As an EDOY leverages his/her past outcomes to improve upon the present efforts, a reinforcement factor is devised as a sigmoid of an average of the (t-1) elapsed values of outcome from i =0 to i=t-1, computed as:

γ(t, k) = , (15)

−∆F(t,k)

1 + e

where the average is given by

1 t−1 1 t−1

∆F(t, k) = ∑i=1 F(rs, w(i, k)) − F(rs, w(i − 1, k)) = ∑i=1 f(i, k) − f(i − 1, k).

t−1 t−1

The above reinforcement factor is chosen to be simple, as it is not associated with a reward function based on some policy. Here, its role is to give weightage to the weight vector of EDO. For instance, we could give more weightage to the latest fitness values and the least to the past values. Note that we have suppressed the abbreviations rs and w in f. The pHT is modelled as pHT weighted with the reinforcement factor that accounts for the past outcomes, given by:

−μP(t,k)wD(t,k,l)

wD(t + 1, k, l) = γ(t, k). wD(t, k, l)e , (16)

−|f(t,k)−f(t−1,k)|

where μP(t, k) = μD(t, k) + vD(t, k) and μD(t, k) = e .

In this, the HT divergence based on the difference between two information values of the best achiever, μ(t, best)w (t, best, l) and the k th contender μ(t, k)w (t, k, l) is computed using Eq. (16) as:

−(μ(t,best)wR(t,best,l)−μ(t,k)wR(t,k,l))

wR(t + 1, k, l) = wR(t, k, l)e . (17) As shown in Eq. (12), the above HT divergence can also be written as :

μR(t, k)wR(t, k, l)

wR(t + 1, k, l) = wR(t, k, l). log( ), (18)

μR(t, best)wR(t, best, l)

where the outcome-based MFs of the best achiever and the kth contender are:

−(fbest−fav)

μ (t, best) = e f ,

and

−(fk−fav)

μ (t, k) = e f .

With fbest=F(w(t, best)), fk=F(w(t, k)), and fav as the average outcome.

It may be noticed that we have associated the advanced concept called pervasive information and reinforcement with the EDO component of learning, as EDOY is entrusted with a plan at his disposal for the next outcome, so it is vested with the ability to utilize the past and present information. This capability is a rare kind of outlook of a contender, whereas an inquisitive higher form of information called transform is bestowed with the ERO component of learning. As ESO has a tendency to steal, we have to brace for a new concept next.

We presume that the characteristic of ESOY is to steal others’ fruit ( i.e., outcome). As per the information set, MF gives an association to a concept, whereas the nMF has no allegiance to the concept. As we know, any person can develop the habit of stealing the outcome of others’ efforts (nMF) in case he/she doesn’t want to earn his/her outcome by his/her efforts (MF) or never wants to exert. Then he/she directs his/her efforts to steal; it can be presumed that ESOY eyes the other’s outcome. In that case, the component of kth ESOY is modelled as:

wS(t + 1, k, l) = vS(t, k, l). f(t, q), (19)

where we make use of the product of the nMF of the kth ESOY, v (t, k, l), and the outcome of the qth contender, f( t, q), to represent the usurping of the qth contender’s outcome by the kth contender that exerts none of its efforts. If an outcome is not produced by one’s efforts, the claim to it is said to be false. Hence, his/her MF cannot be used, but only nMF.

It may be noted that vS(t, k, l)is taken as the Yager complement of μS(t, k, l) that is given by

(wS(t,k,l)−wav(t,k)) −{ 2 }

2σw (20)

μ (t, k, l) = e S ,

2 th

where the mean denoted by wav (t, k) and the variance by σw computed based on the l efforts of all contenders.

The Efforts Based Outlook Learning Model (EBO-LM): having derived all three components of learning, the weight vector is updated as:

w(t + 1, k, l) = w(t, k, l) + r1wD(t + 1, k, l) + r2 wR(t + 1, k, l) + r3 wS(t + 1, k, l), (21)

where r1, r2 and r3 are the random numbers. When t=0, w (0, k, l) = 0, whereas the other three weights are initialized with random values.

We have refrained from discussing several ways by which the variants of the learning models can be generated, as that would distract us from our avowed objectives. So, we present an algorithm for the implementation of EB-OLM.

Step 1. Choose an objective function to be minimized along with the input data. Specify the number of weight vectors (populations) and the number of iterations.

