Original Articletsm, Volume: 12( 3)
Fuzzy Modelling gamma-Radiated Starches as Inactivating Agents of Nuls Lectins
- Isaac W Ofosu, Senior Lecturer, Department of Food Science & Technology, College of Science, KNUST, Kumasi, Ghana, Tel: 233 3220 60352; E-mail: [email protected]
Received: October 12, 2017; Accepted: November 10, 2017; Published: November 19, 2017
Citation: Ofosu IW. Fuzzy Modelling γ-Radiated Starches as Inactivating Agents of Nuls Lectins. Macromol Ind J. 2017;12(3):109
The persistence of heat resisting lectins in foods pose serious health hazards and this has driven studies into finding suitable ways to attenuate their possible risks in foods that contain high levels such as beans. Many of the adverse effects of lectins are attributable to their binding to specific membrane-bound carbohydrates with unique structures. Thus, the aim of this study was to determine the effects of the use of ïÂ§-radiated starches in inactivating lectins in five NULs flours, studied in an extruder serving as a bioreactor. Firstly, radiated starches were prepared using radiation doses from 3 kGy to 42 kGy. Defatted NULs flours were composited at 10% of the radiated starches in respect of the quantities of the native starches present. The composites were agitated in an extruder which operated within intrinsic temperature changes ranging from 2°C to 12°C. Residual lectins from the extrudates were quantified by ELISA analysis. Mamdani type fuzzy logic inference system was used to model the two input variables to predict the optimal lectin inactivation at 100% accuracy. While lectins from Canavalia sp. recorded 83.1% inactivation, lectins from Vigna sp. rather potentiated up to 44%. Thus, ïÂ§-radiated starches, incorporation into NULs flours during low temperature extrusion treatment, inactivated NULs lectins at varying degrees which were adequately predicted by the model.
Fuzzy logic; Lectin inactivation; Radiated starch; Extrusion cooking
Lectins are glycoproteins that abound in plants and animals . They are plentiful in legumes, wheat flour and nuts and are known to resist digestion in the gastrointestinal tract . Consumption of meals containing lectins, because of improper cooking is known to result in conditions such as leaky gut , bacteria and protozoa infections  and hyperplasia and hypertrophy of the small intestine . Such pathologies caused by lectins were avoided or minimized when diets containing lectins were removed, prior to consumption . Many attempts have been made to inactivate lectins, using such processes as fermentation  and dialyzing out metal ions such as Ca2+ and Mn2+, known to associate with legume lectins . Chemical derivatization of soybean lectins  and thermal processing, followed by limited proteolysis have also been used .
Carbohydrates are known to bind to lectins and the mechanism of the binding action of specific carbohydrates to lectins has been explained . Their explanations show that customized carbohydrate-lectin complexes underlie the inactivation process. It has been reported . that some level of disruption to protein structures occur during extrusion cooking at temperatures of about 85°C, as a result of unfolding of protein chains . Though these thermal methods do inactivate lectins to some extent, they also produce unsafe by-products such as Maillard reaction products and advanced glycated end-products . In addition, there is degradation of proteins and amino acids as a direct result of the high temperatures usually employed in extrusion . Beta (1, 3)-D-glucans in plants are carbohydrates that are bindable to some lectins . There is strong evidence showing that increased levels of β (1-3) and β (1-4)-bonded starches in bean and maize flours are produced in a dose-dependent manner during radiation . The mechanism behind the production of β-starches involve the action of free radical reactions which lead to molecular depolymerization . Other studies reveal the formation of dose-dependent depolymerized starch products of varying molecular weight [17,18]. From these studies, it has emerged that native starches irradiated from 2 kGy to 40 kGy, produce depolymerized products of intermediate molecular weight fractions, followed by amylose-like fragments and eventually water-soluble oligosaccharides. Fragments ranging from 2 kDa to 400 kDa in maize and sorghum and also 1 kDa to 300 kDa in beans have been reported in these studies. Therefore, it is uncertain as to what radiation dose would be adequate, just to produce the right molecular weight starch containing the suitable levels of β-starches to inactivate lectins.
