Speaker 1: Hi, welcome to my channel. In this video we are going to see the problem of decision theory under uncertainty. Before we see the problem, please subscribe this channel and hit the bell icon and see the description box to get more information and video links. Now let us see the problem. Let us see what is decision theory briefly before we see the problem. Okay, see decision making is an integral part of any business organization. See decision making is a continuous process which involves selecting the best among several decisions. Okay, see the types of decisions can be classified into three major categories. The first one is decision under certainty and the second one decision under risk and the third one decision under uncertainty. So these are the three decision environment. Okay, three different environments are there. Let us see what is certainty risk and uncertainty one by one. Look at the first one decision under certainty. Okay, see according to this situation if the availability of information for a decision environment is perfect. Okay, then the decision taken under such environment is called decision under risk. Okay, the information can be described in the form of perfect decision because all the information is available. Okay, with that you are going to take a decision is called certainty that is decision under certainty. The second one is decision under risk. See according to this situation if the availability of information for decision environment is partial. Okay, then the decision taken under such environment is called decision under risk. Okay, the information can be described as probability distribution. Okay, so this kind of decision is called decision under risk. Okay, the third one is decision under uncertainty. See here if the availability of information for a decision environment is incomplete. Okay, then the decision taken under such an environment is called decision under uncertainty. Under this environment there are five criteria are there to make a decision. So in this video we will see the problem for decision under uncertainty. Okay, first let us see the five criteria under this environment. Now let us see five criterion which comes under uncertainty. Okay, see the first one is Laplace criterion otherwise called as equal probability or rationality or base criterion. These are the other names for Laplace criterion. Okay, the second one is criterion of optimism. Okay, so under this optimism criterion we have two sub-criterions. The first one is Maxi-Max criterion and the other one is Mini-Min criterion. These are the two different types of criterion which comes under optimism. Okay, and the third one is criterion of pessimism otherwise called as Wald criterion. So here also we have two different types. The first one is Maxi-Min criterion. The other one is Mini-Min criterion. The third one is Maxi-Min criterion. Minimax criterion. So these are the two types of criterion which comes under pessimism. Okay, and the next one is Minimax-Regret criterion otherwise called as Save-Age criterion. So here also we have two different types. The first one for maximization problem. The another one for minimization problem. Okay, and the last one is Horwich criterion otherwise called as criterion of realism. Okay, again it has two types. The first one is Minimax-Regret criterion. The other one is two different types. The first one for maximization problem. The another one for minimization problem. These are the five criterion which comes under decision and uncertainty. Okay, now we are going to see the problem for each and every criterion separately. Now let us see the first criterion under uncertainty. Okay, the first one is Laplace criterion otherwise called as rationality or probability or Bayes criterion. These are the other names for Laplace criterion. Okay, so here first you need to find out the expected value for each and every strategies. Okay, see this is the formula. I will explain this formula along with the problem. Okay, now let us see the problem for Laplace criterion. See, the following matrix gives the payoff of different strategies that is alternative and alternative. So, let us see the problem for Laplace criterion. Let us see the alternatives S1, S2, S3 and S4. Okay, against conditions that is evens N1, N2, N3 and N4. So, this is the payoff matrix. Here we have four alternatives, four strategies are there and four evens, four conditions are there. Okay, now with this available payoff matrix, you have to select the best alternative. That is, you have to select the best strategies. So, we have four strategies, no? So, first you have to apply the formula to find out the expected value for each and every strategy by using this formula to find out the best decision. Okay, first we need to find out expected payoff for each and every alternatives by using the formula. The formula