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# Stochastic - Science topic

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Questions related to Stochastic

Or can we say that if a graph is balanced, its weight matrix is doubly stochastic?

Assume that there are m number of patients. Each patient records his/her pain level in an ordinal scale (from "not at all" to "excruciating") at t_i time point fro i=1,2,...,n_i. Suppose that we want to know whether patients are improving with respect to time or not. Is there any existing literature to test that?

- We know that the stochastic monotonicity condition for the one-dimensional case is as follows: sum_{j>=k}q(j|i)<=sum_{j>=k}q(j|i+1) for all i, k belongs to state space S such that k does not equal to i+1, where q(j|i) is the transition rate associated with the continuous-time Markov chain. NOW, QUESTION is what is about in a two-dimensional case?

Hello,

Can you help me regarding MATLAB solver for a system of stochastic delay differential equations? To be specific the system is delay differential equation where parametric stochasticity is used.

Thank you

Hello,

I am trying to estimate a stochastic frontier model in the panel data set using stata13. In doing so, I prefer to use the TRE model. Even though I am aware that this model allows estimating the frontier model and the inefficiency determinants at a time(following a single step), I am not sure if I am following the correct procedure.

Could someone help me?

sfpanel ln y ln x1 lnx2 .....lnxn, model (tre) dist(hnormal) usigma(z1,z2,z3...zn) vsigma()

The assumption here is z1....zn are inefficiency determinants and also considering heteroscedasticity at the same time.

Thank you!

I have a multi-stage stochastic programming model. I have 3 groups of variables: the first group takes values at the beginning of the planning horizon before the first realization and does not change until the end of the planning horizon and has no t index (they are binary and continuous), the second option is “here and now” variables that before each realization Are taken value and are continuous, the third group are “wait and see” variables that take value after each realization (binary and continuous). The model is SMINLP. I converted it to SMILP through linearization and solved it by CPLEX solver with generating a small number of scenarios ... I want to consider a continuous distribution for the stochastic parameter and generate a large number of scenarios by sampling and run an algorithm for it. nested benders decomposition or progressive hedging algorithms are more efficient for this model?

If anyone has experience, thank you in advance for your help.

I am trying to generate a streamflow series with a stochastic framework. I would like to find some criteria to statistically compare between generated and observed series.

The most important part is that if I am trying to compare between different generators; Am I able to apply criteria in order to get accuracy value for each generator?

Regards,

I am looking for a scientific field or real-life subject where I can use some convex analysis tools like Stochastic Gradient Descent or unidimensional optimization methods. Any suggestions?

Please help,

I ran a Battese and Coelli 1995 sfpanel model in Stata 12.1 of the following translog equation

**sfpanel lny lnl lnm lne lnk lnksq lnlsq lnesq lnklnl lnmsq lnklne lnklnm lnllne lnllnm lnelnm year, model(bc95) dist(tn) emean( for for5 for10 for15 for20 for25 exp_firm firm_size) ort(o)**

Aimed at establishing the effect of FDI on efficiency and productivity at firm level.

I wish to estimate TFP whose components are

**Technical Change(TC),****Technical Efficiency Change (TEC) and Scale Efficiency Change****(SEC)**.- Can this be done directly in Stata?
- And what is the syntax considering the 4-input translog equation?

Thanks.

Dear all,
I would like to test the half-normal distribution (of the error component
from stochastic frontier models) against alternative distributions. Does
anybody have some experience with doing this in stata. could anybody
point me towards relevant literature? Thanks in advance.

I wish to transform the data from long memory stochastic to short memory volatility models to visualize the effects. Is there any transformation protocol to shift the data from long memory stochastic to short memory volatility models or either there is no mathematical relationship between these two models? Further, can we use MATLAB for such transformation?

Dear fellows

I am trying to estimate cost efficiencies using Fourier flexible stochastic cost frontier but I can’t find Stata commands relating to this subject. Kindly assist

Hello,

I am currently working on sensitivity analysis in the context of AHP. I use the online tool BPMSG from Goepel, maybe someone here knows it. However, I have a problem with the traceability of the results. Let's assume that there are exactly 3 criteria in the AHP (C1,C2,C3). Then I would like to know how the final value for an alternative (a1) results if one of the criteria changes in weighting, right?

