Generalized qualitative Sugeno integrals

in Information Sciences (2017), 415-416

Sugeno integrals are aggregation operations involving a criterion weighting scheme based on the use of set functions called capacities or fuzzy measures. In this paper, we define generalized versions of ... [more ▼]

Sugeno integrals are aggregation operations involving a criterion weighting scheme based on the use of set functions called capacities or fuzzy measures. In this paper, we define generalized versions of Sugeno integrals on totally ordered bounded chains, by extending the operation that combines the value of the capacity on each subset of criteria and the value of the utility function over elements of the subset. We show that the generalized concept of Sugeno integral splits into two functionals, one based on a general multiple-valued conjunction (we call integral) and one based on a general multiple-valued implication (we call cointegral). These fuzzy conjunction and implication connectives are related via a so-called semiduality property, involving an involutive negation. Sugeno integrals correspond to the case when the fuzzy conjunction is the minimum and the fuzzy implication is Kleene-Dienes implication, in which case integrals and cointegrals coincide. In this paper, we consider a very general class of fuzzy conjunction operations on a finite setting, that reduce to Boolean conjunctions on extreme values of the bounded chain, and are non-decreasing in each place, and the corresponding general class of implications (their semiduals). The merit of these new aggregation operators is to go beyond pure lattice polynomials, thus enhancing the expressive power of qualitative aggregation functions, especially as to the way an importance weight can affect a local rating of an object to be chosen. [less ▲]

Characterizing variants of qualitative Sugeno integrals in a totally ordered Heyting algebra

in Alonso, José M.; Bustince, Humberto; Reformat, Marek (Eds.) Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (2015, July)

Sugeno integral is one of the basic aggregation operations on a qualitative scale where only minimum and maximum, as well as order-reversing maps are allowed. Recently some variants of this aggregation ... [more ▼]

Sugeno integral is one of the basic aggregation operations on a qualitative scale where only minimum and maximum, as well as order-reversing maps are allowed. Recently some variants of this aggregation operation, named soft and drastic integrals, have been introduced in a previous work by three of the authors. In these operations, importance weights play the role of tolerance thresholds enabling full satisfaction if ratings pass them. These new aggregation operations use residuated implications, hence need a slightly richer structure, and are part of larger family of qualitative aggregations. Based on some properties laid bare in a previous work, this paper proposes characterisation theorems for four variants of Sugeno integrals. These results pave the way to decision-theoretic axiomatizations of these natural qualitative aggregations. [less ▲]