Step 2. Assume random weight vectors. Let Iter be equal to 1.

Step 3. Compute the outcomes due to the randomized weight vectors and find the outcome MFs.

Step 4. Compute the reinforcement factor using Eq. (15) and evaluate the EDO learning component using Eq. (22).

Step 5. Compute the learning component of EROY using Eq. (17) or Eq. (18) by evaluating the outcome-based MFs of the best achiever and the kth contender.

Step 6. Compute the learning component of ESOY using Eq. (19) and find the nMF of ESOY using the effort-based MF using Eq. (20).

Step 7. Update the previous weight vectors using three learning components in Eq. (21).

Step 8. Repeat Steps 3-7 until we achieve convergence in the weight vectors or the minimum objective function value.

In the above algorithm, we have used all three components in the updating equation of the learning model. For the algorithms in [3], three model equations need not be applied. Depending on the objective function, we need one or two model equations, and these are applied sequentially one after another. Very rarely do we need the third model equation. Based on this procedure, the above algorithm is modified.

Step 1. Find the reinforcement factor and evaluate the ENO learning component.

Step 2. Update the model equation with only the ENO component. If the objective function is reduced drastically, go to Step 3.

Step 3. Evaluate the outcome of the membership best performer and also of an EROY. Compute the ERO learning component.

Step 4. Update the model equation from Step 4 with the ERO component.

Step 5. If the objective function is reduced drastically, then go to Step 3.

Step 6. Find the nMF of ESOY using either the outcome-based or the effort-based MF and compute the ESO learning component.

Step 7. Update the model equation from Step 8 with the ENO component.

Step 8. Repeat Steps 3-10 until we achieve convergence in the weight vectors or the minimum objective function value.

The design of classifiers based on information sets can be seen in [16]. Assume that the Feature Vectors (FVs) of a dataset are normalized, and then they are split up into the training and test sets. The number of classes is assumed to be l. The length of an FV is m, and the number of FVs in a class is n. Let ftr (i, j) and fte(j) with i = 1,.., n and j = 1, ..., m be the training and test FVs be abbreviated as tFVs and teFVs respectively. Our objective is to find the statistics of all features in a class. For this, we compute the mean and the variance of each FV across all tFVs of a class to form an information set by fitting the Gaussian MF. By this procedure, we get m MFs yielding m information sets, with each set having n information values. Let μtr(i, j) be the MF vectors of ftr(i, j). Next, we evaluate their HT from:

H −(ftr(i,j).μtr(i,j))

HT,tr(i, j) = ftr(i, j)e . (22)

Approach 1 (Without learning). In this approach, HT is applied to tFVs of a class by finding the MF vector that requires an average tFV and a vector of variances. The FV giving the minimum HF value is termed the support vector of the class based on the certainty concept. All other FVs with higher HF values possess more certainty to the class, and hence they are well within the boundary of a class. But the support vector being on the boundary of the class is most critical. This concept was used in the design of an optimal classifier using the prudent learning model in Grover and Hanmandlu [6]. The support vector for the lth class is computed from:

H −(ftr(i,j).μtr(i,j))

HT,tr(i, l) = {∑ ftr(i, j)e } ; i = 1, . . , Ntr ; l = 1, . . , Nc,

(23)

where Ntr is the number of tFVs of each class and Nc is the number of classes. It may be noted that the subscript l on the r.h.s. of Eq. (23) indicates that the operations in the curly bracket are performed on tFVs of class l. By applying Mini on HT,tr(i, l) fetches us the minimum value of HT for the specific index im, given by

H H −(ftr(im,j).μtr(im,j))

HT,tr(im, l) = Mini{HT,tr(i, l)} = ∑ ftr( im, j)e |l.

(24)

−(ftr(im,j).μtr(im,j))

This Equation leads to a support vector for each l, ftr( im, j)e .

While testing to find the label of a teFV, we will invoke the HT divergence. As we don’t have statistics governing the teFV, we will use the statistical parameters (i.e., mean and variance) of tFVs to compute MF, μte(j) of a teFV. To make it compatible with μtr, the test MF is updated w.r.t. each support vector of class l from:

−(ftr(im,j).μtr(im,j))

μ ̂te(j) = μte(j){e |l, (25)

with the help of μ ̂te(j), we can frame the HT divergence as:

H −(ftr(im,j).μtr(im,j)) −(fte(j).μ ̂te(j))

H∆T(l) = ∑ ftr( im, j){e |l − e }.

