H. Monsef A.M.Ranjbar S. Jadid

Indexing terms: Fuzzy expert system, Power system, Fault diagnosis

Abstract: The paper demonstrates a novel component oriented fuzzy expert system (COFES) developed in PROLOG for power system fault diagnosis. This ‘expert system’ assesses faults on power systems using intelligent techniques that can take account of badlmissed SCADA data. Incorrect operation of protective relays and/or circuit breakers during single as well as multiple faults and corresponding uncertain incoming information render proper fault diagnosis a very involved task. To handle these uncertainties and rank various fault hypotheses a fuzzy signal model based on fuzzy information theory has been developed. The model measures degree of correctness of received and nonreceived input data. The proposed method incorporates fuzzy symbol classification through an enhanced knowledge-base which includes network model, predefined subnetworks, relaying schemes and fuzzy diagnostic rules. This expert system has been applied to a sample power system. The results obtained along with their evaluations are completely reported.

1 Introduction

Since the birth of artificial intelligence (Al), based on symbol manipulation, impressive progress has been made in our understanding of the basic issues related to knowledge representation. However, what is widely acknowledged is that the traditional symbol manipula- tion oriented AI techniques have proved to be much less successful in the realms of the common sense rea- soning. Hence, pure symbol manipulation is a tool, having a very limited effectiveness.

In recent years, several papers have proposed some ideas for using fuzzy logic in power systems. These ideas are closely related to the uncertainties in knowl- edge of the system model. In reality, uncertainties in status of relays and circuit breakers do not have a ran- dom nature and therefore cannot be represented by a 0 IEE, 1997 IEE Proceedings online no. 19970799 Paper first received 6th December 1995 and in revised form 15th July 1996 The authors are with the Artificial Intelligence Group, Electric Power Research Centre, Tehran, Iran

probabilistic approach. Nevertheless, they can be taken directly into account with the aid of concepts from fuzzy set theory which models vague, incomplete knowledge or qualitative information.

One of the most active areas of fuzzy logic applica- tions is in expert systems (ES). A fuzzy ES smoothly interpolates between hard boundary crisp rules. Rules are fired simultaneously, which means an action may fire multiple rules, and hence multiple resultant actions are combined into one or more interpolated results with different ranks.

Process of uncertain information using common sense rules and natural language statements is the basis of fuzzy ESs. The use of relay alarms and breaker trip signals in practical systems involves several tasks. These tasks depend upon the location of fault and operations of main and back up relays and breakers. Fault diagnosis is performed based on the evaluation of data according to a set of rules which the human expert has learned from past experience. Often these rules are not crisp, that is, most of the decisions are based on common sense or personal judgments. Such problems can be addressed by a set of fuzzy variables and rules which, if properly constructed, can make decision as well as an expert.

Several knowledge-based systems for fault diagnosis have already been reported [14]. Each of them uses either of two approaches: rule-based or model-based. The former uses the information of operating relays and tripped circuit breakers to estimate the fault sec- tion using conceptual knowledge about protective relaying schemes. In the latter, structure and functions of the protective relaying system are modelled, and the fault conditions are simulated and diagnosis is made by comparing the simulation results with the actual infor- mation.

The accuracy of the fault diagnosis is greatly affected by the type of data received from the power system. In the developed system we take a fuzzy model representa- tion for data received from the power system. The novel feature presented herein is fuzzy set theory that has been introduced as a mechanism to incorporate uncertainties and qualitative judgments in the status of relays and circuit breakers as well as correctness or incorrectness of their operations. Formulation of obscurity in their behaviours is included in the fuzzy model. Qualitative judgments and criteria are inte- grated into the developed expert system by using fuzzy set theory. Due to unavailability of the input signals’ timestamps, the developed ES does not consider sequence of operation.