I'll just say C1 decreases by x. However, the value x that is taken away from C1 must be distributed to C2 and C3. I just wonder

**which method**is used to do this. Is x simply distributed equally to C2 and C3 or does this happen according to the share of C2 or C3 in the sum of C2 and C3?When I do that, I get the following for the remaining two criteria:

(C1-x) = New C1

(C2 + (C2 / (C2 + C3)) * x) = New C2

(C3 + (C3 / (C2 + C3)) * x) = New C3

Unfortunately, however, I do not know if this is correct. If I multiply the criteria with the corresponding values of alternative a1 and combine the whole thing to a final value, I can calculate the same again with the other alternatives. When I compare the graphs to see how big x has to be to change the final prioritization of the alternatives, I always get the wrong values compared to the online tool. Therefore I would like to know if the redistribution of the weights is correct.

I hope someone can help me despite the long question. Thanks a lot!

Is correct? In stochastic mathematics, the arithmetic mean and standard deviation are important. In fuzzy mathematics and interval reasoning, the arithmetic mean and standard deviation are not always important

Hello everybody

According to what mentioned in the attached snapshot from the appendix of this article

My question is, if we already have the transition probability matrix P, how could we calculate numerically v^=α0(I−P)−1, as the limit of the recurrence v(t+1)=v(t)P+α0?

Hello Everyone,

I am recently working on the topic " Deep Reinforcement Learning in production scheduling".

Most recently I am working on the simulation of the environment, the state and action engineering process.

The uprising question for me here is: how are uncertainty and constraints taken into account in a RL project?

In stochastic optimization there is a probability distribution of several factors which are taken into account. Also the solution space is restricted with constraints.

How are these factors considered in model-free RL? Is the uncertainty included in the simulation of the environment? Are the state or action space restricted through constraints?

Best regards,

Christoph

I want to design different scenarios of wind speed for a day i.e. for 24 hours to do stochastic optimization. Can anyone please provide code or files.

Let me consider harmonic oscillations x'' + x = f_t(t), where f_t(t) describes thermal stochastic force <f_t(t) f_t(t')> \sim \delta(t - t'). I have already understood, that I can switch from such differential equation to the integral equations, where the integrals can be performed in Ito or Stratanovich sense. Which one relates to the real situation?

Another case: escape probability. If I want to numerically extract mean lifetime of a classical particle in a potential well due to thermal fluctuations, what kind of stochastic modeling should I use?

Hi!

I have the following scientific problem: there is a nonlinear SDE

dX = (a(t)+b*(X-X0))*X*dt+c*X*dB

If a = 0 and b is a negative number then the negative feedback "pushes" always back the X path to the direction of X0. I experienced that the mean of the X paths shows some oscillation properties like frequency. My question: what is the name of this phenomen? How should i search after? Is there a book or article about this? I know that stochastic oscillators exist but they are second order ordinary differential equations perturbated by Brownian motion and that is not what i am looking for.

Thank you very much for your help!

Tamas Hajas

There are many methods based on the stochastic arithmetic and also floating point arithmetic. What is advantage and disadvantage of the mathematical methods based on stochastic arithmetic?

Is stochastic gradient descent an incremental machine learning method? How does stochastic gradient descent relate to incremental machine learning/ online learning?

Also, I am new to incremental ML and need to build my knowledge about it .. Any good beginners references you can recommend will be appreciated :-)

Visscher, M. L. (1973). Welfare-Maximizing Price and Output with Stochastic Demand: Comment. American Economic Review, 63(1), 224-229.

The derivation of formula (4) in the literature (Visscher, 1973) involves the derivation of double integral. How are formulas (5) and (6) obtained? In the file added, it provides the process in my opinion, but I can’t get the same result as the equation (5) in the literature. What went wrong in the solution process, I hope you can help me point it out, thank you!

Is there any rational formulation for the velocity slip boundary conditions for the stochastic Landau-Lifshitz Navier-Stokes Equations?

Dear all,

Could anybody provide the names of the researchers and literature in the area:Stochastic Calculus and Stochastic Integration - Ito Integration

Thanks in advance

I have gone through Adrian papers on this topic but details are still missing. Linear stochastic estimation is a powerful tool for vortex packet identification.

What is stochastic and combinatorial optimization problem.

