How to group data in rows regardless of the order of the data in the rows and add group names to each row

Question

Column A contains texts. Each text has values in the neighboring cells. Now I want to check for each row whether the other rows also contain these values. Restriction: At least three values must match and regardless of the order in the row. The rows, which belong together because of at least 3 common values, should be grouped. A group name should be assigned to them dynamically. An example table might look like this: INPUT

Word	Value01	Value02	Value03	Value04
banana	A	B	C	D
sweet banana	L	N	O	J
cheap banana	B	D	A	F
best banana	D	C	A	H
banana banana	N	L	I	O
how to make banana bread	O	A	I	K
I love banana	B	C	A	D
banana bread	I	O	A	C

EXPECTED OUTPUT

Word	Value01	Value02	Value03	Value04	group name
banana	A	B	C	D	banana group 1
sweet banana	L	N	O	J	banana group 2
cheap banana	B	D	A	F	banana group 1
best banana	D	C	A	H	banana group 1
banana banana	N	L	I	O	banana group 2
how to make banana bread	O	A	I	K	banana group 3
I love banana	B	C	A	D	banana group 1
banana bread	I	O	A	C	banana group 3

I tried the following formula:

=ArrayFormula(IF(B1:E1=B1:E8,"banana group 1","banana group 2"))

But the problems are, only the exact match is recognized and I am limited to two group names. Here is a link to the example table: Example Table

Answer 1

There must be a easier way to do this, but this is one (expensive) way to do this. SORT each of row in ascending order, then get all the permutations of each row(for 4 items, that is 24 permutations per row). Check if any permutation match any of the previous row. If it matches, take the group it belongs to(F:F). If not, create a new group based on row number.

F2:

=ARRAYFORMULA(IFNA(INDEX(F$1:F1, MATCH( true,BYROW(B$1:E1,LAMBDA(r, OR(BYROW(REDUCE(TRANSPOSE(SORT(TRANSPOSE(B2:E2))),SEQUENCE(PERMUT(4,4)-1),LAMBDA(a,c,{a;GET_NEXT_LEX(INDEX(a,c,0))})),LAMBDA(perm, SUMPRODUCT(perm=r)>=3 ))))),0)),"group#"&ROW()))

Drag fill down. It gets more expensive based on number of rows.

For this to work, you need to install GET_NEXT_LEX function and it's dependencies from here.

Word	Value01	Value02	Value03	Value04	output
banana	A	B	C	D	group#2
sweet banana	L	N	O	J	group#3
cheap banana	B	D	A	F	group#2
best banana	D	C	A	H	group#2
banana banana	N	L	I	O	group#3
how to make banana bread	O	A	I	K	group#7
I love banana	B	C	A	D	group#2
banana bread	I	O	A	C	group#7

Answer 2

I thought I would take a look at all similarities. But you could get only three if you change just one line. I will point it out below:

function sortgroups() {
  const ss = SpreadsheetApp.getActive();
  const sh = ss.getSheetByName("Sheet0");
  const vs = sh.getRange("A2:E9").getValues();
  let obj = { pA: [] };
  vs.forEach((r, i) => {
    let a = [r[1], r[2], r[3], r[4]];
    obj[r[0]] = { chars: a, sub: [] };
    obj.pA.push(r[0]);
    vs.forEach((s, j) => {
      if (j != i) {
        let b = [s[1], s[2], s[3], s[4]];
        let m = [];//matches
        b.forEach((c, k) => {
          let idx = a.indexOf(c);
          if (~idx) {
            m.push(c);
          }
        })
        if (m.length == 3) {//this is the line to change to limit similarites
          obj[r[0]].sub.push({ p: s[0], chars: m.join(',') });
        } 
      }
    });

  });
  let r = [];
  obj.pA.forEach((p, i) => {
    r.push([p, obj[p].chars[0], obj[p].chars[1], obj[p].chars[2], obj[p].chars[3], '', '']);
    obj[p].sub.forEach((o, j) => {
      r.push(['', '', '', '', '', o.p, o.chars]);
    })

  })
  r.unshift(["Words","Value1","Value2","Value3","Value4","Similar Words","Similarities"]);
  sh.getRange(sh.getLastRow() + 2, 1, r.length, r[0].length).setValues(r);
}

Output:

Words	Value1	Value2	Value3	Value4	Similar Words	Similarities
banana	A	B	C	D
					cheap banana	B,D,A
					best banana	D,C,A
					how to make banana bread	A
					I love banana	B,C,A,D
					banana bread	A,C
sweet banana	L	N	O	J
					banana banana	N,L,O
					how to make banana bread	O
					banana bread	O
cheap banana	B	D	A	F
					banana	A,B,D
					best banana	D,A
					how to make banana bread	A
					I love banana	B,A,D
					banana bread	A
best banana	D	C	A	H
					banana	A,C,D
					cheap banana	D,A
					how to make banana bread	A
					I love banana	C,A,D
					banana bread	A,C
banana banana	N	L	I	O
					sweet banana	L,N,O
					how to make banana bread	O,I
					banana bread	I,O
how to make banana bread	O	A	I	K
					banana	A
					sweet banana	O
					cheap banana	A
					best banana	A
					banana banana	I,O
					I love banana	A
					banana bread	I,O,A
I love banana	B	C	A	D
					banana	A,B,C,D
					cheap banana	B,D,A
					best banana	D,C,A
					how to make banana bread	A
					banana bread	A,C
banana bread	I	O	A	C
					banana	A,C
					sweet banana	O
					cheap banana	A
					best banana	C,A
					banana banana	I,O
					how to make banana bread	O,A,I
					I love banana	C,A

Only Three:

Words	Value1	Value2	Value3	Value4	Similar Words	Similarities
banana	A	B	C	D
					cheap banana	B,D,A
					best banana	D,C,A
sweet banana	L	N	O	J
					banana banana	N,L,O
cheap banana	B	D	A	F
					banana	A,B,D
					I love banana	B,A,D
best banana	D	C	A	H
					banana	A,C,D
					I love banana	C,A,D
banana banana	N	L	I	O
					sweet banana	L,N,O
how to make banana bread	O	A	I	K
					banana bread	I,O,A
I love banana	B	C	A	D
					cheap banana	B,D,A
					best banana	D,C,A
banana bread	I	O	A	C
					how to make banana bread	O,A,I