## Pseudo-additive measures and integrals.(English)Zbl 0611.28010

We suggest pseudo-additive measures based on a pseudo-addition and discuss integrals with respect to pseudo-additive measures. A pseudo- additive measure is a special type of fuzzy measures. To define an integral, a multiplication corresponding to a pseudo-addition is introduced. The resulting integral is an extension of the Lebesgue integral. In this context, Radon-Nikodým-like theorems are shown.

### MSC:

 2.8e+11 Fuzzy measure theory
Full Text:

### References:

 [1] Aczel, J., Lecture on Functional Equations and Their Applications (1966), Academic Press: Academic Press New York · Zbl 0139.09301 [2] Ishii, K.; Sugeno, M., A model of human evaluation process using fuzzy measure, Internat. J. Man-Machine Stud., 22, 19-38 (1985) · Zbl 0567.90059 [3] Ling, C. H., Representation of associative functions, Publ. Math. Debrecen, 12, 189-212 (1965) · Zbl 0137.26401 [4] Mostert, P. S.; Shields, A. L., On the structure of semigroups on a compact manifold with boundary, Ann. of Math., 65, 117-143 (1957) · Zbl 0096.01203 [5] Seif, A.; Aguilar-Martin, J., Multi-group classification using fuzzy correlation, Fuzzy Sets and Systems, 3, 109-122 (1980) · Zbl 0426.68084 [6] Sugeno, M., Theory of Fuzzy Integrals and Its Applications, (Doctoral thesis (1974), Tokyo Inst. of Tech: Tokyo Inst. of Tech Tokyo) · Zbl 0316.60005 [7] Weber, S., ⊥-Decomposable measures and integrals for Archimedean $$t$$-conorms ⊥, J. Math. Anal. Appl., 101, 114-138 (1984) · Zbl 0614.28019 [8] Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.