A Velutinous Referendum Design for Hardware and Software Liability Emollient Systems

DOI : 10.17577/IJERTV1IS6450

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A Velutinous Referendum Design for Hardware and Software Liability Emollient Systems

A Velutinous Referendum Design for Hardware and Software Liability Emollient Systems

Y. Nagendra Kumar1, D. Uma Devi2

1M.Tech II year Student, Department of CSE, Sri Mittapalli College of Engineering,

2Associate Professor, Department of CSE, Sri Mittapalli College of Engineering,

Referending algorithms are used to adjudicate among the consequences of surplus modules in liability- emollient systems. Not exactly, popular allies entail a request-precise Adherent Origin value to be précised, whereas biased standard allies are incapable to generate a compassionate productivity while refusal concurrence exists between the allies inputs. The adherent is tentatively appraised from the summit of vision security and accessibility, and contrast with the imprecise popular adherent in a Triple Modular Redundancy prearranged outline. We show that the velutinous adherent gives extra exact outputs (advanced accessibility) than the wrong popular adherent with petite and hefty slip-ups, fewer false outputs (superior security) than the imprecise popular adherent in the occurrence of tiny slip-ups, and a smaller amount kind outputs than the inaccurate popular choose. The proportion of the kind outputs of the bulk adherents that are fruitfully hold by the velutinous fanatic (ensuing in accurate outputs) is more than the proportion of those that are disastrously determined by the velutinous fanatic (ensuing in erroneous outputs).

Key Words: Velutinous, Adherent Origin, Adherent, allies, Triple Modular Redundancy

  1. In many applications, dependency is going on increasing. These applications incorporate safety- critical computer control systems, recognition of a pattern, hugely dependable applications, and extremely accessible systems. Such applications use idleness to decrease the problems connected with depending upon any single component operating perfectly. Triple Modular Redundancy, TMR, and 3-Version Programming, 3VP, are generally used in liability emollient systems to present reactive redundancy for masking dynamic liabilities at hardware and software

    levels, correspondingly (Fig. 1). The outputs from three equal elements working in similar with the same inputs are passed to a selection unit that decides connecting them to produce an overall output. The selected output will be accurate so long as a particular number of elements (depending on the selection strategy) and the selection unit are functioning properly. The selection unit will be referred as selector in this paper. The outputs of unnecessary elements supply the selector inputs. Due to cost overheads, the amount of unnecessary elements in sensible cases rarely goes beyond 5. There are conditions, yet, where selection of a big quantity of inputs is necessary. Best example is presented in Image Processing filters where, at the time of each pass, pixel assessments can be substituted by assessments determined from selection on an already defined area of a close by position. In this paper, we deal with 3 input adherents regularly used in extremely reliable, very secure, and vastly accessible systems.

    Fig 1: A Triple Modular Redundant System

    Not exactly, many adherents generate an output from unnecessary inputs if there is concurrence between a many numbers of adherent inputs [23]. Biased standard adherents always generate an output despite of the concurrence, or else, between unnecessary inputs by merging the inputs. A key complexity with wrong majority adherents is the need to prefer a suitable origin value [25], which has a straight contact on the adherent presentation [2]. The difficulty of all recognized biased regular adherents is their failure to generate a gentle output (e.g., no output or secured output) in cases of entire divergence between the adherent inputs. Mutually, categories of adherents are also incapable to survive with doubts linked with adherent inputs generated from untrue

    software, strident situation, or strident hardware elements (Fig 2). In this, we initiate a novel referendum design based on the fuzzy set theory which addresses both of these harms. It lessens the ruthless behavior of the inaccurate majority adherent in the neighborhood of the Adherent Origin, and can be observing as a horizontal simplification of the inaccurate majority adherent.

    Fig 2: An imprecise adherent with an active origin

    The narrative velutinous adherent is the first reported use of an entire velutinous adherent in liability emollient systems, and varies from the further types of fuzzy referendum designs described in the literature [1,3,14,21,22] which are mostly used for model identification principle, and merging numerous organization systems.


