Fuzzy Systems: An Overview, Communications of the ACM, Vol 37, No 3, pg 69-76, 1994

4. Carey Williamson, CPSC 641: Performance Issues in High Speed Networks Homepage, Retrieved on 8 February 2005 from http://pages.cpsc.ucalgary.ca/~carey/CPSC641/

5. Anirban Mahanti, CPSC 441: Computer Communications Homepage, Retrieved on 8 February 2005 from http://pages.cpsc.ucalgary.ca/~mahanti/CPSC441/

6. S. Kaehler, Fuzzy Logic Tutorial, Retrieved on 4 February 2005 from http://www.seattlerobotics.org/encoder/mar98/fuz/flindex.html

7. C. Elkan, The Paradoxical Success of Fuzzy Logic, Proceedings of the Eleventh National Conference on Artificial Intelligence, pg 698—703, AAAI Press, 1993.