There are uncertainties about specific temperatures employed in extrusion to achieve the desired protein inactivation, while maintaining food functional proteins or even avoiding harmful side-products. Firstly, there are different sources and levels of lectins even in the legumes, that would require different operational temperatures for their inactivations. Secondly, it can be deduced from studies  that starch with various molecular sizes and physicochemical properties are produced when they undergo doses of radiation ranging between 2 kGy and 40 kGy. In the use of radiations, there are also uncertainties as to whether low, moderate, or high radiation doses must be used to treat starches to produce β-starches with specific structures for the inactivation of lectins. Situations, where imprecise variables must be studied simultaneously before a decision is taken, often times put strain on time and resources. Fuzzy logic thus, become appropriate because of its ability to arrive at a decision, in the absence of precise mathematical models. Thus, the fuzzy inference system, based on fuzzy logic is used as a decision-making tool to arrive at timely decisions . Fuzzy logic extends the principles of the classical set theory  and uses intersections of crisp sets and by extension, the “if-then” rules. In fuzzy logic, crisp sets are transformed to fuzzy sets due to the imprecise nature of the elements in the set . Thus, fuzzy sets contain elements that have various degrees of memberships in those sets. While it offers elements that have strong membership in one set, it shows a weak membership in another set at the same time, on a scale ranging from 0-1 . By using the classical set operators of intersections; and “∪” and or “∩” , fuzzy variables are mapped to outputs in an “if-then” rule relations in order to arrive at a decision. Thus, fuzzy logic is a process of representing data and knowledge closer to human-like thinking . There is fuzziness about temperature requirements in extrusion cooking  but in particular, extrusion cooking at moderate to high temperatures has been reported to inactivate lectins up to 98% . In fact, extrusion cooking at 85°C has been reported  to remove some lectins. However, other studies show that such high temperatures required for lectin inactivation could potentially render the extrudates unsafe . Thus, it is uncertain as to what temperature would be adequate, just to inactivate lectins while ensuring the safety of extrudates.
Radiation has been used on starches to produce starches of varied molecular weights  and unique carbohydrate structures, however, advantage has not been taken of these starches to inactivate lectins. Such starches can rapidly be produced by simply employing radiation technology. Though extrusion cooking alone can inactivate lectins at high temperatures, there is the attendant potential formation of unsafe extrudates. The main drive behind this work is to evolve appropriate lectin inactivation techniques for some locally consumed NULs involving the use of low temperature-driven extrusion treatment and β-starches produced by radiation. To be able to monitor the processing conditions of this study quickly and reliably, fuzzy logic was used as a tool to predict the outcome of imprecise input variables required to achieve the lectins inactivation processes. The study was in two parts; the production of lectins-inactivated NULs flours by making use of β-starches, obtained from radiation and composited with the flour in extrusion treatment. Secondly, construction of a prediction model for the inactivation process of the lectins using fuzzy modeling.
Materials and Methods
Preparation of legume flours
Five legumes (Canavalia sp., Vigna sp., Phaseolus sp., Mucuna sp. and Cajanus sp.) were obtained from six locations in the mid-west districts of Ghana; specifically, Abofuor, Techiman, Drobo, Mampong, Ejura and Amantin. The legumes were dried in a solar tent dryer (36 h) with a temperature range of between 40°C to 60°C. The beans were then sorted, cleaned and subsequently milled into flour in a Tecator cyclotec hammer mill (1093, Sweden) fitted with 1 μm screen/sieve. The flours were packaged in plastic bags, sealed, labelled and stored at 4°C pending further use.
Food grade native cassava starch (labelled as tapioca starch) was obtained from Ayensu Starch Limited (Ghana). Irradiation was carried out using the Cobalt 60 gamma irradiation facility (RTC, GAEC, Kwabenya, Accra) with ethanol chlorobenzene (ECB) dosimetry. One kilogram each of the starch was separately weighed into plastic containers and 100 ml of distilled water was sprinkled on them and sealed. Three groups of the sealed starches weighing 1 kg each, were labeled to give a total of nine samples and exposed to the following linguistic radiation dose variables low (3 kGy, 5 kGy, 8 kGy), moderate (13 kGy, 15 kGy, 18 kGy) and high (35 kGy, 38 kGy, 42 kGy). The dose rate was emitted at 2.14 kGy/h. Thus, depending on the dose required the samples were kept in the radiation chamber for different proportionate times, to achieve the required radiation doses.
