Construction of Fuzzy Measures over Product Spaces

Fernando Reche, María Morales and Antonio Salmerón
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Fernando Reche: Department of Mathematics and Center for the Development and Transfer of Mathematical Research to Industry (CDTIME), University of Almería, 04120 Almería, Spain
María Morales: Department of Mathematics and Center for the Development and Transfer of Mathematical Research to Industry (CDTIME), University of Almería, 04120 Almería, Spain
Antonio Salmerón: Department of Mathematics and Center for the Development and Transfer of Mathematical Research to Industry (CDTIME), University of Almería, 04120 Almería, Spain

Mathematics, 2020, vol. 8, issue 9, 1-18

Abstract: In this paper, we study the problem of constructing a fuzzy measure over a product space when fuzzy measures over the marginal spaces are available. We propose a definition of independence of fuzzy measures and introduce different ways of constructing product measures, analyzing their properties. We derive bounds for the measure on the product space and show that it is possible to construct a single product measure when the marginal measures are capacities of order 2. We also study the combination of real functions over the marginal spaces in order to produce a joint function over the product space, compatible with the concept of marginalization, paving the way for the definition of statistical indices based on fuzzy measures.

Keywords: fuzzy measures; monotone measures; product spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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