is 1 by N into P1 plus P2 till PN. See, N represent number of, okay? For the first strategy, how many evens are there? N1, N2, N3, N4. Four evens are there, no? So, N represent number of evens. Okay, and P1, P2, P3 represent the payoff value of each and every alternatives. For the first alternative, these are the P values. That is, P1, P2, P3 and P4. Okay, now we have to apply the formula to find out the expected payoff for each and every alternative. So, we have to apply the formula to find out the expected payoff for each and every alternative separately. I'll show the calculation for the first one. First alternative is S1 is equal to 1 by N represent number of evens. Here, we have four evens, no? So, 1 by 4 into, for the first alternative, P1 is 1000, P2 1500, P3 750, P4 0. So, just add 1000 plus 1500 plus 750 plus 1500 plus 1500 plus 1500 plus 1500 plus 1500 plus 1500 plus 1500 plus 1500 plus 1500 plus 0. Okay, you will be getting rupees 812 50 pais, 812 rupees 50 pais. So, this is the expected payoff for the first alternative. Okay, in the same way, you have to find out the expected payoff for S2, S3 and S4. For S2, 1 by 4 into 250 plus 2000 plus 3750 plus 3000. So, this is the expected payoff for S1. Answer is rupees 2250. In the same way, for S3, 1 by 4 into minus 500 plus 1250 plus 3000 plus 4750. You will be getting rupees 2125. For S4, 1 by 4 into minus 1250 plus 500 plus 2250 plus 4000. You will be getting rupees 1375. Okay, these are the expected payoff for each and every alternatives. Now, you can enter the value in the respective alternatives. See, the expected payoff for the first alternative is 812.5. Okay, for the second alternative, the expected payoff is 2250. Okay, for S3, alternative 3 is the value 2125. For the fourth alternative, 1375. Now, we have the expected payoff for S3, 2125. For S4, 1375. Now, we have calculated expected payoff for four alternatives. Okay, now, see the problem. Since the problem is payoff matrix, so we need to select the maximum expected payoff. See, see the payoff matrix. For the first alternative, expected profit is 812.5. For S2, 2250. For S3, 2125. For S4, 1375. Now, since the problem is payoff matrix, since this is the payoff matrix, you have to select the maximum expected payoff. Which one is highest value? 812, 2250, 2125, 1375. So, 2250 is the highest value. So, now, you have to select this one. That is, S2 is the best alternative. We are going to select S2 as the best alternative among the four alternatives. See, since the problem is payoff matrix, so we need to select S2 as the best alternative. problem is payoff matrix, we need to select the maximum expected payoff. Which one is maximum value? S2 is the maximum value. So, for payoff matrix, S2 gives the maximum expected payoff. That is, 2250. Okay, in case of cost matrix, see, in case of cost matrix, instead of payoff matrix, you need to apply the same formula. To find out the value for each and every alternatives, then you have to select the least value. Okay, which one is least value? 812.5 is the least value. Okay, you have to select S1 as the best alternative out of four other alternatives. Okay, so for payoff matrix, you have to select the maximum value. So, S2 gives the maximum benefit. In case of cost matrix, you have to select the minimum value. 812.5 is the minimum value. No, so S1 is the best alternative out of four alternatives. So, for the cost matrix, you have to select based on minimum value. For payoff matrix, you have to select based on the maximum value. According to the problem, you have to take a decision. This is the way to take a decision under Laplace criterion. Now, let us see the second criterion. Look at the second one. The second criterion is criterion of optimism. In the optimism, it has two subdivisions. The first one is MaxiMax criterion which is applicable for payoff matrix. Okay, and the second one is Minimin criterion which is applicable for cost matrix. Okay, now let us see the solution how to find out the best alternative according to MaxiMax and Minimin criterion. Look at the first one. According to MaxiMax criterion, first you need to find out the maximum value for each and every alternatives. Look at the first alternative. Which is the maximum value? 1500. So, first find out the maximum value. For the first alternative, 1500. For the second alternative, which is the highest value? 3750. For the third alternative, highest value is 4750. For the fourth alternative, 4000 is the highest value. Okay, after finding the maximum value for each and every alternatives, according to MaxiMax criterion, we need to select the maximum of maximum value. So, which is the maximum value out of the maximum values? So, here 4750 is the maximum of maximum payoff. So, S3 is the best alternative to be selected for implementation. So, S3 is to be selected as a best alternative according to MaxiMax criterion. Now, look at the Minimin criterion. See, according to Minimin criterion, so this is applicable only for cost matrix. So, here first you need to find out the minimum value for each and every alternative separately. Look at the first alternative. Which is the least value? 