Also, How I can identify the problem i am working is

**Continuous or Discrete Optimization.**Most of the optimization methods utilize the upper and lower bounds constraints to handle this issue. At the same time, each variable can significantly affect the direction of the optimization method to find its optimal value. Thus, returning to the lower or/and upper values leads to a delay in finding the optimal values in each iteration.

Hi all,

Does anyone have an idea about how to make a stochastic based crack distribution model which we can use further in the finite element model to predict the growth?

For orientation I am looking for theories as a basis of an goal-based investment approach. So far I found some appraoches using

- Portfolio Optimization with Mental Accounts (POMA)
- Asset Liability Management (ALM)
- Stochastic Dominance (SD)

Do you have any other suggestions?

Which approach is most common and accepted?

Hi everyone, Below references written by latex and I need a help to identify which the style are written. I need the style used and the supported packages for it.

Thank you

H. Crauel and F. Flandoli, Attractors for random dynamical systems, Probab. Th. Relat. Fields 100 (1994) 365–393.

H. Kunita, Stochastic Flows and Stochastic Differential Equations (Cambridge Univ. Press, 1990).

R. Lefever and J. Turner, Sensitivity of a Hopf bifurcation to external multiplicative noise, in Fluctuations and Sensitivity in Nonequilibrium Systems, eds. W. orsthemke and D. K. Kondepudi (Springer-Verlag, 1984), pp. 143-49.

P. Ruffino, "Rotation numbers for stochastic dynamical systems", PhD thesis, University of Warwick, 1995.

Elections, not just voting, can become trustworthy.

Additional methods to the ones that made voting trustworthy (choose your favorite) can be applied. Eiections are not used to choose the captain of a ship, said Socrates, 2500 years ago. One can use technology to help. One has to verify competence, reciprocity, and (for fairness) anonymity.

Although voting is deterministic (all ballots are counted), information can be treated stochastically using Information Theory. Error considerations, including faults, attacks, and threats by adversaries, can be explicitly included. The influence of errors may be corrected to achieve an election outcome error as close to zero as desired (error-free), with AI providing many copies of results without voter identify. A voting method to do so, is explained at https://www.researchgate.net/publication/286459956_The_Witness-Voting_System

How about the next step, fair elections? Can one learn from the events in the US in Jan/6?

Instead of manual tuning of algorithm's parameters, it is recommended to utilize automatic algorithm configuration software. Mostly beacuse it was shown that they increase manyfold the algorithm's perfomance. However, there are some differences among the proposed configuration software and beside those listed in (Eiben, Smit, 2011) it is important to gather experiances from the researchers. I would like to hear how does one decide on the stopping criteria, or values for parameters, for heuristic steps within the stochastic algorithm... there are so many questions.

I am trying to understand Parametric weather generator models for the purpose of downscaling GCM data. This is my first time working on this topic, and I am finding it hard to understand how exactly these weather generators are used. Do you use a package in a software like R or are there pre-existing weather generator softwares or programs that can be directly used to generate results? While there is literature regarding the theory of parametric weather generators, I cannot find any resources that help with understanding the implementation. Any resources or explanation regarding this will be helpful!

Hello, I would like to know any experiences about stochastic optimization software or possibility to prepare it in Python for example. I am looking for an optimization process in Revenue Management. Many thanks for your answers. MP

There has been rich literature describing how to reformalize stochastic MPC in linear systems into deterministic optimization. However for nonlinear system, propagation of uncertainty through time seems very complicated, so most literature I find solve nonlinear stochastic MPC with probabilistic constraints using sampling based approaches. I am new to nonlinear stochastic MPC, so I am wondering whether there's any existing library/toolbox for nonlinear stochastic MPC with probabilistic constraints? Or if there's no such convenient tools, based on your practical experience, which paper do you recommend me so that I can implement the algorithms myself?

Please, I need to know the best meta-heuristic and hybrid meta-heuristic algorithms (except for Genetic Algorithm) for finding the optimal or near optimal solution of stochastic scheduling problems.

Please kindly suggest some good FEM softwares for the numerical solution of both time-dependent and time-independent stochastic PDEs.

I would be grateful for suggestions to solve the following problem.