(26)

The identity (Id) of the unknown class is found by determining the infimum out of all classes from:

Id = Infl{H∆T(l)}. (27) Approach 2 (With learning). As we had both FVs and MF vectors, there was no need for a learning model in the above classifier. But to see the power of the learning model, we shall introduce a power β on ftr( i, j) and initialize its values randomly. We create as many values as the number of tFVs of a class and form an effort vector. We aim to find the support vector of each class for learning β. So, we compute the uncertainty representation of each tFV of the lth class using the HT divergence as:

β −(f (j).μte(j)) H −(ftr(i,j).μtr(i,j)) te

H∆T(i, l) = ∑ f ( i, j){e |l − e }.

tr (28)

Let H∆T(i, l) be considered as the fitness/outcome value, f(t, k, le), where t denotes the iteration; k denotes the ith contender, and le denotes the effort/weight vector. We invoke the learning model by providing it a set of fitness values and effort vectors. The learning model delivers the minimum value of H∆T(im, l) for the index im from tFV. Next, identifying the class label of teFV using Eqs. (25)-(27) is a cake walk based on the HT divergence.

Forecasting is an important problem in many applications such as forecasting of weather, demand, rain, stock market, election, etc. In this work, we address this problem under the framework of information set theory. For simplicity, we consider two categories of variables: endogenous and exogenous. Both of these types may refer to any quantities depending on an application. We would like to adopt the window-based approach in which we fix the time slot that could be a month, a year, or several years. In this time slot, the data is procured either day-wise or week-wise, and consideration of the lead time varies accordingly. Let us denote Iy as an independent or endogenous variable and Ix as an external or exogenous variable. The past values of these variables are assumed to form fuzzy sets. Let Hy be the information set of endogenous variables Iy, and Hx1, Hx2,.., Hxq be the information sets of exogenous variables Ix1, Ix2,.., Ixq respectively. These variables take mostly real values, but a few of them may have truth/binary values; then we consider their probabilities. To represent the past values, an integer of 1 is subtracted from an instant, k. The number of past values to be considered for each exogenous variable depends on how much influence it has on the endogenous variable. To determine this dependency, one way is to perform correlation analysis between the endogenous variable and the exogenous variables. The choice of the number of past values of the endogenous variable can be determined by performing clustering on the values of the endogenous variable or can be arrived at by a trial-and-error process. Alternatively, we can also go in for the structure determination approaches of fuzzy modeling. In the present study, we intend to develop an information set-based regression model linking an endogenous variable with the exogenous variables.

The proposed regression model gives a relation between the present endogenous value and the past information of values of the endogenous and the exogenous variables. This model is mathematically expressed as:

ly lx lx H H H

yf(k/k − l) = ∑ wy. Hy (k − l) + ∑ wx1. Hx1 (k − l) + ∑ wx2. Hx2 (k − l) + ⋯

l l l

lx (29)

+ ∑ wxq. Hxq (k − l),

where the information values are taken as Hy (k − l) = Iy(k − l). μy(k − l) and Hxi(k − l) = Ixi(k − l). μxi(k − l). The MFs are assumed to be triangular or trapezoidal. We can also use pMF to improve the regression model. The unknown weight parameters in Eq. (29) are learned using OLM. In case the forecasting error is to be utilized as another exogenous variable, it can be included as an additional term in the model, shown as under:

Iyf(k + 1/k) = Iyf(k/k − 1) + we. ef(k/k − 1),

(30)

where ef(k/k − 1) = Iy(k) − Iyf(k/k − 1).

In this context, development of the information set-based regression model can be seen in [17].

The concepts of EB-OLM can be easily ported to deep learning neural networks in creating new architectures from them. We have already made a step in this direction by creating HanmanNets through the modification of ResNet [18]. Inspired by this work, DeepInfoNet is evolved from two handcrafted Convolutional Neural Networks (CNNs). We intend to design the information set-based GAN architecture using DeepInfoNet. A brief description of this net is as follows: the specialty of DeepInfoNet is that it is built block-wise with the scaffolding of two convolutional layers and one pooling layer in every block. A specific number of kernels /filters of size 3x3 is engaged in a convolutional layer, whereas a stride of 2x2 is made in the max-pooling layer. Each kernel performs a convolution operation on an input image, and this is followed by batch normalization.

