Equivalence & Tolerance Relations | Fuzzy Logic

Topics covered:
00:00 Introduction
00:43 Reflexivity
01:34 Symmetry
02:32 Transitivity
03:31 Crisp Equivalence Relation
03:46 Crisp Tolerance Relation
04:05 Reforming tolerance to equivalence relation
04:38 Solved Example - Crisp equivalence & tolerance relations
11:29 Reflexivity, Symmetry and transitivity for fuzzy relations
12:17 Fuzzy Equivalence Relation & Tolerance Relation
12:39 Solved Example -Fuzzy equivalence & tolerance relations
Out music:
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[@bhavanimurugesan9026]

Good Explanation.
Pls check
1. The condition given for symmetry property of fuzzy relation , instead of mentioning they should be equal, it is given as they should be equal to 1
2. In the example, for transforming tolerance relation into equivalence relation
R2 = fuzzy max min composition of R1 and R is correct ( but it is shown as R1 o R1

[@Topperly]

Thank you Bhavani for pointing out the unforeseen mistakes.
To all viewers,
1. Please make note of point 1 she mentioned above. The definition given for symmetry of fuzzy relation at 11:30 is wrong. I made a mistake while preparing slides. The condition of symmetry is that diagonally opposite elements should be equal. This is correctly shown at 13:07 in the solved example.
2. The second mistake she pointed out is already corrected with a pop-up pointing out the mistake.
Apologies to everyone for these mistakes.

[@SamiHajjaj287]

@@Topperly with regards to the first issue ... I think you meant "diagonally opposite elements should be EQUAL" .. and not equal to zero ... as mentioned in the original comment and in your video at 13:07 ...
still .. great work guys :))

[@alihaneren9]

I just discovered this channel. These videos are amazing. I realized that you have multiple playlists on different topics. I hope this channel gets more subscribers. Thank you for the effort sir

[@Topperly]

Thank you for your kind words :)

[@dawoodkhattak2087]

Amazing

[@Topperly]

Thank you :)

[@ashutoshyadav7537]

Nice explanation sir ❤

[@Topperly]

Glad you liked it :)

[@sunainatiwariST]

Sir , which composition method u used to get R . R in Fuzzy Relation ? max-min composition or max product composition ?

[@Topperly]

Hi,
I have used max-min method :)

[@sunainatiwari8297]

Ok sir. Thank you so much 🙏 🙏

[@vaibhavgagneja822]

you have performed composition on crisp set on what basis ?

[@Topperly]

Hi Vaibhav,
Sorry, I didn't get the question. Could you please elaborate?

[@vaibhavgagneja822]

Hi @@Topperly
I meant is it min max or max product

[@Topperly]

It doesn't matter. As I have explained in previous video on compositions, for crisp sets, you'll get same results using max-min as well as max-product methods :)