Choquet integral‐based measures of economic welfare and species diversity. Issue 4 (15th August 2021)

• Record Type: Journal Article
• Authors: Beliakov, Gleb; James, Simon
• Other Names: Caraffini Fabio guestEditor.; Chiclana Francisco guestEditor.; Moodley Raymond guestEditor.; Gongora Mario guestEditor.
• Is Part Of: International journal of intelligent systems. Volume 37:Issue 4(2022)
• Page Start: 2849
• Page End: 2867
• Publication Date: 2021-08-15
• Subjects: buoyancy -- Choquet integral -- economic welfare -- fuzzy measure -- optimisation -- Pigou–Dalton principle; Artificial intelligence -- Periodicals; Expert systems (Computer science) -- Periodicals; Intelligence artificielle -- Périodiques; Systèmes experts (Informatique) -- Périodiques; 006.3
• DOI: 10.1002/int.22609
• Languages: English
• ISSNs: 0884-8173

Abstract

Abstract: Measures of diversity, spread and inequality can be important indicators in domains as diverse as ecology, economics and health. One of the key characteristics of such indices is the Pigou–Dalton (P‐D) principle, also known as the principle of progressive transfers, whereby proportional redistribution from larger to smaller arguments should increase (or decrease, depending on the context) the overall measure of social or economic welfare, diversity and so on. Previous studies have identified the ordered weighted averaging operators as being appropriate for welfare measurement, subject to conditions on the weighting vectors. We propose the Choquet integral, defined with respect to a capacity or fuzzy measure, as a candidate for defining nonsymmetric measures of welfare. This allows for importance and interaction to be modelled between inputs while still satisfying the P‐D principle. We extend the buoyancy concept to fuzzy measures and characterise the resulting classes of buoyant and antibuoyant fuzzy measures. We then turn to the problem of optimisation of the Choquet integral subject to linear constraints, which in the case of antibuoyant fuzzy measures permits an efficient linear programming solution.