Decision making over necessity measures through the Choquet integral criterion

Analysis of Possibility Theory for Reasoning under Uncertainty

“…In [27] the concept of Choquet integral is used in decision making over a necessity measure by simply ranking such measures with the use of its Choquet expected utilities. This method is relatively similar to Von Neumann and Morgenstern's method of decision making under risk, and provides a category of information which is made available by its Choquet expectation of the fuzzy set.…”

A study on interval-valued necessity measures through the Choquet integral criterian

“…We remark that Ω  Ω is not convex (see [11]). We also list non-additive measures, possibility measures, and necessity measures.…”

“…      ⊂  ⊂ Ω stands for the upset generated by . Then these sets of subsets of Ω are known as filters(see [11]), we denote the set of filters by Ω. We recall that a family  of subsets of Ω is said to be a filter if…”

“…Y. Réballé [11] discussed the representation of necessity measure through the Choquet integral criterian. He also considered a decision maker who ranks necessity measures related with Choquet integral representation.…”

“…He also considered a decision maker who ranks necessity measures related with Choquet integral representation. Another researchers have been studying topics related with Choquet integrals, for examples, preference representation theorem(Y. Réballé [11]), integral representation(D. Schmeidler [12]), subjective probability and expected utility without additivity(D. Schmeidler [13]), interval-valued Choquet price functionals(L. Jang [8]), applications in pricing risks(L. Jang [9]), etc.…”