For example with enriched labels of Type 1, if the label L1 , L1**(1) represents the linguistic variable** Good, then L1(ǫ1) represents either the reinforced or discounted L1 value which depends on the value taken by ǫ1**. In** this example, ǫ1 represents the (numerical) supporting degree of the linguistic value L1 = Good. If ǫ1 = 1.2, then we say that the linguistic value L1 **= Good has been reinforced by 20% with respect to its nominal/neutral** supporting degree. If ǫ1 = 0.4, then it means that the linguistic value L1 **is discounted 60% by the source.**
With enriched labels of Type 2, if one chooses by example X = {NB, NM, NS, O, P S, PM, P B}**, where**
elements of X have the following meaning: NB , "negative big", NM , "negative medium", NS ,**"negative**
small", O , "neutral" (i.e. no discounting, neither reinforcement), P S , "positive small", PM ,**"positive**
medium" and P B , "positive big". Then, if the label L1 , L1(O**) represents the linguistic variable** Good**, then**
L1(ǫ1), ǫ1 ∈ X, represents either the qualitative reinforced or discounted L1 **value which depends on the value**
taken by ǫ1 in X. ǫ1 = O means a neutral qualitative supporting degree corresponding to ǫ1 **= 1 for enriched** label of Type 1. ǫ1 represents the qualitative supporting degree of the linguistic value L1 = Good. If ǫ1 = P S,
then we say that the linguistic value L1 **= Good has been reinforced a little bit positively with respect to its** nominal/neutral supporting degree. If ǫ1 = NB, then it means that the linguistic value L1 **is discounted slightly**
and negatively by the source.

We denote by L˜(ǫ) any given set of (classical/pure) linguistic labels L˜ = {L1, L2, . . . , Ln} **endowed with the**
supporting degree property (i.e. discounting, neutral and/or reinforcement). In other words,

## L˜(Ǫ) = {L1(Ǫ1), L2(Ǫ2)**, . . . , L**N(Ǫn)}

represents a given set of enriched linguistic labels6. We assume the same order relationship ≺ on L˜(ǫ**) as the one** defined on L˜. Moreover we extend L˜(ǫ**) with two extreme (minimal and maximal) enriched qualitative values**
L0(ǫ) and Ln+1(ǫ) in order to get closed under qe-operators on L(ǫ) , {L0(ǫ),L˜(ǫ), Ln+1(ǫ)}**. For working**
with enriched labels (and then with qualitative enriched basic belief assignments), it is necessary to extend the previous q-operators in a consistent way. This is the purpose of our new qe**-operators.**
An enriched label Li(ǫi) means that the source has discounted (or reinforced) the label Li **by a quantitative**
or qualitative factor ǫi. Similarly for Lj(ǫj ). So we use the q-operators for Li, Lj **labels, but for confidences we** propose three possible versions: If the confidence in Liis ǫi and the confidence in Lj is ǫj **, then the confidence** in combining Li with Lj **can be:**
a) either the average, i.e. (ǫi + ǫj )/2; b) or min{ǫi, ǫj};
c) or we may consider a confidence interval as in statistics, so we get [ǫmin, ǫmax], where ǫmin , min{ǫi, ǫj}
and ǫmax , max{ǫi, ǫj}; if ǫi = ǫj **then the confidence interval is reduced to a single point,** ǫi.

In the sequel, we denote by "c" any of the above resulting confidence of combined enriched labels. **All these**
versions coincide when ǫi = ǫj = 1 (for Type 1) or when ǫi = ǫj = O **(for Type 2), i.e. where there is no**
reinforcement or no discounting of the linguistic label. However the confidence degree average operator (case a) ) is not associative, so in many cases it's inconvenient to use it. The best among these three, more prudent and easier to use, is the min operator. The confidence interval operator provides both a lower and a upper confidence level, so in an optimistic way, we may take at the end the midpoint of this **confidence interval as a confidence level.**
The new extended operators allowing working with enriched labels of Type 1 or Type 2 are then defined by: - qe**-addition of enriched labels**
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