covS vs covU from minimize()

[Yves Boulmer]

dear all, I hope you have had a nice summer

In my current study, I rely on minimize() from the R package QCA. I am working with fuzzy sets. I arrive at an intriguing result (see below): the solution reveals two conjunctions. In term 1) the condition ~S, in term 2) the condition S. Irrespective of the other conditions the cases cannot be in both terms. I have checked the specific cases and none are common, none have set-mship of 0.5. 

I would therefore expect covS and covU to be the same but they are not. I had not been really aware of this until now writing about my findings. I cannot find why these parameters differ and I would be thankful for any input you might have!

I thank you in advance!

Best

Yves  

M1: ~S*~W*~F*~E*~P + S*~V*~F*~E*~P -> ~Y inclS PRI covS covU --------------------------------------------- 1 ~S*~W*~F*~E*~P 0.825 0.653 0.467 0.293 2 S*~V*~F*~E*~P 0.871 0.503 0.251 0.077 --------------------------------------------- M1 0.816 0.632 0.545

[Ingo Rohlfing]

Dear Yves,

all cases in your data are members of both conjunctions regardless of their constitutive conditions. Unless a case is a full member or non-member, it has a partial membership in both configurations. For this reason, it is usually unlikely that covS and covU are identical when working with fuzzy sets.

Kind regards

Ingo

[Yves Boulmer]

Ingo, thank you!! 

of course, bien sûr! I was thinking in terms of the formula itself and could not get my mind out of this train of thoughts; but yes you are of course right, we are back to the concept of fuzzy sets and Ragin's (2008) illustration of the concept of coverage at p. 60 in his book. I hope I am not the only one who is regularly getting confused.

best regards

Yves