Determination of starch content of legume flour samples
The starch content of each of the five flours samples were determined, using the Megazyme protocol, based on the original  total starch assay. The total starch contents were as follows; Phaseolus sp. (46.1%), Mucuna sp. (27.9%), Cajanus sp. (35.3%), Vigna sp. (46.7%) and Canavalia sp. (44.3%).
Conditioning of the NULs flours
Conditioning of the NULs flours were achieved by adding to each of low, moderate and high radiated starch samples equivalent to 10% starch content of each NULs flour, as reported in the starch analysis. The conditioning was done similar to other studies, where samples have been conditioned between 0.5%-5.0% [29,30]. The conditioning was up to 10% excess to allow the favorable inactivation of all available lectins that may be present in the NULs flours.
The five separate NULs flours, weighing approximately 5 kg each were cold-defatted (at 10% w/v, in three replications), using 45% n-hexane (Bitolea, Italy). The defatted flours were air-dried, packaged in plastic containers and stored at -20°C until further use. The experiments were run using Clextral BC 45 (Framatome, France) twin-screw extruder which had two sections (front and rear of the barrel) heated by induction coils. Circulating water run around the barrel of the extruder to maintain constant operating temperatures.
In all, the composite NULs flours containing 10% of radiated starches totaled 15 samples, excluding the native unconditioned flours. These composites were separately fed into the feed receptacle. Treated water was injected into the composite flour at mark 75 flow rate, by the time the feed reached the screw or shearing region. Preliminary runs were undertaken before settling on feed meal rate of 200 rpm and twin-screw speed at 900 rpm. The extrusion barrel which had two independent heating points (front and rear) had their extrinsic temperatures set at 50°C for the incoming feed meal and 70°C as the extrudate exited the die of 4 mm diameter. The extrudates presented specific intrinsic temperatures as the extrinsic temperature reached 50°C at entry point and again as they exited the die at extrinsic temperature 70°C. As the extrudates exited, samples were immediately taken and sealed in plastic containers for further analyses. The intrinsic temperature change was calculated as the arithmetic difference between the initial and final intrinsic temperatures, recorded at the two temperature sensors. The first sensor recorded the initial intrinsic temperature as the initial extrinsic temperature registered 50°C. The second intrinsic temperature was then recorded at the exit point of the extrudate as final extrinsic temperature eventually registered 70°C.
Determination of legume agglutinins using ELISA
Five (5) grams each of the extrudates flour samples were weighed and blended into a total of 30 ml phosphate buffer saline and quantitatively transferred into 50 ml Falcon tubes. Samples were then agitated at 250 rpm on Pro Digital Orbital Shaker (SK-O330, US) overnight, at room temperature. After centrifugation at 10, 000 rpm for 5 min, 500 μl supernatant was collected into 1.5 ml Eppendorf tube. Determinations of lectins were done, using ELISA with plant soybean agglutinin (Gentaur Molecular Products, BVBA (Belgium) as a standard, like other studies [31,32].
Data analysis based on fuzzy logic model
First, there is the input variables unit, linked to a fuzzification interface which transforms the crisp numerical input variables into linguistic fuzzy variables. A fuzzy inference process is composed of a series of 4 instructional units (Figure 1) designed to perform unique functions as outlined in the overview (Figure 2). This is followed by the database unit where selection membership functions of each fuzzy sets occur. Then, making use of the rule-base, which contains fuzzy “if-then” rules, decision-making inference operations are run.
Consequently, a fuzzy truth reference table, representing all possible outputs for all possible inputs are obtained. Lastly, a defuzzification interface transforms the fuzzy output results into crisp numerical output results. In the fuzzy logic tool box , the initial step of fuzzy modelling is the fuzzification process, where the numerical data set obtained in the study (Table 1a) were expressed as fuzzy data (Table 1b).
|Input variable||Output variable|
|Dose/kGy||Intrinsic temperature/°C||Lectin content: mg/g (db)|
Table 1a: Percentage lectin inactivation obtained from treatments with two crisp variables; radiated starches and intrinsic temperature change in extruder.
