Dear Manish Jain,

I suggest you to see links and attached files on topic.

https://www.semanticscholar.org/paper/Some-Results-on-Fuzzy-Metric-Spaces-Rashid/77f9abcdceeaae54c7cd68b717b58477a53eb334

https://www.hindawi.com/journals/jfs/2021/9936992/

Article The strongest t-norm for fuzzy metric spaces

Best regards

this metric can by define on crisp set and we change the condition of t-norm but stay continuous function

Dear Manish,

Each George and Veeramani fuzzy metric is so in the context of Kramosil and Michalek by defining M(x,y,0)=0 for each x,y in X, whenever the axiom that demands lim_t M(x,y,t)=1 is not considered in this last one. So, the example that you are seeking does not exist for any contiunous t-norm. Nevertheless, if we consider the aforementioned axiom in the notion of Kramosil and Michalek, we can define on X=(0,1] the next fuzzy set: M(x,y,t) = min{x,y} for each distint x,y in X and M(x,x,t)=1, for all t>0. It is not hard to check that M is a GV fuzzy metric for the inimum t-norm whih is not a KM fuzzy metric if we define M(x,y,0)=0.

Dear all,

I have successfully formulated the example. Thanks all...