The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....

Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although several similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, no one has considered the use of the Sugeno integral to define them. Since the Sugeno integral provides an expected-value-like operation, it can be a useful tool i...

This paper clari es the connection between multiple criteria decisionmaking and decision under uncertainty in a qualitative setting relying on a nite value scale. While their mathematical formulations are very similar, the underlying assumptions di er and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can represent ...

We introduce and study implicator and coimplicator integrals, and investigate their possible application in defining the possibility and necessity of fuzzy sets. First, the definition and properties of implicators and coimplicators on bounded posets are discussed. Then, in analogy with the theory of seminormed and semiconormed fuzzy integrals, implicator and coimplicator integrals are defined. ...

This paper deals with decision making under uncertainty when the worth of acts is evaluated by means of Sugeno integral. One limitation of this approach is the coarse ranking of acts it produces. In order to refine this ordering, a mapping from the common qualitative utility and uncertainty scale to the reals is proposed, whereby Sugeno integral is changed into a Choquet integral. This work rel...

This paper clari es the connection between multiple criteria decisionmaking and decision under uncertainty in a qualitative setting relying on a nite value scale. While their mathematical formulations are very similar, the underlying assumptions di er and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can represent ...

We propose the concepts of superadditive and of subadditive transformations of aggregation functions acting on non-negative reals, in particular of integrals with respect to monotone measures. We discuss special properties of the proposed transforms and links between some distinguished integrals. Superadditive transformation of the Choquet integral, as well as of the Shilkret integral, is shown...

An overview of the use of the discrete Sugeno integral as either an aggregation tool or a utility function is presented in the qualitative framework of two decision paradigms: multi-criteria decision-making and decision-making under uncertainty. The parallelism between the representation theorems in both settings is stressed, even if a basic requirement like idempotency should be explicitely st...

Recently, the study of fuzzy integral inequalities has gained much attention. The most popular method is using the Sugeno integral 1 . The study of inequalities for Sugeno integral was initiated by Román-Flores et al. 2, 3 and then followed by the others 4–11 . Now, we introduce some basic notation and properties. For details, we refer the reader to 1, 12 . Suppose that Σ is a σ-algebra of subs...

We present a survey of various approaches for the refinement of the Sugeno integral, based on the lexicographic order or the principle of discarding common values between acts. We try to relate these different approaches and compare their merits.