Fuzzy valued measure is a mapping which maps a σalgebra to a set of fuzzy set with convex compact σlevel defined on banach space (β). In this paper, we investigate the notion of decomposition and representation of fuzzy valued measure (F.V.M) is given in the sequence of singular valued measure. Also we have been studied and develop the notion of integrals with the aid of F.V.M under closed inte...

The concept of universal integral, recently proposed, generalizes the Choquet, Shilkret and Sugeno integrals. Those integrals admit a discrete bipolar formulation, useful in those situations where the underlying scale is bipolar. In this paper we propose the concept of discrete bipolar universal integral, in order to provide a common framework for bipolar discrete integrals, including as specia...

In this paper we study the extension of Choquet integrals to ordinal scales. We show that two different integrals can be defined on the basis of two different but equivalent expressions in the numerical case. We prove some properties of the Choquet integrals and show their application to aggregation.

Expectation is the fundamental concept in statistics and probability. As two generalizations of expectation, Choquet and Choquet-like expectations are commonly used tools in generalized probability theory. This paper considers the Stolarsky inequality for two classes of Choquet-like integrals. The first class generalizes the Choquet expectation and the second class is an extension of the Sugeno...

Abstract: In this paper, we introduce Interval valued q- Rung Orthopair Hesitant fuzzy sets (IVq-ROHFS) with motivation of pythagorean [44] as a new concept. Then, give some basic operations complement, union, intersection, addition, scalar multiplication, power. Also, combine to and choquet integral , together aggregating operators, develop rung orthopair hesitant Choquet averaging operator (I...

The evaluation of quantified sentences is used for solving several problems. Most of the methods proposed are not satisfactory because they do not verify some intuitive properties. In this paper we propose an extension of both possibilistic and probabilistic methods, based on the Sugeno and the Choquet fuzzy integrals respectively, for the evaluation of type II sentences, the most general kind ...

The bounded convergence theorem on the Riesz space-valued Choquet integral is formalized for a sequence of measurable functions converging in measure and in distribution. 2010 Mathematics Subject Classification: Primary 28B15; Secondary 28A12, 28E10