1.4 Determine whether the following fuzzy sets are convex or not.a) A= fu,(x)/x where µ,(x) =1/(1 + x³)b) B= [u,(x)/x where µ,(x) =1/(1 + 10x)"?1.5 Prove that all the a-cuts of any fuzzy set A defined on R" are convex ifand only ifH.(år + (1- A)s) 2 Minſ u,(r), 4.(s)

(a) A=∫μA(x)/x where μA(x)=11+x2, -∞<x<∞ It is clear that z=λx+(1-λ)y, 0≤λ≤1 For x,y ∈ℝ…

1.4 Determine whether the following fuzzy sets are convex or not. a) A- Ju,(x)/x where ,(x) =1(1 + x*) b) B- Ju,cx)/x where 4,(x) =1/(1 + 10x)"? 1.5 Prove that all the a-cuts of any fuzzy set A defined on R" are convex if and only if u.(dr + 1- 02 Min

1.4 Determine whether the following fuzzy sets are convex or not. a) A- Ju,(x)/x where ,(x) =1(1 + x*) b) B- Ju,cx)/x where 4,(x) =1/(1 + 10x)"? 1.5 Prove that all the a-cuts of any fuzzy set A defined on R" are convex if and only if u.(dr + 1- 02 Min

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

1.4 Determine whether the following fuzzy sets are convex or not.
a) A= fu,(x)/x where µ,(x) =1/(1 + x³)
b) B= [u,(x)/x where µ,(x) =1/(1 + 10x)"?
1.5 Prove that all the a-cuts of any fuzzy set A defined on R" are convex if
and only if
H.(år + (1- A)s) 2 Minſ u,(r), 4.(s)

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