0 is the least value. So, find out minimum value for each and every alternative. For the first one, 0. For the second alternative, 250. S3 is the least value. For S3, which is the least value? Minus 500 is the least value. S3 is the least value. For S4, which is the least value? Minus 1250 is the least value. So, now you have to select the best alternative according to Minimin criterion. So, according to Minimin criterion, now you have to select the minimum of minimum values. So, out of the minimum, minimum values which is the most minimum value minus 1250 is the most minimum value out of the minimum values. So, S4 will be selected as the best alternative according to Minimin criterion. Here, according to MaxiMax criterion, we have selected maximum of maximum value. Okay, according to Minimin, we have selected minimum of minimum values. Okay, so these are the two sub criterion which comes under optimism that is criterion of optimism. Now, let us see the third one. So far, we have discussed two criterion. The first one is Laplace and the second one is optimism. Now, let us see the third one that is criterion of pessimism or Wald criterion. Okay, according to pessimism, it has two subdivisions. The first one is Maximin criterion. The second one is Minimax criterion. See, the Maximin criterion is applicable. The Maxi value is there. So, Maximin is applicable for payoff matrix. Okay, the second one is Mini value is there. So, Minimax criterion is applicable for cost matrix. Okay, now let us see how to take a decision based on Maximin and Minimax. Now, let us see the first one that is Maximin criterion. I will tell you how to do this problem in a simple way. So, let us see the first one that is Maximin. Okay, first you have to do minimum. You have to find out the minimum values for each and every alternative and after finding the minimum value, then you have to decide based on the first term. Okay, first you have to complete the first one, find the minimum value, then you have to take a decision based on the maximum value. I will show how to calculate. So, minimum. First, you need to find out the minimum of each and every alternative. For the first alternative, minimum value is zero. Okay, for the second alternative, minimum value 250. For the third alternative, minimum value minus 500. For the fourth alternative, minimum value minus 1250. Now, after finding the minimum values for each and every alternatives, now you have to decide which is the best one. For that, you have to select maximum. First, we have to calculate minimum. Then, you have to decide based on the maximum value. This is the first step and this is the second step. Now, we have to find out maximum of minimum value. So, now, which is the maximum value out of these minimum values? 250 is the maximum value. So, S2 is the best alternative among all other alternatives. So, S2 has to be selected as best alternative for implementation according to Maximin criterion. Now, let us see Minimax criterion. Okay, so this criterion is applicable for cost matrix. Assume this matrix is a cost matrix. Now, you have to find out maximum value. Okay, just divide the term into two parts and first you need to find out the maximum value for each and every alternatives and then you have to select the minimum of maximum value. So, first you have to do the this one that is maximum. Find out the maximum values for each and every alternatives. For the first one, maximum value is 1500 and for the second alternative, 3750. For the third one, 4750. For the fourth one, 4000. So, these are the maximum value for each and every alternatives. Now, you have to select minimum of maximum value. So, you have to select minimum of maximum value for each and every alternatives. Okay, so now which is the minimum value? 1500 is the minimum value. So, according to Minimax criterion, S2 is the best alternative to be selected for implementation. See, according to Maximin criterion, we have selected maximum of minimum value that is S2 is selected as a best alternative. According to Minimax criterion, we have selected minimum of maximum value that is S1 has to be selected as the best alternative. So, you have to be selected this is the way to select the best alternative according to pessimism okay so far we have discussed laplace criterion criterion of optimism and criterion of pessimism under uncertainty okay in the next video we will see minimax regret criterion and horwich criterion okay please see the description box to find the links okay hope you like the video and please share with your friends thank you you