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2 view

Necessity of fuzzy fault diagnosis: a general

One of the problems in monitoring power system oper- ations is the huge number of alarms generated during disturbances. An experienced operator in a dispatching centre is required to monitor the inflow of disturbance data and alarms to diagnose the cause of the problem and decide about the appropriate correcting action. Particularly, in emergencies, operators usually face an avalanche of alarm messages from faulty devices and protective equipment. These alarms are sent through communication links and may be spoiled by various measuring instruments and/or environmental factors [5 ] . Moreover, the protective fault clearing devices may misoperate/maloperate in response to a fault. Perform- ance of a fault clearing device (FCD) may be classified in eight different cases [3]: (i) FCD operated correctly and its alarm has been received (system correct operation) (ii) FCD operated correctly and its alarm has not been received (signal missing) (iii) FCD operated incorrectly and its alarm has been received (maloperation) (iv) FCD operated incorrectly and its alarm has not been received (maloperation + missing) (v) FCD did not operate and its operation is correct and also its alarm has been received (noise) (vi) FCD did not operate and its operation is correct and also its alarm has not been received (system intact) (vii) FCD did not operate and its operation is incorrect and also its alarm has been received (failure or out-of- service f noise) (viii) FCD did not operate and its operation is incorrect and also its alarm has not been received (failure or out- of-service)

In the case of correct device operation and lack of noise and missing information, (i) and (vi) above, fault diagnosis is a simple task. However, the above men- tioned factors create a lot of complexities in process of diagnosis, which in turn reduce the certainty degree of the results appreciably. As a consequence, the diagnos- tic system based only on the crisp logic principles may demonstrate different scenarios of equal rank which are not very useful to the operator.

When we reason, we make use of not only the infor- mation in which we firmly believe, but also some expectations which have guided our beliefs, without being part of that information [6]. For modelling these expectations and poorly measured or intrinsically uncertain information, several representation tech- niques can be used in which, at every instant, incoming data may be false or true or have not been received at all. Some techniques may have a random nature like throwing a dice and the others may not. The system behaves normally rather than according to possible exceptions, which may generate numerous hypotheses. To handle such problems several techniques can be used [7]. One widely used technique is based on Baye- sian system, like MYCIN [SI. But using this technique requires estimation of joint probabilities in order to find various ranks, which is a very difficult task and makes this technique intractable.

To reduce the complexity of a Bayesian reasoning system, one can introduce some approximations to this

IEE Proc.-Gener. Transm. Distrib., Vol. 144, No. 2, March 1997

approach, which results in some other techniques. One of them is fuzzy logic, which is best suited to reach conclusions in environments where conditions are rap- idly changing under a variety of interactions.

There are two concepts within fuzzy logic which play an important role in its application. The first is the lin- guistic variable, that is, a variable whose values are words or sentences in a natural synthetic language. The second is a fuzzy if-then rule in which the antecedent and consequent are propositions containing linguistic variables, which exploits the tolerance for imprecision and uncertainty [9]. As a result, with fuzzy logic the rules are expressed in their natural form.

B1 82 8 3 a

L1 L2

b 8 2 63

CB31 CB41

Fig. 1 Three networks a showing an alarm that breaker CB1 has opened b as for case a but also showing RLY 1 alarm c another network showing the same alarms as in case b

To illustrate some of the uncertainty issues in fault diagnosis, consider the example in Fig. 1. In case a, circuit breaker (CB1) is tripped with no relay (RLY) alarm message. One can suppose several hypotheses with various degrees of uncertainty: for example, (Hl) CBI trip signal is false (noise), (H2) CB1 has tripped incorrectly (self operation) and (H3) line L1 has a fault, CB1 has tripped correctly, alarm of RLYl is missed, alarm of RLY2 and trip signal of CB2 or back up devices are missed.

Case b is similar to case a but RLY 1’s alarm message has also been received, without any other signals. In this case we can give similar hypotheses but with differ- ent ranks from those of case a. Possibility of noise (HI) or operation of CB1 due to incorrect operation of RLYl (H2) is lower than those of case a. Moreover, presence of RLYl alarm increases the possibility of fault on line, L1.

In case e, network configuration is different from previous cases. Here, possibility of false signals (HI) or simultaneous incorrect operation of CB 1 and RLY 1 (H2) has been increased due to protective scheme on lines L21 and L22.

Fuzzy logic is highly applicable when multiple fault sections produce multiple scenarios. In these cases ranking of the scenarios as well as faulted sections is inevitable.

3 Fuzzy information theory

The presentation of the idea of fuzzy set theory for the first time by Zadeh [lo], motivated a revolution in the field of decision making and control theory. This sec- tion illustrates a general theory of fuzzy information.