        From the previous issues of social sciences, referendum is an admired system amalgamation process in various engineering disciplines, especially in safety-critical computer control systems, recognition of a pattern, hugely dependable applications, and extremely accessible systems. In hugely dependable applications, referendum will be functional at dissimilar planes; for model:

        • at sensor stage to combination of information attained from simulated sensors [6];

        • at actuator stage as used in x-by-wire systems and space shuttle [11];

        • at control stage, where three hardware elements execute the similar manage task to generate a single output as used in FTMP [13], Tandem Integrity S2 Computing System [15], K-1 Active Dispenser [20], and safety-critical PLC;

        • at software level, where three software program execute the similar control actions to generate a single output as used in SIFT [31];

  2. Selection on the outcomes of surplus components with distinct values is simple, and is called as accurate choice. The 3-input accurate majority adherent, for example, generates an output when 2-out-of-3 of its inputs are identical. However, exact selection on the outputs of unnecessary elements with real number outputs is not apt. The necessary variations might happen from dissimilarities in sensor calibration, data communication faults, quantization, instances, and/or rounding faults [10]. A number of explanations have been projected to tackle this trouble. In those explanations, the simple and easy method is dependent on the usage of median-sector algorithm [16], and it is very much useful for dealing with the output of unnecessary sensors. In this algorithm, it chooses the mid-value of the adherents input and then it utilizes that input value directly as the adherent output.

    Another explanation for dealing estimated unnecessary values is the use of imprecise (origin) adherents. In imprecise referendum, a little difference between the inputs is permitted; contract now means that the unnecessary outputs are not accurately the similar, but the dissimilarity among them is less than an exacting origin. The value of this origin is called the consensus origin and it is functioning precise. Deliberating the limits on the standard divergence among the outputs of unnecessary units for a systems complete processing time gives an approximation for the value of consensus origin. There have been done numerous trials for formalizing, applying and choosing an absolute value from the approved input values, and selecting the origin value of imprecise adherents on this basis [2, 18, 19, 25, and 28]. However, the use of imprecise adherents with a flat origin value at the control and computing levels is difficult for some reasons: (i) the choice of th origin is important and there is no logical loom for setting this value; (ii) a few suitable unit outputs may be denied when using a fixed origin value; and (iii) adherents with fixed origin values are incapable to differ their reaction in the appearance of dissimilar levels of deviation in safety-allied functions such as phased-mission systems. Imprecise referendum with an active origin has been suggested as a way of solving problems (i) and (ii) [28]. In this adherent, the value of the origin is determined on-line as a role of input curve and input data values in each referendum cycle. Experimental outputs reveal the advantage of an adherent with an active origin value adherent with a flat origin in conditions of

    system safety and dependability. In recent times, the notion of a flexible origin as the basis of a novel adherent was represented [8]. This adherent permits the user to set a range, as an alternative of a permanent value, as an adherent origin. It levels the go/no-go performance of the imprecise adherent with an unchanging origin value at the locality of the origin, and determines all of the troubles declare above for permanent-origin adherents. The origin range is again function-precise. Flexible adherents perform as a biased standard adherent within the origin range, and as an imprecise majority adherent outside this range.

    An imprecise adherent with an unchanging origin value may cause troubles in many real time control systems. In multi-state security-critical systems some of the prepared modes are more serious than the others; in a flight control system, for example, take-off and landing modes are more liability/fault-level than the rising, sliding, and cruising modes. Thus the liability emollient methods used for lofty-serious outfitted modes must vary from that of the fewer-serious modes. While using a TMR liability pretense approach, the previous modes need a referendum algorithm with a suspiciously chosen origin value whereas the end modes are possible to work properly with a better origin value. The use of condition-based referendum origin values is also states by the range of data formed by many unnecessary elements. Assume that in the ready state A, the adherent is faced with data from the period [1 5], and in state B it is tackled with data from the period [100 150]. At this time, decision among unnecessary data from the two dissimilar periods with the same origin value (e.g., 1.0) is doubtful. Clearly, judging among unnecessary small numbers needs a smaller origin value than arbitrating linking the unnecessary large real numbers. To facilitate, for state A the adherent inputs {1 2 3} (with the divergence of 1.0 from each other) are more likely considered in disagreement whereas for state B, adherent inputs {120, 121, 122} with the same divergence are measured in concurrence. This is the foundation for selecting an origin value for the novel adherent. The adherent origin is relative to the predictable numerical values of its inputs. The relative coefficient is a function detailed restriction.

