Fuzzy measures and integrals for bipolar scales

Fuzzy Number Fuzzy Measures and Fuzzy Integrals

By using the concepts of fuzzy number fuzzy measures and fuzzy valued functions a theory of fuzzy integrals is investigated. In this paper we have established the fuzzy version of Generalised monotone Convergence theorem and generalised Fatous lemma. 1. Introduction In the preceding paper [2], it is introduced that a concept of fuzzy number fuzzy measures, defined the fuzzy integral of a functi...

a cauchy-schwarz type inequality for fuzzy integrals

نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.

Fuzzy Measures and Integrals: Recent Developments

This paper gives a survey of the research done on fuzzy measures and integrals since Sugeno proposed in 1974 the concept of fuzzy measure, with an emphasis on recent results. This field of research lies at the intersection of several independent domains, which makes it very active and attractive, namely, measure theory, theory of aggregation functions, cooperative game theory, combinatorial opt...

Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based on fuzzy measures (capacity) and fuzzy integrals, essentially the Choquet and Sugeno integral. A first section sets the position of the problem of multicriteria decision making, and describes the various possible scales of measurement (cardinal unipolar and bipolar, and ordinal). Then a whole section is devoted to each...

Quadrature Rules for Fuzzy Integrals