A fuzzy logic variable A is a variable involving some concepts without clearly defined boundaries. In fact, it can be proclaimed as an extension of Lukasiewicz’s tri- valued variable [ I l l , that maps a gradual, rather than

187

an abrupt transition from membership to nonmember- ship into a set. In addition, it allows us to represent set membership as a possibility distribution. These mem- bership functions belong to a fuzzy environment which must be handled by fuzzy models, in terms of fuzzy relational equations [l I]. Consider the following fuzzy variables:

X : X ---+ [O, 11 and Y : Y + [0,1] ( l a )

The correspondence between X , Y and R can be expressed in different forms [la]. In fact, to extend sev- eral algebraic fuzzy sets, a min-max approach has been used which is much simpler than a probabilistic approach. But we rarely make decisions based only on maximum and minimum, and these functions do not completely match with the real logic world. One can use a variety of operators other than min-max [13, 141.

In the further discussion, attention is focused on fuzzy models of fault diagnosis signals and an operator to combine various fuzzy information.

R : X B Y 4 [ 0 , 1 ] O b )

3. I Fuzzy model of fault diagnosis signals In fault diagnosis process we encounter various types of signals such as circuit breakers and relays operation alarms, some of them may be missed due to communi- cation failures but are expected to be available. In addition, some of the received signals may be false due to communication channel noise. Receipt of a single alarm by a diagnostic system may not contribute to the final decision on the faulted component because it may raise into various hypotheses. Similarly, in the case of multiple input signals, numerous hypotheses can be concluded. It should be noted that all of the hypotheses produced by the fault diagnosis system cannot be equally ranked. The following paragraphs describe the application of fuzzy relations to various types of legal or illegal signals generated by the protective devices to rank suitably the final concluding hypotheses for fault diagnosis.

In general, power systems are designed to operate through very reliable SCADA equipment and instru- ments including remote terminal units (RTU), commu- nication links and communication interface units (CIU). These apparatus have high availability indices, hence rate of failures and unavailability are very small. Considering these facts, the membership functions of system correct operations and its intactness are taken to be higher than those of noise and signal failures (sig- nal missing). Due to above considerations, we assign a fuzzy membership degree (FMD) to each received or expected nonreceived signal, depending on its availabil- ity as shown in Fig. 2.

Figs. 2a and 2b show two typical assigned FMDs to the possibility of correctness and incorrectness of the received signal which mean whether the received signal reflects the real operation of the device or it is a noise and the device has not operated at all (p , - (X l ) and ~ E ( X . ) , repectively). Similarly, Figs. 2c and 2d are FMDs indicating the possibility of correctness and incorrectness of the nonreceived signal. These functions indicate either the expected signal was issued but has not received, (signal missing), or was not issued at all ( p ; ( X l ) and p;(X2), respectively).

Fuzzy memberships of each signal may be different from those depicted in Fig. 2. Five ratio codes, very low (VL), low (L), medium (M), high (H) and very

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high (VH) are classified for correctness or incorrectness of each received or nonreceived signal. Fig. 3 shows these fuzzy subsets of signals and corresponding mem- bership functions.

a b

C d Fig.2 Vuriour fuzzy membership functions XI possibility of correctness of signal X, possibility of incorrectness of signal bE fuzzy measure (membership degree) due to received signal kz fuzzy measure (membership degree) due to nonreceived signal

0 0.25 05 0.75 1 X Fig. 3 FUZZJJ subsets of received/nonreceived signals VL = very low; L- = low; M = medium; H = high; VH = very high

The signals required to diagnose a fault are always more than one and hence both the above cases (Figs. 2a and 26) and (Figs. 2c and 2 4 can be applied to each received or nonreceived signal, respectively. Therefore, a need for combined inferences based on fuzzified data is felt. This combination uses fuzzy data as input and generates fuzzy output data and is called fuzzy relation.

3.2 Fuzzy relations on fault diagnosis signals The received as well as expected nonreceived signals are fuzzified by the following membership functions: (i) received signal by ,&XI) and p;(X2) and (ii) expected nonreceived signal by p;(X,) and p;(X2). These func- tions can also be combined through fuzzy relations with other fuzzified signals where these combinations change all the FMDs. Receiving of any other signal associated to a particular subnetwork (Section 4.2) increments the p;(Xl) of itself and other related received signals, and accordingly decrements p~(X2) of itself and others. Similarly, in the case of an expected nonreceiving signal ( p;(Xl)) associated to a subnet- work, the p;(X,) of other related received signals are decremented and their p,-(X2) are incremented. Hence, the effects of these signals on each other may increase or decrease their own FMDs, according to Table 1.