The task is to fit a mechanistically-motivated nonlinear mathematical model (4-6 parameters, depending on version of assumptions used in the model) to a relatively small and noisy data set (35 observations, some likely to be outliers) with a continuous numerical response variable. The model formula contains integrals that cannot be solved analytically, only numerically. My questions are:

1. What optimization algorithms (probably with stochasticity) would be useful in this case to estimate the parameters?

2. Are there reasonable options for the function to be optimized except sum of squared errors?

In a population dynamical system, the non-explosion property is often not good enough but the property of ultimate boundedness is more desired. The conditions for the ultimate boundedness are much more complicated than the conditions for the non-explosion.

The nonexplosion property in a population dynamical system is often not good enough but the property of ultimate boundedness is more desired

In the article Random Ordinary Differential Equations, Journal of Equations Differentials 7, 538-553 (1970), by JL Strand, reference refers to his doctoral thesis: Stochastic Ordinary Differential Equations, University of California (Berkeley), 1968, and also to doctoral thesis: Random Ordinary Differential Equations, University of California (Berkeley), 1968, by R. Edsinger.

Do you know how to get these two doctoral theses or does anyone have these two papers?

Stochastic Mortality Models (SMM) have often be used by insurance coy to model the risk of mortality in general, but I want to apply and restrict it to childhood mortality. How do I go about it?

Dual control in Stochastic optimal control suggests that control input has probing action that would generate with non zero probability the uncertainty in measurement of state.

It means we have a Covariance error matrix at each state.

The same matrix is also deployed by Kalman filter so how it is different from Dual Control

I'm working on comparing latent space representations of image patches which are encoded as multivariate normal distributions over the respective latent space.

Which metrics - besides (symmetric) KL-divergence, Hellinger distance and Bhattacharyya distance - exist to measure the distance between multivariate normal distributions, ideally fulfilling the mathematical definitions of a metric?

Second, from what I've noticed, Hellinger distance has a very small "window of sensitivity" - meaning that if I compute the similarities between encoded distributions, I get small values for identical image patches and values close to 1 for everything else, while symmetric KL divergence covers a wider range of values and also measures small distance between non-identical input. Any ideas on this?

Hello

I was wondering if there is such a big enough data set available in oder to estimate the stochastic distribution of Covid 19-related symptoms in relation to location and time. This could be helpful for detecting variations/mutations in the disease and support diagnosis.

Thank you.

I am using benchmarking package of in R to analysis the energy efficiency of firms by stochastic and deterministic methods. I am getting the dmu score more than 1 or equal to one or less than 1. Can anyone help me in this regard?

Hello All,

I am working on stochastic upscalling of damage in concrete microstructure. Can someone provide a UMAT for Mazar's damage model or any resource to help me create UMAT on my own.

Thank you.

Vasav Dubey

Texas A&M University

Texas, USA

I want to study stochastic finite element, Can any one introduce a straight forward reference in simple method?

Euler method and the Milstein method

We are working on a large number of building-related time series data sets that display various degrees of 'randomness'. When plotted, some display recognisable diurnal or seasonal patterns that can be correlated to building operational regimes or the weather (i.e. heating energy consumption with distinct signatures as hourly and seasonal intervals). However some appear to be completely random (Lift data that contains a lot of random noise).

Does anyone know if an established method exists that can be deployed on these data sets and provide some 'quantification' or 'ranking' of how much stochasticity exists in each data set?

Once we select the appropriate model specification and estimation of panel stochastic production frontier model what robustness checks are required before the results are used for discussion? Since I am using Stata 12.1 version, I would appreciate if anyone knows the stata command as well.

I develop vehicular emissions inventories at street level and I would like to run dispersion models for

*scientific*applications with my outputs. After some literature research, I have found some models like**Model of Urban Network of Intersecting Canyons and Highways**(MUNICH) https://www.geosci-model-dev.net/11/611/2018/**R-LINE**(CMAS): https://www.cmascenter.org/r-line/**Stochastic Time-Inverted Lagrangian Transport model**(STILT-R version 2) https://www.geosci-model-dev.net/11/2813/2018/

However, it seems that there are many other models.

Do you know more models?

How was your experience?

Where can I download them?

Many thanks!