The features extracted from feature maps of the first block are examined first. If they fail to meet the requisite classification accuracies, then these features are concatenated with those from the feature maps of the second block for the purpose of reevaluation. If the concatenated features succumb to the same fate, accessing the feature maps of the third block is the last and final recourse.

Let us allot one network for the generator DeepInfoNet catering to the training and another for the adversary DeepInfoNet catering to the testing. A kernel function convolving with the input image at every pixel location incarnates into an MF matrix. Let NF denote the number of feature maps, also referring to the number of kernels/filters, and xy, a pixel location in a feature map. The pixel intensity in a feature map μ′xy is designated as the MF, whereas μ′n,xy is the nMF, with both having the superscript apostrophe ('). Resizing of the input image Ixy to that of the feature map makes it appear as Ixy. The conglomeration of the pixel intensities from all feature maps at a location xy gives rise to MF as μ′xy,j and to nMF as μ′nxy,j , j=1 to NF.

To show how to generate ftr(i, j) and fte(i, j) in the context of GAN, we define the MH intuitionistic fuzzy entropy function as:

1 α β α β

MH γ −(c1(.)μ +d1(.)) γ −(c2(.)μ +d2(.))

xy n,xy

HF = ∑ ∑ μxye + μn,xye .

2 (31)

x=1 y=1

First of all, we set β = γ and α = 1 in Eq. (31), and this substitution leads to:

1 γ γ

MH γ −(c1(.)μ +d1(.)) γ −(c2(.)μ +d2(.))

xy n,xy

HF = ∑ ∑ μxye + μn,xye .

2 (32)

x=1 y=1

We derive two functions; the first one with different gain functions while the second one with the same gain functions. For the first one, the substitution is: c1(.)=c2(.)=1 and d1(.)=d2(.)=0 and but for the second one, c1(. ) = μn,xy and c2(. ) = μxy with d1(.)=d2(.)=0. The resulting intuitionistic fuzzy functions are:

1 γ γ

MH γ −μ γ −μ

xy n,xy

HF1 = ∑ ∑ {μxye + μn,xye } ,

2 (33)

x=1 y=1 MH γ −(μ μ ))

xy n,xy

HF2 = ∑ ∑ {Pxy e , }

2 (34)

x=1 y=1

γ γ γ

where Pxy = μxy + μn,xy. The bracketed terms can also be called the embedded MFs. To reflect that the below are derived from the feature maps, we place an apostrophe on all the functions:

NF NF

1 ′γ ′γ

′MH ′γ −μ γ −μ

xy n,xy

HF1 = ∑ ∑ {μxye + μ′n,xye } , (35)

NF

x=1 y=1 NF NF

1 ′ ′ γ

′MH ′γ −(μ μ ))

xy n,xy

HF2 = ∑ ∑ {Pxy e }. (36)

NF

x=1 y=1

′ ′MH ′MH

In moving from a fuzzy set to an intuitionistic fuzzy set, μxy gains the bracketed terms (HF1,xy and HF2,xy), and this is the handiwork of the Intuitionistic MH fuzzy entropy function that has imparted structures to it. Let Ixy be the input image with its size reduced to that of the MF matrix. The information values could be of

′ ′ ′ ′MH ′ ′MH

three kinds: Ixyμxy, IxyHF1,xy and IxyHF2,xy. We can choose any one of these as the DeepInfoNet feature, as they are tapped from the feature map of this architecture.

For validation, the training and test sets have to be separated, and the corresponding DeepInfoNet feature sets are assigned to Gen and Adv, which stand for the Generator and Adversary modules of GAN. So, we can designate DeepInfoNet as GAN-DeepInfoNet or simply GAN-InfoNet and name its modules as Gen-InfoNet to deal with ftr(i, j) and similarly Adv-InfoNet, to deal with fte(j). The FVs and MFs involved in the GAN-InfoNets are elaborated as:

′i ′

ftr(i, j) = Itr,xy; fte(j) = Ite,xy.

′i ′i,MH ′i,MH ′ ′ MH ′ MH th

μtr(i, j) = {μtr,xy, H , H } and μte(j) = {μte,xy, HFte1,xy, HFte2,xy), where we have denoted the i IS

Ftr1,xy Ftr2,xy

vector and MF vector by the superscript, i and j correspond to xy. We have to make sure that the tFVs of each class must be separated out. It is now imperative to make an analogy with the classifier above in assigning the roles to the two modules. The task of Gen-Net is to determine the support vector of each class using Eq. (36), and that of Adv-Net is to use the support vectors furnished by the Gen-Net and apply the criterion function to find the class label of the tFV using Eqs, (25) to (27). The value of γ is a design parameter, chosen to be less than 1 by trial-and-error till we achieve the desired performance. Here the services of the learning model are no longer needed.