In this table, arrows in columns a show the change in FMD on its own row created by the FMD on its own column. Conversely, the arrows in columns b show the

IEE Proc.-Gener. Transm. Distrib., Vol. 144, No. 2, March 1997

change in FMD on its own column created by the FMD on its own row. Decision making rules that map the input space to the output space are shown in Table 2.

Table 1: Cross interaction between FMDs

a b a b a b a b

PE(X1)

P.,(XA

PE (XI)

P8 CX,)

Table 2: Combination of fuzzy membership functions

VL L M H VH

VL VL VL L L M L VL VL L M H

M L L H H

H L M H VH VH

VH M H H VH VH

* ‘H‘ if received signal, ’L‘ if nonreceived signal VL = very low; L = low; M = medium; H = high; VH =very high

*

To demonstrate how this method works consider the network in Fig. 4, in which trip signal of circuit breaker CBI has been received. Here, we have the membership functions as shown in Fig. 5, where pc(X,) is membership function of possibility of the received trip signal of CB1 to be correct (correct operation), and pc(X2) is membership function of possibility of the received trip signal of CB1 to be incorrect (noise).

CBO CB1 CB2 CB3

B1 RLY 1

Fig.4 Sample network

a b Fig.5 Sample network CBI S FMDs

0 0.25 0.5 0.75 1 XI 0 0.25 0.5 0.75 1 X2

a b Fig. 6 Changes in FMDs of sample network

Moreover, if the alarm of RLYl having possibility functions similar to those of CB1 (as shown in Fig. 5), is received, the above membership functions will be

IEE Proc.-Gener. Transm. Distrib., Vol. 144, No. 2, March 1997

I

t

working memory

t hypothesis generator

I- - - - - - - - - + -I-+ -- - -- -- -7

I L____-_____-__________ knowledge base

Fig. 7 Developed expert system block diagram

The process of fuzzy fault diagnosis carried out by this ES is demonstrated in the flow diagram shown in Fig. 8. According to this flow diagram, the inferences made are based on input data set without considering the time tags. Hence, delayed signals do not affect the operation of this system and in this case only rediagno- sis should be done. The details of power system model, subnetworks and rule base of the developed fuzzy ES are described as follows.

4.1 Power system model In the developed ES a node-branch model is used to show the overall configuration of power system [15]. This model is adopted due to its special structure to demonstrate network interconnections which enables the ES to find the extension of fault.

189

irput signal pool 0 read and tuzzifyone signal I

1 -1

select corresponding subnetwork

select respective nagbout-s of each subnetworks from database 1

I

generate different hypothese based on subnetworks and corresponding neighbours

I

fuzzify all of the hypotheses with respect d

next subnetwork processed ?

select one hypothers from working memory

I ‘ 1 I

with their membership degrees to make this

hypotheses in working

memory processed ? > display the hypothesis in the working memwy according to their highest membership degrees up to low degree

Fig. 8 Developed expert system execution flow diugrum

For example, in Fig. 9 circuit breakers and power system components are represented by branches and nodes, respectively. This model is represented by a set of PROLOG clauses in the ES data base as follows:

net(comp-i, cbxtame, comp-j, status)

where ‘comp-i’ and ‘compj’ are components that are connected to each other through circuit breaker ‘cb-name’, and ‘status’ of the circuit breaker may be open or close.

190

In this model an isolator in series with a circuit breaker or a single isolator alone or only a circuit breaker between two components is considered as only one branch. The presence of initial branch status (ini- tial status of isolators and breakers) determines the pri- mary topology of the system.

CB3 CB4 CB5

& C 82

L1 1 I w 12 I . ~~ ,

1 B2 I a

CBI CB4 2 CB9 B3

CB3 ICBi6 G2 CB2 T2 CB7 L2 CBlO 84

b Fig.9, Sumplepower system a one line diagram b node-branch model

4.2 Subnetwork This ES divides all of the power system network into some predefined frames, named subnetworks. Their fault as well as the fault occurring in their neighbour- ing subnetworks are represented as rules with different FMDs. These rules are written in PROLOG and are saved in the rule base of the ES. Fig. 10 shows these frames of subnetworks. Neighbours of the affected sub- networks for which some of their related signals have been received, are found from power system model. Their FMDs are determined with respect to the related subnetwork.