    The Fig 2 structure is making clear by using a theoretical flight managing example shown in Table 1. In this example, it is expected that in elevated- significant modes (take-off and landing) the adherent is bumped with small input values (from the range [1 5]), therefore a small origin value has been set for this

    mode ( 1 aemax = 0.48, where aemax is the higher posse

    1 0

    of the range). For less-significant modes (e.g., cruising

    mode) the adherent is encountered with large numbers (from the interval [10 20]), and therefore, a large origin value is chosen ( 1 aemax =3.11).


    Table 1: An example for setting an Adherent Origin

    Ready Mode

    Pointer of the Mode

    Range of

    adherent output

    Adherent Origin

    Flight Taking Off


    0 < ae 5

    1 aemax




    5 < ae 10

    1 aemax




    5 < ae 10

    1 aemax




    10 < ae 20

    1 aemax


    Flight Landing


    0 < ae 5

    1 aemax


    In this paper, we introduce a velutinous referendum design, an improvement of the imprecise mainstream adherent. Beneath this loom, the primary difficulty of selecting a permanent value or a flexible range for adherent origin is largely curved, and the force of doubts are considered into account. In addition to this, the central fuzzy rules allocate a zero weight value for all adherent inputs in whole divergence Referending cycles.

    Fig 3: Configuration of a 3-input Velutinous Referendum unit

    The later potential outputs in a kind output (e.g., a secure output) for the adherent, and increases its security level. The fuzzy set theory has previously been used for calculating the ultimate adherent output, among the arranged adherent inputs, of an imprecise adherent [19]. In the previous issues, a transitive fuzzy correspondence relative was defined and included in

    conventional consensus and utmost probability Referending systems to good result. Fuzzy set theory has also been used to develop the consistency of categorization procedure in pattern recognition systems [5]. However, the use of fuzzy set theory for arbitrating between unnecessary values is narrative.

  3. With the preceding assistance, the velutinous

    Omn= |im-in|, where m n (1)


    c b = b a (2)

    where a, b and c are real numbers, and a<b<c


    1: Omn a,

    adherent utilizes fuzzy logic to create the weights essential for calculating a biased standard adherent output. Fig. 3 shows the basic Configuration of a 3- input Velutinous Referendum unit.

      1. Calculating the Velutinous Results of Adherent inputs:

        b Omn

        (b a)

        low = : a Omn b,

        0 : b Omn

        0 : Omn a,


        In this, the first pace in the loom needs the definition of a velutinous variation inconsistent to illustrate each pair of inputs to the adherent. For each pair im and in with statistical orbit Omn, based on the triangular relationship services shown in Fig. 4, we delineate a velutinous variation inconsistent represented by a set of relationship grades µR (Omn) where R: {low; average; high}. At the time of using balanced sets, this needs two bound values to be particular. On the basis of statistical variation between any two inputs, a non- zero relationship grade will be allotted to one or two of


        Omn a

        : a Omn b,

        (b a)

        c O


        mn : b Omn c,

        (c b)

        0 : c Omn


        0 : Omn b,


        the fuzzy sets defined for the consequent velutinous variation inconsistent. For expediency, triangular velutinous relationship services are used. This

        definition was implemented as a normal development

        Omn b

        (c b)

        high = : b Omn c,


        from the simpler flexible adherent described in [27] which an incline service in place of the fixed rigid origin found in conventional imprecise common adherents.