In the next step, ranges of the crisp inputs (Table 2a) and output (Table 2b) variables were set, together with their membership functions (Figure 2). The ranges refer to the corresponding crisp input and output values based on their universe of discourse (universal set).
|Input variables||Output variables|
|Sample flours||Dose/kGy||Intrinsic temperature change/°C||% Lectin change|
|Caj lo||Low||Modest||Moderate decrease|
|Phal lo||Low||Modest||Moderate decrease|
|Phal me||Moderate||Modest||Slightly low decrease|
|Phal hi||High||Modest||Slightly low decrease|
|Vig lo||Low||Big||Moderate decrease|
|Vig hi||High||Big||Slightly low decrease|
|CanEs lo||Low||Small||Intense decrease|
|CanEs me||Moderate||Small||Intense decrease|
|CanEs hi||High||Small||Intense decrease|
|Muc lo||Low||Small||Moderate decrease|
|Muc me||Moderate||Modest||Moderate decrease|
|Muc hi||High||Modest||Intense decrease|
Table 1b: Percentage lectin inactivation obtained from treatments with two crisp variables; radiated starches and intrinsic temperature change expressed as fuzzy linguistic responses.
Membership functions are depicted in graphical forms to characterize the degree (between 0 and 1) of the fuzziness of each of the elements in a linguistic variable in a fuzzy set . The option exists to choose from among several membership functions such as; triangular, gaussian and trapezoidal. For this study, triangular membership function (Figure 3) was selected for each of the input and output variables based on better performance relative to other membership functions .
The range of radiation dose of between 3 and 42 kGy was selected because of their applications in dose-response production of β-starches . The three-radiation dose fuzzy sets, were specifically defined as; low (3 kGy, 5 kGy, 8 kGy), moderate (15 kGy, 18 kGy, 20 kGy) and high (35 kGy, 38 kGy, 42 kGy) (Table 2a) for this study. However, the radiation doses also overlapped with starch fractions presumably representative of intermediate fractions, amylose-like fractions and water-soluble oligosaccharides respectively . The intrinsic temperature change required during extrusion cooking, were similarly linguistically defined; small (2-3°C), modest (4-10°C) and big (8-12°C) for this study (Table 2b). The various levels of lectins remaining after treatments were arbitrarily classified into four fuzzy linguistics terms. The fuzzy linguistic set; potentiation (+1 to +44%), was based on increased activity of lectins rather than inactivation. The fuzzy linguistic set; slightly low decrease (0 to -19%), was based on minimal inactivation of up to 20%. On the other hand, the fuzzy linguistic set; moderate decrease (-20 to -49%) was selected based on the inactivation of lectins up to 50%. The intense decrease (-50 to -83.1%) fuzzy linguistic set, was based on inactivation of upwards of 50% inactivation.
|Inputs||Fuzzy set/Linguistics||Range of data|
|Radiation dose/kGy||Low-Moderate-High||3-42 kGy|
|Intrinsic temperature change/°C||Small-Modest-Big||2-12 °C|
Table 2a: Fuzzy sets and the linguistics of inputs and their specific ranges.
|Output||Fuzzy set/Linguistics||Range of data|
|% Lectin change||Intense decrease-Moderate decrease-Slightly low decrease-Potentiation||-83.1 -44.0%|
Table 2b: Fuzzy sets linguistics of the output response range.
Potentiation is said to occur when after thermal treatment, the activity of lectins increases several folds, compared to their native states . In Mamdani fuzzy inference, both the input and the output variables were transformed into fuzzy propositions  as outlined in (Figure 2). Takagi–Sugeno (TS) fuzzy model is another type, but it is usually selected if the input variable is a fuzzy proposition while the output variable is a crisp function .
Next, was the establishment of a fuzzy rule relation, using the “if-then” commands to generate the 15 rules (Table 3), together with their simulations and the relational graphs. The simulations of the input variables were able to predict to 100% accuracy, the optimum inactivation of lectins at 83.1% that was recorded when intrinsic temperature change was modest and radiated starch dose was high (Figure 4). From the rule relations, it is observed that an “AND” function, also known as the algebraic product function , was used as fuzzy operator to aggregate the two inputs, in order to get the output; lectin inactivation value. Just as input and output crisp data were initially transformed to fuzzy data set, processed and the output inferred, there is also the need to defuzzify the output, in order to obtain crisp value. To defuzzify is to select a single optimal point from the aggregated domain of a fuzzy membership function. In performing the defuzzification step, the mean-of-maximum (MOM) was used as the defuzzifier among several approaches [22,36].