4.3 Rule base The proposed ES represents its diagnostic knowledge as a set of rules. Each rule is associated with a certainty measure according to the component type, protection scheme and configuration of predefined subnetwork for which it is designated. The consequence of each rule is accompanied by a certainty measure which is obtained through application of fuzzy relations (Tables 1 and 2) to conjunction or disjunction of clauses in the anteced- ent of respective certainty measure. A typical COFES’ rule related to a line fault (Fig. 4) looks like: If

There is an evidence that alarm of RLYl has been received (RLYlFM = H), AND There is an evidence that alarm of CB1 has been received (CBlFM = H), AND There is an evidence that alarm of RLY2 has been received (RLY2FM = H), AND There is an evidence that alarm of CB2 has been received (CB2FM = H).

There is suggested evidence that line L has a fault (LINEFM = VH).

then

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Fig. 10 Frames of subnetworks

B

B B L f

I

Such rules are actually represented internally in PRO- LOG predicates as follows: find-FM ( h e , [CBlFM ,RLY 1FM ,CB2FM ,RLY2FM] ,LINEFM) :-

findrslt (CBlFM,RLYlFM,RSLTl),

find-rslt (CB2FM ,RLY2FM ,RSLT2),

find-rslt (RSLT1 ,RSLT2,LINEFM)

where RSLT1, RSLT2 and LINEFM are found with respect to Table 2 based on FMDs of CB1, CB2, RLYI, and RLY2. Such rules have been written for its existing neighbours having different FMDs and also for other received signals’ related subnetworks as well as their neighbours. According to the flowchart shown in Fig. 8, when there is no other input signal, the net- work components are ranked with respect to their fault and the process of diagnosis is terminated.

Table 3: Set of received signals

Substation Relay alarm Breaker alarm

Boostanow Distance (AB813-22) Distance (AB814-Z2)

Bandarlength Distance (H B8 14-22)

Bandarabbas Overcurrent(Gen)

West Bandarabbas Distance (AW808-Z2)

Sirjan Distance (SA905-Z2) Distance (SA906-Z2) Distance (CS807-Z3) Distance (CS808-Z1)

Sarcheshmeh Distance ICS808-Zl)

CBI

CB2

CBI

CBI CB2

CBI CB9 CBI0

CB2

5 Example

As an example, consider a portion of the Iranian 400kV-230kV power system network shown in Fig. 11, which is chosen to illustrate the implemented fault

diagnosis methodology. Each diagnosis requires a set of input data which consists of operated relay and cir- cuit breaker signals. These data are received from indi- vidual substations as shown in Table 3. These input signals are processed by the expert system according to the execution flow diagram, Fig. 8. The resulting diag- nosis of this ES is shown in Fig. 12.

&operated breaker loIy operated distance relay

erated overcurrent

Jahrom

Laar

bus-1

n

Bandarabbas Boost 22

G1 -G4 Fig. 11 Sample power system

This ES, with respect to the signals shown in Table 3 , generates several hypotheses with different ranks. Breaker and relay failures/missed signals are reported in each hypothesis. Because of the component oriented feature of this ES, multiple faults can be diagnosed, as shown in Figs. 11 and 12.

IEE Proc.-Gener. Transm. Distrib., Vol. 144, No. 2, March 1997 191

-MULTIPLE FAULT DETECTED-

FAULT 1:

-->FAULT ON BUS-1-BANDARABBAS, BUSFM= VH BREAKER FAILURE: CB2 BOOSTANOW RELAY FAILURE. DIFFERENTIAL(BUS-1, BANDARABBAS) RELAY FAILURE: OVERCURRENT(T5, BANDARABBAS) BREAKER MISSING: CB2-SIRJAN RELAY MISSING: DISTANCE(AW-XO7, WESTBANDARABBAS)

-->FAULT ON LINE AB-813, LINEFM= H BREAKER FAILURE: CBZ-BOOSTANOW RELAY FAILURE: DISTANCE(AB-81 3, BANDARABBAS) RELAY FAILURE: OVERCURRENT(T5, BANDARABBAS) BREAKER MISSING: CB2-SIRJAN RELAY MISSING: DISTANCE(AW-807, WESTBANDARABBAS)

-->FAULT ON LINE AB 814. LINEFM= H BREAKER FAILUREICB~-BOOSTANOW RELAY FAILURE: DISTANCE(AB-8 13, BANDARABBAS) RELAY FAILURE: OVERCURRENT(T5, BANDARABBAS) BREAKER MISSING: CB2-SIRJAN RELAY MISSING: DISTANCE(AW-807, WESTBANDARABBAS)