        Fig 4: Definition of the variation inconsistent relationship services, µR (Omn) where R: {low; average; high}

        We describe the inconsistent and velutinous relationship services as follows:

        Dissimilarity among two adherent-inputs:

        1: c Omn

        Commonly, in a k-way adherent, there are k (k-1)/2 velutinous variance variables. For every change, the design will effect in a non-zero relationship assessment being dispersed to one or two of the fuzzy sets separate for that inconstant.

        Inthe extreme circumstance of a=b=c (which we word inflexible differencing), we identify that two inputs will be consigned fixed (unity) relationship of either the low or the high variance set. In this structure, the velutinous adherent repeats a customary secure- origin popular adherent.

        The classification of the velutinous variance sets consents the narration of the velutinous adherent to be regulated. There is a chance to describe different modules of velutinous adherent in which the parameters a and c are fixed with reverence to the particular inflexible origin of the popular adherent. Fig. 5 illustrates two qualitatively distinct velutinous variance in constants. In the first case, there is an important section in which two inputs which contrast

        by a non-zero extent are considered as being in certain arrangement; a midway section in which the variation is identified using dialectal inconstant that may be correct to a slighter of larger amount (for instance, the variation among two inputs may be such that a non- zero relationship is presented to the low and average velutinous variation sets); and a third section which classifies inputs that are in fixed divergence. In the second case, velutinous inconstant, there is no province of certain arrangement identified, while there is a section of fixed divergence.



        Fig 5: Qualitatively dissimilar descriptions of velutinous variances.

      2. Outlining the Velutinous Disposition of Every Input:

    Per every inputs of im, before we express a velutinous disposition inconstant, µS(wtm) with reverence to the other inputs. The velutinous disposition assessment is a quantity of the degree to which an input accepts with the other two inputs. Respect to this, the loom is parallel to the biased regular adherents which determine the weights as a purpose of the orbit among deviations.

    For every velutinous disposition inconstant, we describe five intersecting fuzzy sets S: (vsmall, small, average, large, vlarge). An example of the fuzzy

    set definition is shown in Fig. 5. The velutinous disposition inconstant is essentially definite above the range [0 1]. The disposition measure (and disposition evades) is took out from the error model [2], where any adherent input is labelled as out of range, improper, adequate, and accurate value. Varying the constraints j, k, and l has straight effect on the output of the adherent which, in order, vagaries the security and obtainability concert of the adherent. The velutinous disposition value is used to identify the biased involvement of the consistent input to the adherent output. The greater the disposition of an input, then the greater its allowance in the control of the adherent output.

    3.3. Fuzzy rule set description: qualitatively mapping velutinous dissimilarities to velutinous disposition:

    From the below Table 2, it describes a rule matrix that go over one feasible set of fuzzy rules for joining and plotting velutinous dissimilarity values onto a velutinous disposition value in a 3-input system. In this, the matrix will be steady with the categorization of adherent input inconsistencies shown in [25]. Other developments of the rules are potential, but we have to bind our own to the subsequent in this paper, because it has the majority expected elucidation.





    Omp Low












    Table 2: Rule matrix used for velutinous input inconstant

    For instance, let us take a three input adherent with inputs i1, i2 and i3. At this time, we can describe a set of fuzzy rules to explain the disposition of input i1 (i.e., the measure of its concurrence with the other two inputs) in accordance with Table 2 as follows:

    1) IF (O12 is low) AND (O13 is low) THEN i1-disposition is vlarge.

    2a) IF (O12 is low) AND (O13 is average) THEN i1- disposition is large.

    2b) IF (O12 is low) AND (O13 is low) THEN i1-disposition is large.

    3a) IF (O12 is high) AND (O13 is low) THEN i1- disposition is average.

    3b) IF (O12 is low) AND (O13 is high) THEN i1- disposition is average.

    4) IF (O12 is average) AND (O13 is average) THEN i1- disposition is small.

    5a) IF (O12 is high) AND (O13 is average) THEN i1- disposition is vsmall.

    5b) IF (O12 is average) AND (O13 is high) THEN i1- disposition is vsmall.

