Application of fuzzy probability in water quality management of a river system

Wafer quolify munagemenf of0 river sysrem is addressed i n n fizzy andprobobilisric framework. Two ryper of uneerfoinry, namely randomness and vagueness. ore rreared simrrlfonmii.dy in the monogemmf problem. A.fuzzy-ser-bo.~ed dqfinifion rhaf is a more general case offhe existing crisp-set-based dqfmirion of low w l e r qualify is infroduced. The evenr of low wafer qu01it)i af r? check-poinr in rhe river syrrsm i.s considered as n fuzzy even?. The rirk of low ~ , a f e r qualify ir rhen definedm rhepobabiliry of rhe fuzzy even1 s f l m wafer qu01if.y. Insreadof consfrainiag fhe risk ofviolafim of warw quality srmdord by nfinile value of risk throuplr a chance con.~framr. LI furry sef sf low risk rhaf con.sidws a range ofri.yk levels with approprioc membership values i$ inrroduced. Diffkrmr goalr o.wocioird with rhr manopemenf problem m e expressed as ,fuzzy iei-i. The rcirrlring manapmenf prohlem ir furmuluiedas a,fuzzy mslriobjperive oprimimtinn nrohlem