I have a stochastic mixed-integer non-linear model and it is difficult to be solved. So I want to write the constraints with uniform distribution in the sub-model that is found in the whole model. what are the steps for this? Thanks

I am struggling over the search for studies showing that the age of an individual has an impact on the increased prevalence of Rheumatoid diseases. Wouldn't that be rather a stochastic issue (the longer the time, the higher the chance)? While I could imagine, how increased incidences of cancer correlate with age or that infections result in increased mortality with age, I am struggling about how the cellular age results in autoimmune disorders. I read about thymic atrophy/less T cell variablity and changes in B cell responses and alterations in Tfh cell reactivity and alteration in phagocyte functions (less phagocytosis, less radical synthesis), but does that necessarily lead to an increased incidence of autoimmunity? And if autoimmunity is posively correlated with age, shouldn't the overall response during a particular period be stronger in old organisms than the same disease of comparable period in younger organisms?

UPDATE (March2020): I would say that depending on the autoimmune disease, age shows a positive or negative correlation. However, I am still looking for publications with valid in vivo models showing the age effect on the disease outcome or not.

Dear Researchers,

I have time series data & I’m running OLS regression on Stata.

I want to de-trend a variable while taking into consideration that the trend is stochastic not linear. This is the code I found while searching but I’m not sure if it treats the trend as stochastic:

**reg x time**

**predict x_detrended, resid**

In fact, when I plotted the detrended series (x_detrended) with the time variable (quarter in my case) to see the trend, the extracted trend seems to be linear not stochastic. I’m attaching the graph below.

So, I want to know the command on Stata that detrend the series given a stochastic trend not linear.

I will appreciate your help.

Thank you very much

Suppose there is a regression model y=Ax+e which A is stochastic. and objective function is Huber function. as you see in attached file if A is deterministic equation (4-58) reduces to (4-60). but if it is not, what happens for equation (4-58)

I would appreciate if anyone tell me how i can solve it or suggest papers, books.

stochastic differential equation

dX(t)=sin(X(t))dt +dW(t)

I am looking to solve a Two-Stage Stochastic Mixed-Integer optimization problem in GAMS for a pre- and - post-disaster resource allocation problem.

Dear friends,

I have a problem with the derivation of the expected value of a stochastic variable. my question is if the following relation is correct or not:

tau (t)

_{ }is stochastic variable follow Bernoulli distribution if :\frac{d}{dt} E\{\tau(t)\}= E\{ \frac{d \tau(t)}{dt} \}.

if this relation not correct.

There are two types of mathematical models: Deterministic and Stochastic.

Explain them with proper examples.

In 2 stage stochastic optimization, why I found that the optimization problem has equations for the 1st stage and equations for the 2nd stage but those two groups are solved simultaneously however I think that we first solve the 1st stage equations then take the results and substitute in the 2nd stage equations (new problem) or there is something I overlooked?

Also why we dont combine the equations for 1st and 2nd stages as they are solved simultaneously ?

my case study is for power systems with renewable energy uncertainty when I make day ahead decisions for the power dispatch, power dispatch of each generator are computed (1st stage decisions) then after the realization of uncertain events (renewable energy) redispatch is done in the 2nd stage using reserve or may some load shedding is done.

My question is how the decisions of the 2 stages done simultaneously as I see from some papers. why we optimize the 1st stage first and run our optimization then take the results and apply them in the 2nd stage problem and run it again? and if the optimization of the 2 stages made simultaneously, why we did not combine the equations (constraints) of the 2 stages together ? as I see 1st stage constraints and 2nd stage constraints.

For stochastic adaptive systems important is to consider local ergodic system, Markov chain, local Monte Carlo simulation and maximum entropy method to be more efective.

I have a model free based method for scenario generation to be used in stochastic optimization problem. But the problem is after scenario generation I want to assign a probability fro each scenario How can I do this?

Hello! I want to solve a stochastic PDE-constrained optimization problem and so I want to use an existing FEM open-source package (Python/C/C++) to solve the following stochastic PDE constraint:

F(u,z;w) := - \nabla . ( k(w) \nabla u) - z = 0

where u is the state variable, z is the control variable and w the stochastic variable. I want to use the adjoint approach to compute the gradient of the objective function, i.e., the gradient of \tilde{J}(z) = J(u(z),z). Therefore, I hope that the FEM solver can provide the derivative of F(u,z) w.r.t. u and z.

I have found the dolfin-adjoint package but I find it not suitable for my stochastic application. Could you please help me with your advice?