    5c) IF (O12 is high) AND (O13 is high) THEN i1- disposition is vsmall.


    Low Average High

    operation rule [24]. With the usage of velutinous disposition sets defined earlier, the three central sets (small, average and large dispositions) are balanced and the two risky sets (vsmall and vlarge) are abstract to be disallowed at the margin. The tiniest and determined distinct values that we defined are 0 and 1, correspondingly. The described five sets are must and should have to be located in the same region. Now, it is essential to have a general awareness on cancroids, Q, for defuzzification of each of the disposition sets showed in Fig 5. The design continues as follows:

    Qvsmall = 0, Qsmall = 0.25, Qaverage = 0.50, Qlarge = 0.75,

    Qvlarge = 1 (11)


    Low Vlarge Average Large

    Average Average Small Vsmall

    aggSet = {vsmall, small, average, large, vlarge},

    High Large Vsmall Vsmall

    m: wtm =

    nagg Set

    disposition m , n Q n


    Table 3: Different, Unusable rule matrix

    For this, we dont have any common explanation for logical operators. All together, the connection of two fuzzy set is executed by a t-norm operator, and the combination of two fuzzy set is anecdotal by an s-norm operator. In the following execution of the rules, t is represented by the min operator, and s is represented by the max operator [32]:

    naggSet disposition m,n

    An additional option, and further common loom, to defuzzification (using Larsens product rule), is competent of getting the result of a velutinous inconstant distinct more than any number of randomly sized sets by enchanting into description the areas of the fuzzy sets that lie down within the distinct variety of the set. In this case, the velutinous value is given by

    the following equation where Expansen is the region of the set within the distinct variety of the inconstant.

    (1´) µvlarge (wtm) = min {µlow (Omn), m n} (6)

    (2´) µlarge (wtm) = max {min [µlow (Omn), µaverage (Omp),


    q =

    disposition m, n Expanse n Qn

    p: p m, n], n: n m} (7)

    (3´) µaverage (wtm) = max {min [µlow (Omn), µhigh (Omp),




    disposition m, n Expanse n

    p: p m, n], n: n m} (8) (4´) µsmall (wtm) = min {µaverage (Omn), m n} (9)

    (5´) µvsmall (wtm) =max {{min [µlow (Omn), µhigh (Omn),

    p: p m, p n], n: n m}, {µhigh (Omn);

    3.5 Biased adherent output computation:

    The bias values wtm are used in the usual biased standard adherent outline for calculating the adherent output j:

    m n}} (10)

    Rather than a Takagi Sunego loom, with its


    j = m 1

    i m w t m


    undeviating task in the rule output, that A Mamdani Larsen differencing method was used which well discards a collective-logic verdict of which inputs was maximum identical, and does not need the assortment of output task limitations [29].

    3.4 Results of velutinous disposition to its input bias standards:

    The easy and best way for getting the velutinous results is MIRROR RULE [12] and Larsens Product

    k w t m

    m 1


    The particlars of new assessment connection for software adherents used in this toil, and the technique of tests have been represented in [4], and are momentarily explicated beneath.

    4.1. Assessment connection structure:


    [1 1 1.5]




    [1 1 12]




    [1 1.1 1.7]




    [1 1.4 2.1]




    [1 1.5 1.9]




    [1.3 1.8 2.1]




    [1.2 1.7 2.5]




    [1.1 1.6 2.3]



    [1 1.6 2.3]



    [1 1.6 3.1]


    [1.2 1.6 2.8]



    [1 1.5 0.2]



    [1 1.7 22]


    The traditional new assessment connection, shown in Fig. 6, suggests a TMR system. It includes an input aid originator, three defilers (to insert mistakes to pretended input data), an adherent, and a comparator. The aid originator constructs one imaginary accurate output in each assessment cycle. This series of figures replicates equal accurate outputs created by surplus units. Duplicate of the imaginary accurate output are sent to each defiler in each cycle. The defilers can be independently planned to initiate unit faults, according to preferred arbitrary allocation. In an agreed set of experiments one, two or three defilers may be triggered to suggest unit output faults on the adherent inputs. The results of all defilers are preferred to be scanned adherent, and adherent result is evaluated by the cycle imaginary accurate output by ways of the comparator.

