Possibility and necessity integrals

Possibility and necessity integrals

Abstract: In this paper, we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures. These confidence measures have a field of sets as their domain, and a complete lattice as their codomain. In introducing these integrals, the analogy with the classical introduction of Legesgue integrals is explored and exploited. It is amongst other things shown that our integ...

Possibility and necessity in weighted aggregation

Yager [14] discussed the issue of weighted min and max aggregations and provided for a formalization of the process of importance weighted transformation. Generalizing Yager’s principle we suggest the use of fuzzy implication operators for importance weighted transformation.

Possibility measures and possibility integrals defined on a complete lattice

We consider the definition of possibility measures on complete lattices rather than on complete Boolean algebras of sets. We give a necessary and sufficient condition for the extendability of any mapping to such a possibility measure. We also associate two types of integrals with these possibility measures, and discuss some of their more important properties, amongst which a monotone convergenc...

The construction of consistent possibility and necessity measures

Possibility and Necessity Evaluations based on Ordinal Comparability

Subjective uncertainty is one of the most essential subjects for evaluation that was the reason Fuzzy theory was proposed. Related research areas are widely spread such as decision making, data analysis, information retrieval, psychology, and human computer interaction and so on. As a basis for various researches mathematical interpretation of evaluation methods occupies an important position. ...