Figure 4: Simulations showing 83.1% lectin inactivation making a 100% accuracy prediction for modest intrinsic temperature change and high radiated starch.
|1.||If (Dose is Low) and (Intrinsic Temperature change is Modest) Then (%Lectin Change is Moderate Decrease)|
|2.||If (Dose is Medium) and (Intrinsic Temperature change is Small) Then (% Lectin Change is Potentiated)|
|3.||If (Dose is High) and (Intrinsic Temperature change is Small) Then (% Lectin Change is Potentiated)|
|4.||If (Dose is Low) and (Intrinsic Temperature change is Modest) Then (% Lectin Change is Moderate Decrease)|
|5.||If (Dose is Medium) and (Intrinsic Temperature change is Modest) Then (%Lectin Change is Slightly Low Decrease)|
|6.||If (Dose is High) and (Intrinsic Temperature change is Modest) Then (% Lectin Change is Slightly Low Decrease)|
|7.||If (Dose is Low) and (Intrinsic Temperature change is Big) Then (%Lectin Change is Moderate Decrease)|
|8.||If (Dose is Medium) and (Intrinsic Temperature change is Big) Then (% Lectin Change is Potentiated)|
|9.||If (Dose is High) and (Intrinsic Temperature change is Big) Then (%Lectin Change is Slightly Low Decrease)|
|10.||If (Dose is Low) and (Intrinsic Temperature change is Small) Then (%Lectin Change is Intense Decrease)|
|11.||If (Dose is Medium) and (Intrinsic Temperature change is Small) Then (% Lectin Change is Intense Decrease)|
|12.||If (Dose is High) and (Intrinsic Temperature change is Small) Then (% Lectin Change is Intense Decrease)|
|13.||If (Dose is Low) and (Intrinsic Temperature change is Small) Then (%Lectin Change is Moderate Decrease)|
|14.||If (Dose is Medium) and (Intrinsic Temperature change is Modest) Then (%Lectin Change is Moderate Decrease)|
|15.||If (Dose is High) and (Intrinsic Temperature change is Modest) Then (% Lectin Change is Intense Decrease)|
Table 3: ?If-then? rules showing 15 rules truth reference table.
In the MOM process, the fuzzy logic controller identifies and then determines the membership function with the greatest degree of membership and determines the numerical value for that membership function . It was the MOM rather than the center-of-arithmetic-mean (COAM) which when used, predicted the greatest accuracy of 100%, even though COAM is the popular choice in Mamdani type of fuzzy inference system. In the COAM process, the fuzzy logic controller determines the y-coordinate of the center-of-arithmetic-mean of the area under the aggregated fuzzy membership functions and uses it as the optimal point .
Results and Discussion
Residual lectin activities of composite extrudates
Potentiation is said to have occurred if after thermal treatment the activity of lectins increases several folds, compared to their native states. The residual lectin activities obtained from this study was categorized into four residual lectins with distinctive linguistic fuzzy set defined by lectin activities described as potentiation, slightly low decrease, moderate decrease and intense decrease. Three exudates; Cajmo, Cajhi and Vigmo, (Table 4) showed potentiation of residual lectin activities up to 44% at moderate radiation dose and big intrinsic temperature change. Studies have shown that some lectins such as phasins (obtained from red kidney beans) are lethally toxic  even at the levels of 5 mg/kg body weight. Therefore, reports of potentiation are a serious matter of concern. From the studies, there is some evidence that lectins from Cajanus sp. were likely to potentiate. The cause of potentiation has been attributed to the tertiary and quaternary structures of lectin polypeptide subunit structures, enabling them to bind to specific sugars . Sometimes, disruption of the polymeric and oligomeric structures of lectins may cause unfolding and so expose extra binding sites, to resist thermal processing. Soybean lectin for instance, is known to possess tetrameric subunits  which offer higher level of stability and resilience . In this study, lectins potentiated up to 44% within an extrinsic temperature between 50°C and 70°C, compared to phasin, which potentiated five folds at 80°C .
|Lectin activities in Extrudates||Extrudates||Treatment conditions|
|Intense decrease||Muck, CanEsio, CanEsmo, CanEshi||a) Small IT/moderate dose
b) Modest IT/High dose
|Moderate decrease||Cajto, PhaLto, Vigo, Muck, Muemo||Modest to big IT/low to moderate dose|
|Slightly low decrease||PhciLia, Phal hi, Vighi||Moderate to high dose/Small or big TT|
|Potentiation||Cajmo & Ma, Vig.||Moderate dose/Big IT.|
Table 4: Extrudates treatments conditions and residual lectin activities.