    Imaginary Accurate Output

    Fig 6: Assessment Connection Structure

  5. CASE








    [1 1.1 1.2]



    This primary trial is traditional that the velutinous adherent carries out properly; contrast its consequences with those of the imprecise greater part adherent in some preferred input situations. Table 4 demonstrates the output of the fuzzy-A and imprecise greater part adherents in 14 autonomous cases. In these cases the estimated accurate output is implicit to be 1. The primary channel of equally adherents is subjected to tiny slip-ups while the additional two channels are subjected to huge blunders.

    Table 4: Illustrated Adherent Outputs

    In the above circumstances 17, all adherents have related act. Like to the common adherent, the velutinous adherent is capable to effectively reject a remote input when creating the adherent result. In the circumstance 8, the common adherent creates an erroneous result but the velutinous adherent gives an accurate output. Yet, in 9 and 10 circumstances, the common adherent produces no output but the velutinous adherent generates erroneous results. In the circumstance 11 both of the adherents provide no output, as estimated. In 1214 circumstances, which replicate an absolute failure in one of the inputs, the common adherent gives no result but the velutinous adherent is capable to generate accurate outputs.

    The outputs of probing the adherents with a lot of additional input cases direct us to the subsequent preliminary ending.

    1. When the common adherent does well in generating the result, either accurate or erroneous, the velutinous adherent also is successful. That is, na (vel)

      na (com).

    2. In a lot of circumstances in which the common adherent generates a gentle output, the velutinous adherent can generate a result. To perceive that what proportion of such results is accurate or erroneous, we composed the outputs from 1000 selection cycles (Fig. 7). On this stature, nd(com) shows the amount of gentle results of the common adherent (gentle cycles); nd(vel), nc(vel) and nic(vel) represent the amount of kind, accurate and erroneous results correspondingly of the

      velutinous-A adherent during those gentle cycles of the common adherent. For this reason, nd(com)=nd(vel)+nc(vel)+nic(vel). The stature represents that:

      • The amount of gentle results of the velutinous adherent is constantly less than that of the common adherent: nd(vel) nd(com). This means that velutinous adherent is proficient of managing number of several fault cases than the common adherent.

      • The common adherent produces some gentle results up to emax =1 (i.e., tiny faults). This means that it cannot manage some of the numerous fault cases generated by tiny faults. The velutinous adherent effectively manages all such numerous faults, and generates an accurate result in every case.

    Fig 7: The amount of gentle cycles of the common adherent and all various (gentle, accurate, and erroneous) results of the velutinous-A adherent product during the gentle cycles of the common adherent.

      1. Security and Ease of Use Assessment with Tiny Faults:

        Fig. 8 represents the security and ease of use assessment designs of the common, vel-A and vel-B adherents for tiny faults. Vel-A adherent has higher security (35%) and ease of use (815%) than the other adherents in the occurrence of tiny faults. Such developments are considerable in many security-related and hugely accessible applications. Vel- B adherent gives more security than the common adherent only up

        to point emax =0:9 but offers huge accessibility than that adherent for all tiny faults.

        Fig 8: Adherent Presentation with tiny faults a) Security

        b) Ease of use

      2. Security and Ease of Use Assessment with Huge Faults:

        Fig. 9 represents the security and ease of use assessments of the compared adherents for an extensive range of faults. With huge faults (i.e., where emax

        >~1.2) the ease of use of the velutinous adherents is larger than that of the common adherent, significantly so in the circumstance of adherent vel-A. Though, for such huge faults and in contrast to the tiny fault case, the common adherent has a 38% improved security presentation than the velutinous adherents, with

        adherent vel-B performing better than adherent vel-A in most circumstances.

