3.7 3.7 There is an imprecise relationship between the flexural strength and volumetric strain of aconcrete beam. Let X be a fuzzy set of flexural strength (units of ksi) and Y be a fuzzy setof volumetric strain (units of inches/inch per cubic feet of beam) and membership func-tions are given as follows:[0.6 0.7 0.8 0.9+X =+(0.3, 0.6, 0.8 0.7, 0.4)Y =(0.7 * 0.8 * 0.9 * 1.0* 1.1++a. Find the Cartesian product represented by the relati on R = X × Y. Now, suppose wehave a second fuzzy set of flexural strength given as(0.1 0.2 0.3 0.4 0.5)* 5* 6* 7%3!+Find the following fuzzy sets:b. Find S =Z•R using max-min compositionc. Find § = Z•R using max-product composition.

Answered: Image /qna-images/answer/b52f674d-e3cc-4f8d-ba2a-b7fbeec0041d.jpg

3.7 There is an imprecise relationship between the flexural strength and volumetric strain of a concrete beam. Let X be a fuzzy set of flexural strength (units of ksi) and Y be a fuzzy set of volumetric strain (units of inches/inch per cubic feet of beam) and membership func- tions are given as follows: S0.6 0.7 0.8 09 (0.3 0.6, 0.8 0.7 0.4) = + 10.7 " 0.8 " 0.9 "1.0 " 1.1 a. Find the Cartesian product represented by the relation R = X × Y. Now, suppose we have a second fuzzy set of flexural strength given as

3.7 There is an imprecise relationship between the flexural strength and volumetric strain of a concrete beam. Let X be a fuzzy set of flexural strength (units of ksi) and Y be a fuzzy set of volumetric strain (units of inches/inch per cubic feet of beam) and membership func- tions are given as follows: S0.6 0.7 0.8 09 (0.3 0.6, 0.8 0.7 0.4) = + 10.7 " 0.8 " 0.9 "1.0 " 1.1 a. Find the Cartesian product represented by the relation R = X × Y. Now, suppose we have a second fuzzy set of flexural strength given as

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 85PQ

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