If γ is to be learned, we go in for the learning model by adopting the procedure outlined above. Here, γ replaces β, all other things remaining the same. This GAN-InfoNet is designed to act as a classifier, and depending on the application, we can alter its architecture.

Along the lines of rough fuzzy sets, we would like to create rough information sets. The concept of a rough fuzzy set is very useful if the IS/attribute values display two different distributions. In the analysis of a texture image, we can carve out both the smooth and rough constituents by decomposing it into an approximation image (i.e., smooth) and the composite image (i.e., rough) from it. The composite image is constructed from the diagonal and off-diagonal sub-bands arising from decomposition. It is easy to infer that by applying DeepInfoNet on these images, we can get the two types of MF matrices from the respective feature maps representing smooth and rough distributions. These, along with the pixel intensities of the reduced input images, help generate smooth-DeepInfoNet and rough-DeepInfoNet features.

The MF, μ′n,xy and the nMF, μ′n,xy function values belong to the smooth and rough MF values, respectively, with γ acting as a roughness factor. The correct choice of γ is very important for the delineation of smooth and rough MF values. The resulting information values formed from both the smooth and rough values constitute rough information sets. The roughness factor delineated as the ratio of smooth certainty information divided by the rough certainty information is given by:

n1 n1 ′ ′γ

∑x=1 ∑y=1 Is,xyμxy

RF = γ . (37)

n2 n2 ′

∑x=1 ∑y=1 Ir,xyμ′

n,xy

In addition to the two case studies in the medical domain, some of the applications of the EB-OLM could focus on different types of forecasting like weather, stock market, sales, etc. It can be applied to solve industrial problems such as decision-making, identification of fake news, recommender systems, cybersecurity, sentiment analysis, etc. The miscellaneous applications include areas of Biometrics, Image processing, and pattern recognition.

We can also cash in on the learning abilities of EDOY and EROY in the design of classifiers for the classification of deep information set features extracted from the feature maps of any deep learning neural network architecture by assigning the roles of objective functions to the transforms, i.e., high-level entropy functions used for the uncertainty representation of features.

This comparison is undertaken on the following benchmark functions for optimization to learn their parameters:

I. Powell function f1(x).

II. Rosenbrock function f2(x).

III. Dixon and Prince function f3(x).

IV. Schwefe126 function f4(x).

V. Rastrigin function f5(x).

VI. Griewank function f6(x).

VII. Qing function f7(x).

VIII. Alpine01 function f8(x).

IX. Ackleley function f9(x).

X. Perm function f10(x).

All these functions have the same global minimum of zero. The different metaheuristic techniques chosen for comparison are: Whale Optimization Algorithm (WOA), Artificial Fish Swarm Algorithm (AFSA), Krill Herd (KH), HEFAG [4], CCLM [5], Black Widow Optimization (BWO), Red Deer Algorithm (RDA), and Sandpiper algorithm. Here, we have not considered the Genetic Algorithm (GA) for comparison, as it requires several parameters such as the number of chromosomes, fitness function, population size, crossover and mutation operators, and the number of iterations. The correct choice of these parameters is fraught with many difficulties. In contrast, in the proposed learning model, the population size (i.e., the number of contenders) is set to 30. Table 1 shows the results of optimization obtained with the meta-heuristic techniques on 10 benchmark functions having 50 parameters each. We have carried out 24 runs, and each run has 1000 iterations. We have also computed the mean, standard deviation, and the median over the 24 runs. As can be noticed from this table, the EB-OLM surpasses other meta-heuristic techniques after convergence is attained. Figs. 1-3 show the implementation of different meta-heuristic techniques like EB-OLM, WOA, LOA, GBC, and RDA on Powell, Rastrigin, and Grievank functions, respectively. It is clear from these figures that the values of these functions converge to zero with EB-OLM.

To showcase EB-OLM, the two real-life applications taken up include: 1) detection of retinal diseases from retinal images, and 2) prediction of heart diseases from ECGs of patients.

