Moon Project Models: Choquet Bargaining Path for Real Time Applications

Choquet Bargaining Path for Moon Project Models on Real Time Application Surfaces: Presenter: Sulaiman Sani Department of Mathematics, Faculty of Science and Engineering, University of Eswatini, Kingdom of Eswatini, Southern Africa

What We Say About If we don t bargain scientific models in application, we are into a catastrophic application because of varying surfaces.

Between the Blue and the Red: (Moon Project): A regulated management problem T for an austere company X such that no new program p is mounted with less than k N inputs. If a new p is mounted, this p cannot have less than k N inputs throughout level 1 of p P; the least level in the p P hierarchies. Otherwise, this particular p is terminated for austerity reasons. Let s denote a finance project function for X. A measurable function s(X, .) that associates the two goods with unavoidable costs like the fees (w) paid, staff costs (x) incurred, consumables (y) used, the cross subsidization cost (z) within variables and so on as constraints of X for each p P is called the Moon project. (Moon Project Models): A set M of cost models for program p P during austerity in X. Place your data in this space

From the Horses Mouth: Choquet Bargaining Path for a Model Let ( , , ) be a measurable space with - capacity on ( , , ) representing the decision-maker's uncertainty measure about the states of the world such that : be a utility function, representing the decision-maker's preferences over outcomes. Let x, y, z be three outcomes. The Choquet Bargain between x, y and y is C (x, y, z) = (xu ( ) + yu ( )+zu ( )) d ( , , ) u ( ), u ( ), and u ( ) represent the quantile functions of the utility distribution. https://www.bing.com948117

The Moon Project Models: Associated Choquet Bargains The Basic Moon Project Model Used: T(t, .) = N0exp[( 1 2?2)t + B(t))] , N0 k The General Choquet Model Constructed: ?(?) N0(w, x, y, z, ... | p P) = ?(?) ? ? ?(?)?(?) 2??(?) ? Three Choquets: (Min, Max, Average): Lie Bracket {N0, F(T0 )}

Constructed Choquets Rules First Choquet Rule: Suppose that pI (D) has Choquet bargaining path { I,j: j = 1, 2, 3, 4, ..., J}. Then, any Choquet bargaining path I,k; k J with total selling price FI,k > TI,k { I,j } is a good bargaining path for pI (D) in X. Second Choquet Rule: Suppose I,k and I,m are good Choquet bargaining paths for pI (D). Then I,m is to be preferred over I,k only if the measurable map (m) (I, m, t, ) is better than (k) (I, k, t, ).

Constructed Choquets; Contd Third Choquet Rule The mean Choquet bargaining path for pI (D) is a preferred Choquet only if other good Choquet bargaining paths are nowhere good bargaining paths for pI (D). From Moon to Earth: Consider a Company X with departments DI : I N each working under certain specific constraints to mount some new programs pI. What are the Choquet bargaining paths for these projects and the optimal path for each program in X.

Down to Earth: Definitions X: University of the Moon. XI: Faculty of Science and Engineering. D1: Mathematics. D2: Physics. D3: Chemistry. D4: Biology. D5: Geography. D6: Engineering. D7: Computer Science. p(D): Programs existing in D pm(D): The m = 1, 2, 3, ... programs to be mounted in D. N = (n1, n2): Constraint numbers at minimum and maximum.

The Constraints Distribution: Choquet Questionnaire Derivative Table 1 Constraint Mix for Finding the Lie Bracket {N0, F (Tn) } pm(D) 2 2 3 1 4 2 1 Tp(n1, n2, a R) 684075 534075 384075 434075 364075 309075 306575 D 1 2 3 4 5 6 7 p(D) 2 3 4 2 3 5 3 n1 7 4 6 5 3 2 1 n2 8 7 7 9 4 5 5 Tp(n1) 1200000 900000 700000 700000 700000 500000 440000 Tp(n2) 1500000 1200000 800000 1000000 720000 700000 750000

The Lie Bracket for X Table 2 Lie Bracket {N0, F (Tn)} for D(XI) N 0 F (Tp(n1, n2, a R)) D F (Tp(n1)) F (Tp(n2)) N0(n1) N0(n2) D1 D2 D3 D4 D5 D6 D7 32537 10819 14332 25063 5212 3125 2459 41347 15038 18593 68964 7728 10741 18797 27557 15550 17317 32592 12321 12552 14400 37 83 49 28 134 160 179 36 80 43 15 93 65 40 26 48 30 18 65 64 63

From Moon to Earth Contd Results The Case of Mathematics Explained: From Table-2, With pm(D1) = 2, n1 = 7 constraints, D1 should admit N0(n1) = 37 students at entry point and charge F(Tp(n1)) = 37, 537.00 USD as the (First Choquet Bargain). Under n2 = 8 constraints in D1, N0(n1) = 36 at 41, 347.00 USD (Second Choquet Bargain). Go for the average Choquet that admits N0 = 26 at 27, 557.00 USD (Third Choquet Bargain). OPTIMAL Choquet is Choquet Bargain 2.

From Moon to Earth Contd Results The Case of Computer Science Explained: Three good Choquets in respect of the Rules. Choquet 3 is OPTIMAL in this case. Choquet Feasibility Analysis: For Another Day.

Some References: 1. Bodner, G.M., and Domin, D.S., (2000). Mental models: The role of representations in problem solving in chemistry. University Chemistry Education, vol. 4, no. 1, pp. 24-30. Golany, B., (1988). An Interactive MOLP Procedure for the Extension of DEA to effectiveness analysis. Journal of Operational Research Society, vol. 39, no. 8, pp. 725-734. Grosslight, L., Unger, C., Jay, E., and Smith, C.,(1991). Understanding models and their use in science: Conceptions of middle and high school students and experts. Journal of Research in Science Teaching, vol. 28, no. 9, pp. 799-822. Mangaraj, B.K., (2016). Relative effectiveness analysis under fuzziness. Procedia Computer Science, vol. 102, pp. 231-238. Merton H. M., and Daniel O., (2009). Mathematical Models for Financial Management. Graduate School of Business, University of Chicago. 2. 3. 4. 5.

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