Thanks in advance

in my project, I deal with stochastic data by markov model through a short study period, hence I will do a simulation to reach sufficient sample size, however my question how can do that and what the best performance to estimate transition probability matrix some of the papers use norm but I do not understand how did that.

Chemical reaction systems can be modeled through a deterministic or stochastic approach. However, it is common to introduce new variables in order to perform dynamic analysis in deterministic systems. Could these reduced forms be directly used to derive stochastic equations or is it necessary to start from the original expressions? It is common for many concentrations to be normalized after these procedures.Does this affect the construction of stochastic models?

I've already estimated the technical efficiency model, technical inefficiency effects model, and got the values of log likelihood, σ2, γ, and I just want to test the hypotheses concerning the model parameters.

Attached is an example of a table containing the results of a stochastic frontier model (Cobb-Douglas production function), in addition to the results of the technical inefficiency effects model (10 business environment variables (Zi)). Could you please, given the estimated parameters in table (1) tell me how to test the following hypothesis:

1. Cobb-Douglas does not the appropriate production function form

(H0: β3 = β4

**=**β5 = 0)2. No Technical inefficiency effects

(H0: γ = δ1 = δ2 = …= δ10 = 0)

3. No stochastic inefficiency

(H0: γ = 0)

4. No joint inefficiency variables

(H0: δ1 = δ2 = …= δ10 = 0)

Thank you very much in advance for this valuable help.

Can one use the L-shaped method for solving a two-stage stochastic program with binary variables in the first stage and integer and continuous variables in the second stage?

As you know in stochastic programming, it is common that we consider data with normal distribution. why normal ? What properties does a normal distribution have that made it important?

**Stochastic Gradient Descent:**

Uses only single training example to calculate the gradient and update parameters.

**Batch Gradient Descent:**

Calculate the gradients for the whole dataset and perform just one update at each iteration.

**Mini-batch Gradient Descent:**

Mini-batch gradient is a variation of stochastic gradient descent where instead of single training example, mini-batch of samples is used. It’s one of the most popular optimization algorithms.

If so, what does this say about having a high number of references?

If not, then are recommendations predictable? If so, how? If not, why not? Are stochastic signals being a basis of the human brain a reason to say there is no hope in predicting the work you do here?

I solved a mixed integer nonlinear nonlinear program by using the genetic algorithm in global optimization toolbox of MATLAB. However, the minimized objective value was different when I solved the problem by running the algorithm several times.

Genetic algorithm is a stochastic algorithm so it may give different solution at each run, but I think that I am dealing with premature convergence issue in my case.

Premature convergence is probably due to loss of diversity in the population but the MATLAB genetic algorithm for MINLPs overrides any crossover and mutation functions.

Is it appropriate to obtain multiple solutions by running the algorithm several times and choose the best solution among them?

For given samples X1...Xn, which follow the distribution F with parameters p1,...pm, one may use the maximum likelihood method to estimate p1,...pm. In the technical process, the method is only an optimization problem in m-dimensional field.

In some cases, it is irritating to acquire different estimated values of p1,...pm than the one acquired if one only estimate p1 (assuming this parameter does not depend on p2,...pm). E.g. the joint estimators (\mu, \sigma) may be different than \mu, when estimated alone. Since \mu is reserved for expected value, which one is "correct"? the joint-\mu or the single-\mu?

1) if the joint one is correct, then any single estimator should be doubted.

2) if the single one is correct, then joint-model does not have any values. So one should always choose univariate model.

In some cases, the joint-\mu does not make any sense. The interpretation that \mu is an expected value is somehow no longer valid in a joint-model.

I find fuzzy and stochastic is being used inter-changeably for uncertainty in literature. Stochastic LP model is being referred as LP under uncertainty. Fuzzy AHP is being referred as MCDM model under uncertainty. But the approach to solutions are different. Can we have Fuzzy Stochastic Model such as Fuzzy TOPSIS where ratings are done in linguistic terms to which FTN values assigned but ratings by group of decision makers are random and have variance. Can we apply stochastic modeling as done in Stochastic LP model ? I have come across Fuzzy MCDM models like Fuzzy AHP, Fuzzy TOPSIS etc. Can we have Stochastic AHP, Stochastic TOPSIS, Fuzzy Stochastic TOPSIS ?