Case Study 1 (Detection of retinal diseases). The retinal images are of high resolution, captured under a variety of imaging conditions. A clinician rates the presence of Diabetic Retinopathy (DR) in an image on a scale of 0 to 4, with the following categories/classes: 0 - No DR, 1 – Mild DR, 2– Moderate DR, 3 –Severe DR, and 4 - Proliferative DR. A total of 88, 702 images exists and out of these 54,000 are set aside for the training and the rest for the testing. A typical retinal image for each category of DR is shown in Fig. 5. In this study, the probabilistic feature called the hybrid Hanman-Rényi-Tsallis transform derived in [16] is found to be most suitable, as under:

HRT .α.log(Px)/(1−α) (Px−Px )/(α−1)

Hk = ∑ Px{e + e }, (38)

where , the probability of the pixel intensity is computed from the histogram of a window in a retinal image, and α is set at 1.6. The size of the window is selected as 15x15 after experimentation. While learning the parameter β of the classifier using EB-OLM, the population size is fixed at 40 and the number of runs at 24. Within each run, 1000 iterations are executed. The widely used classifiers like Random Forest (RF), CNN, Naïve Bayes classifier, and K-Nearest Neighbour are compared in Table 2 for the detection of DR.

The proposed classifier is shown to outperform the well-known classifiers compared. As evident from Table 2, the proposed methodology gives an accuracy of 97.5% and outperforms other classifiers.

Case Study 2 (Prediction of heart diseases). The status of a heart, whether it is healthy or defective, is dealt with in [19]. The 13 attributes in the heart dataset include: age, sex, cp: chest pain type; trestbps: resting blood pressure; chol: serum cholesterol; fbs: fasting blood pressure; restecg: resting electrocardiographic results; thalach: maximum heart rate; exang: exercise-induced angina; oldpeak: ST depression induced by an exercise relative to the resting; slope: the slope of the peak exercise ST segment; ca: number of major vessels colored by fluoroscopy; thal: thalassemia.

In this dataset, the variables such as sex, fbs, rest ecg, and exang are binary, whereas slope takes values (0, 1,2), and the variables cp, ca, and thal take integer values (0, 1, 2, 3). So we find the probability of each integer variable separately and then compute the probabilistic uncertainty using the Hanman-Tsallis transform [17], given by:

HTs (Px−Px )/(α−1)

Hx = Pxe . (39)

This Equation is derived from the Tsallis entropy function [20], defined as:

n n α

∑i=1 pxi − ∑i=1 pxi

H = . (40)

α − 1

One term on the r.h.s. of Eq. (40) can be written as:

pxi − pxi

Hx = . (41)

α − 1

Using Hx as the exponential gain function of HT leads to the Hanman-Tsallis transform in Eq. (39).

The variables age, trestbps, chol, thalach, and oldpeak are considered as features denoted by Qx where x stands for each of these variables numbering q=13; hence we fit the Gaussian MF, μx by computing the mean and variance of the distribution underlying each feature. Here, we make use of the possibilistic Rényi entropy

(1−Qx)

function, μ ̅̅̅ xe derived by Bhatia and Hanmandlu [21] from the probabilistic Rényi entropy function [22]. As the sigmoid function representing the uncertainty in the distribution/variation of each feature is found to be more effective than the possibilistic entropy function, it is given by:

RS

Hx = , (42)

−̅ μ ̅̅̅e(1−Qx)

1 + e x

where μ ̅̅̅ x is its complement MF. The weights (i.e., efforts) to be learned are those of 13 features.

Implementation aspects: before implementing the prediction using Eq. (41), we need to initialize all the weights with random values. Taking each sample at a time, we have to plug in the information values of features. If a feature is an integer, we have to get its probabilistic uncertainty, but if it is real, then its possibility certainty. Using the initial weights and the information values, the output is computed. By invoking EB-OLM, we get the updated values of the weights. In the next iteration, the computed output is considered as the 14th feature, and then it is weighted to serve as an additional input to improve prediction, thus making the number of weights equal to 14. The output weight is assumed to be a random number. This procedure is repeated until all the training samples are utilized. Table 3 gives a comparison of our methodology with literature detectors on the prediction of heart diseases and outperforms other classifiers.

We now take a respite to deliberate on the contributions made in this paper. These include: 1) formulation of three efforts-based learning models, 2) development of design models for classifier, predictor, and GAN architecture, and 3) Presentation of two case studies for the vindication of the certainty/uncertainty representation.