--> FAULT ON TRANSFORMER T5, TRANSFM= M BREAKER FAILURE: CB2-BOOSTANOW RELAY FAILURE: DIFFERENTIALfT5. BANDARABBAS) RELAY FAILURE OVERCURRENT(T5, BANDARABBAS) BREAKER MISSING CB2-SIRJAN RELAY MISSING DISTANCE(AW-807, WESTBANDARABBAS)

FAULT 2:

-->FAULT ON LINE CS-808, LINEFM= VH MESSAGE: DE-ENERGIZED LINE CS-807 NOT FAULTED CORRESPONDING RELAY OPERATED DUE TO OVERLOAD

Fig. 12 Result example of fault diagnosis

6 Conclusions

This paper has presented a component oriented fuzzy knowledge based ES for power system fault diagnosis and has illustrated how this ES handles uncertain inputs and how it processes them to obtain a ranked judgment about faulted components. The diagnosis carried out by this ES did not consider time stamps because sequence of operation was not required. Quali- tative judgements and criteria have been included by the use of fuzzy set theory to obtain an appropriately ranked diagnosis. To determine fuzzy membership degrees of received or nonreceived signals in the initial stages, one can incorporate the environmental factors such as type, substation voltage level, age of protective

devices as well as their qualities, related communication channel reliability etc. The results may be modified with some additional input data that are provided by operator.

Acknowledgement

The authors would like to record their appreciation to Dr S.C. Samani and Mr A.H. Farzam of the Iranian Electric Organization for their direction and helpful suggestions in the development of this system.

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eferences

GIRGIS, A.A., and JOHNS, M.B.: ‘A hybrid expert system for faulted section identification, fault type classification and selec- tion of fault location algorithms’, IEEE Trans. Power Delivery, Apr. 1989, 4, (2), pp. 978-985 FUKUI, C., and KAWAKAMI, J.: ‘An expert system for fault section estimation using information from protective relays and circuit breakers’, IEEE Trans. Power Delivery, Oct. 1986, 1, (4),

MONSEF, H., RANJBAR, A.M., and JADID, S.: ‘A rule-based expert system for power system fault diagnosis’. Proceedings of the 9th international power system conference, St. Petersburg, July 1994, pp. 357-365 OKAMOTO, H., YOKOYAMA, A., and SEKINE, Y.: ‘A real time expert system for fault section estimation using cause-effect network’. Proceedings of the 10th PSCC, Austria, Aug. 1990, pp.

‘Human factors review of electric power dispatch control center’, 1-6, EPRI EL-1960, Electric Power Research Institute, Palo Alto, CA GARDENFORS, P., and MAKINSON, D.: ‘Nonmonotonic inference based on expectations’, Trans. Artificial Intelligence, 1994, 65, pp. 197-245 RICH, E., and KNIGHT, K.: ‘Artificial intelligence’ (McGraw- Hill. New York. 1991. 2nd edn.). Chao. 8

pp. 83-90

905-912

SHORTLIFFE,’ E.H.’: ‘Computer-based medical consultation : MYCIN’ (American Elsevier, New York, 1976) ZADEH, L.A.: ‘Outline of the new approach to the analysis of complex systems and decision processes’, IEEE Trans. Syst., Man Cybern., Jan. 1973, 3, (l), pp. 2 8 4 4

10 ZADEH, L.A.: ‘Fuzzy sets’, In$ Control, Aug. 1965, pp. 338-353 11 KLIR, G.J., and FOLGER, T.A.: ‘Fuzzy sets, uncertainty and

information’ (Prentice-Hall, New Jersey, 1988) 12 PEDRYCZ, W.: ‘Applications of fuzzy relational equations for

methods of reasoning in presence of fuzzy data’, Fuzzy Sets Syst., 1985, 16, pp. 163-175

13 DOMBI, J.: ‘A general class of fuzzy operators, the De Morgan class of fuzzy operators, and fuzziness induced by fuzzy opera- tors’, Fuzzy Sets Syst., 1983, 11, pp. 115-134

14 GUPTA, M.M., and QI, J.: ‘Theory of T-norms and fuzzy infer- ence methods’, Fuzzy Sets Syst., !991, 40, pp. 431450

15 TRACA-DE-ALMEDIA, A.: Substation interlocking and sequence switching using a digital computer’, IEEE Trans. Power, Appar. Syst., June 1981, 100, (6), pp. 3002-3007

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