        Fig 9: Adherent Presentation with Huge Faults

        1. Security b) Ease of use

A velutinous referendum design has been introduced in this paper. It can be regarded as a curved imprecise common adherent. When the imprecise

common adherent succeeds in generating a result, either accurate or erroneous, the velutinous adherent does well. The velutinous adherent softens the rough performance of the imprecise common adherent in the region of the pointed Adherent Origin, and manages doubts and some of the numerous fault cases in the location distinct by the velutinous input inconstant.

The adherent works by captivating the arithmetical orbit among the input pairs as input parameters, and connecting it with a velutinous linguistic inconstant defining low, average, and high dissimilarities between each input pair. Five simple fuzzy rules are used to determine the velutinous disposition of each input with respect to theothers. The disposition inconstant describes the extent to which an input selectively agrees with both of the other inputs. The velutinous disposition of each input is then defuzzified to give the crusty values wtm that are used as the biasing factor of the adherent inputs when calculating its concluding result

Experimental results showed that the velutinous adherent gives low gentle results than the imprecise common adherent. The proportion of the gentle results of the imprecise adherent are effectively managed by the velutinous adherent is more than the proportion of those that are ineffectively cleared by the velutinous adherent. In the experiments carried out, both transformation of the velutinous adherent produces larger accessibility than the standard imprecise common adherent; so they are probably an appropriate contender for large obtainable systems. On the other hand, from the security viewpoint, velutinous adherents are better to the common adherent only in the presence of tiny faults. Apparently, a suitable change of velutinous inconstants perk ups their presentation.


The authors gratefully acknowledge the contributions of the reviewers. Their comments have considerably improved the quality of this article. We, authors express gratitude to all the anonymous reviewers for their affirmative annotations among our paper.

  1. J.F. Baldwin, J. Lawry, T.P. Martin, A mass assignment theory of the probability of fuzzy events, Fuzzy Sets and Systems 83 (3) (1996) 353367.

  2. J.M. Bass, P.R. Croll, P.J. Fleming, L.J.C. Woolliscroft, Three domain voting in real-time distributed control systems, Proc. 2nd Euromicro Workshop on Parallel and Distributed Processing, 1994, pp. 317324.

  3. N. Belacel, M.R. Boulassel, Multicriteria fuzzy classi6cation procedure PROCFTN: methodology and medical application, Fuzzy Sets and Systems 141 (2) (2004) 203217.

  4. S. Bennett, G. Latif-Shabgahi, and Evaluation the performance of voting algorithms used in fault tolerant control systems, Proc. 14th World Congress of Internat. Federation ofAutomatic Control, Vol. Q, Beijing, PR China, July 59, 1999, pp. 525530.

  5. V. Chatzis, I. Pitas, Fuzzy cell hough transform for curve detection, Pattern Recognition 30 (12) (1997) 20312042.

  6. D. Chen, A. Albrecht Schmidt, H. Gellersen, 1999. Architecture for multi-sensor fusion in mobile environments, Proc. Internat. Conf. on Information Fusion, Sunnyvale, CA, USA, Vol. II, pp. 861868.

  7. A. Davies, J.F. Walkerly, Synchronisation and matching in redundant systems, IEEE Trans. Comput. 27 (6) (1978) 531539.

  8. A.D. De Leon, Voting algorithms, M.Sc. Thesis, Department of Automatic Control and Systems Engineering Department, The University of Sheffield, Sheffield, UK, 2003.

  9. D. Dubois, J.-L. Koning, A decision engine based on rational aggregation ofheuristic knowledge, Decision Support Systems 11 (4) (1994) 337361.

  10. Z. Georgiev, M. Stojcev, VLSI common voting module for fault-tolerant TMR system in industrial system control applications, Internat. J. Electron. 76 (2) (1994) 163205.

  11. B. Hendentz, R. Belschner, Brake-by-wire without mechanical backup by using TTP-communication protocol, URL:

    http://www.vmars.tuwien.ac.at/projects/xbywire/project s/new-BBW.html.