Moderate dose radiated starches, which probably produced amylose-like products, showed moderate decrease in lectin activity in Cajanus sp. (Table 4). It is to be noted that small to modest intrinsic temperatures did not favor inactivation of lectins in Cajanus sp. flour when moderate to high dose radiated starches (which probably produced amylose-like fragments and soluble oligosaccharides) were used in replacement of the native starches.
This observation is premised on the fact that Cajanus sp. lectins are known to be specific for α-mannose and α-glucose  but not the β-starches produced by the irradiation of starches .
Residual lectins present in the composite extrudates from this study ranged from 14.4 mg/g flour in Cajanus sp. composited flour, to 83.9 mg/g in Canavalia sp. composited flour. However, the native NULs flours had previously been determined to have lectins ranging from 64 mg/g in Phaseolus sp. flour to 414 mg/g in Canavalia sp. flour before compositing. The treatment of legume flours in this study recorded about 83.1% reduction (Figures 5a and 5b) in lectin activity.
Figure 5a: Surface view of the impact of two inputs (radiation dose of starch and intrinsic temperature change during extrusion) and output (% Lectin change).
Figure 5b: Pseudo colour view of the impact of two inputs (radiation dose of starch and intrinsic temperature change during extrusion) and output (% Lectin change).
These observations were made in Canavalia sp. extruded with high dose radiated starches, with modest intrinsic temperature change and Mucuna sp. extruded with small intrinsic temperature range with low radiated starches. The high radiation dose starch which probably contained smaller amylose-like fragments and soluble oligosaccharides , meant Canavalia sp. lectins had affinity for low molecular size β-starches. On the other hand, low-dose radiated starches meant Mucuna sp. lectins might probably have affinity for relatively larger molecular size β-starches for inactivation.
It could also mean lectins from these NULs were not oligomeric to have their lectins to be buried in the native state but become exposed when their structures become unfolded upon intrinsic temperature agitation. A closer observation shows that Canavalia sp. lectins, initially at 83.9 mg/g rapidly inactivated between 11.6 mg/g and 22.5 mg/g. There seem to be certain characteristic features about the lectins in Canavalia sp. that could warrant this observation. This may probably be due to a strong affinity for soluble oligosaccharides that cluster the binding sites of lectin polypeptides  to inactivate them subsequently. Thus, it may be inferred that the molecular size of the specific starches contributed little to inactivate the lectin but rather, it was the affinity to bind to these specific starch oligomers that had the desired impact.
Extrudates such as Cajlo, PhaLlo, Viglo, Muclo, Mucmo (Table 4) exhibited moderate decrease in their legume lectin activity of between 20% and 50%. However, it appears low to moderate radiated starches (probably containing amylose-like and soluble oligosaccharides) coupled with modest intrinsic temperatures effected moderate decreases of lectin activity, no matter the source of the legume lectin. Vigna sp. lectins seem to be difficult to inactivate. The treatments for Vigna sp. flour could cause a moderate decrease in lectin activity but could also cause potentiation (Table 4). A review of the protein database specifically on the molecular structure of lectins in Vigna sp. showed a paucity of information . However, it may probably be similar to peanut agglutinin judging from the resistance of its lectin activity . Lectin resistance may also be possible if the specific starches are not suitable due to steric hindrances, or there is hydrophobicity of the complimentary amino acids (Weis and Drickamer, 1996). There could also be the potential to expose previously partially buried lectin polypeptides that would then confer carbohydrate binding activity [43,44].
For extrinsic temperature range of between 50oC and 70oC, Canavalia sp. and Mucuna sp. lectins could inactivate over 80% at low to moderately radiated starches within short to modest intrinsic temperature. Other composited flours recorded varying inactivation degrees of lectins at different molecular weight β-starches and different intrinsic temperatures. But lectins from Vigna sp. are likely to potentiate independent of the degree of the radiated starches or the intrinsic temperature applied. Thus, care must be taken to inactivate legume lectins with this procedure, since all lectins of NULs did not behave similarly. The Mamdani type fuzzy logic achieved a prediction of 100%, showing that fuzzy logic inference system as used in this study is capable of being used to predict responses of lectin inactivations.
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