  12. A. Hopgood, Intelligent Systems for Engineers and Scientists, 2nd Edition, CRC Press, Boca Raton, FL, 2001.

  13. A.L. Hopkins, T.B. Smith, J.H. Lala, FTMPa highly reliable fault-tolerant multiprocessor for aircraft, Proc. IEEE 66 (1978) 12211239.

  14. H. Ishibuchi, T. Nakashima, T. Morisawa, Voting in fuzzy rule-based for pattern classi6cation problems, Fuzzy Sets and Systems 103 (2) (1999) 223238.

  15. D. Jewett, A fault-tolerant unix platform, Digest of IEEE 21st Ann. Internat. Symp. on Fault-Tolerant Computing Systems, June, Montreal, Canada, 1991, pp. 512519.

  16. B.W. Johnson, Design and Analysis ofFault- Tolerant Digital Systems, Addison Wesley, Reading, MA, 1989.

  17. P.J. Keleher, Decentralised replicated-object protocol, Proc. 18th ACM Symp. on Principles ofDistributed Computing, April 29May 6, Atlanta, USA, 1999.

  18. K. Kim, M.A. Vouk, D.E. McAllister, An empirical evaluation ofmaximum likelihood voting in failure correlation conditions, Proc. ISSRE96 pp. 330 339.

  19. K. Kim, M.A. Vouk, D.F. McAllister, Fault tolerant software voters based on fuzzy equivalence relations, Proc. IEEE Aerospace Conf. 4 (1998) 519.

  20. D. Kohrs, S. Knowles, D. Cochran, R. Curtis, G. Lai, Beyond LEO: the K-1 active dispenser, Presented at the Space Technology and Applications Internat. Forum, Albuquerque, New Mexico, February 1114, 2001, URL:


  21. L.I. Kuncheva, C.J. Whitaker, C.A. Shipp, Is independence good for combining classi6ers?, Proc. Internat. Conf. on Pattern Recognition, Barcelona, Spain, 2000.

  22. L. Lam, C.Y. Suen, Application of majority voting to pattern recognition: an analysis of its behaviour and performance, IEEE Trans. Man Systems Cybernet. A: Systems Humans 27 (2) (1997) 553568.

  23. G. Latif-Shabgahi, J.M. Bass, S. Bennett, A taxonomy for software voting algorithms used in safety-critical systems, IEEE Trans. Reliability (2004), in press.

  24. C.C. Lee, Fuzzy logic in control systems: fuzzy logic controllerpart I, IEEE Trans. Systems Man Cybernet. 20

    (1990) 404418.

  25. P.R. Lorczak, A.K. Caglayan, D.E. Eckhardt, A theoretical investigation ofgeneralised voters, Digest ofIEEE 19th Ann. Intenat. Symp. on Fault-Tolerant Computing Systems, Chicago, IL, 1989, pp. 444451.

  26. H. Nurmi, A fuzzy solution to a majority voting game, Fuzzy Sets and Systems 2 (2003) 187198.

  27. M.K. Stojcev, J.Lj. Djordgevic, M.D. Krstic, A hardware mid-value select voter architecture, Microelectron. J. 32 (2001) 149162.

  28. M. Tagvaei, Experimental evaluation of voting algorithms, M.Sc. Thesis, Automatic Control and Systems Department-, The University of Sheffield, Sheffield, UK, 2001.

  29. K. Tanaka, An Introduction to Fuzzy Logic for Practical Applications, Springer, New York, 1996.

  30. H. Theuretzbacher, VOTRICS: voting triple modular computing system, Digest of IEEE 16th Ann. Internat. Symp. on Fault Tolerant Computing Systems, Vienna, Austria, 1986, pp. 144150.

  31. J.H. Wensley, L. Lamport, J. Goldberg, M.W. Green, K.N. Levitt, P.M. Miller-Smith, R.E. Shostak,

    C.B. Weinstiock, SIFT: design and analysis of a fault- tolerant computer for aircraft control, Proc. IEEE 66 (10) (1978) 12401255.

  32. H.J. Zimmermann, Fuzzy Set Theory and its Application, 3rd ed., Kluwer Academic Publishers, Dordrecht, 1996.

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