ANALYSIS OF A KARSTIC AQUIFER MANAGEMENT PROBLEM BY FUZZY COMPOSITE PROGRAMMING1

ABSTRACT: A multiple objective framework for water resources problems possessing uncertain or imprecise elements is provided using distance-based concepts, fuzzy set theory, and fuzzy arithmetic. The case of regional management of a karstic aquifer in Hungary in which six conflicting objectives and six alternatives have been identified illustrates the methodology The objectives are classified into three groups of two objectives each, namely: (1) environmental (aesthetics, thermal springs temperature), (2) economic (mining, tourism), and (3) water quality (nitrates, phosphates). Both environmental objectives are formulated under fuzziness, and all objectives are scaled using the extension principle. Fuzzy compromise programming (FCP-I) is then applied; here, all six objectives are entered in a single l_p norm measuring the distance between each alternative and an ideal point. Next, fuzzy composite programming (FCP-II) is developed; here, a trade off is first made within each group of objectives, and then an upper level trade-off takes place between the three groups. The fuzzy numbers describing each alternative as a result from applying these techniques are ranked to yield an ordering of the alternatives. The results of applying FCP.I, FCP-II, and two different ordering techniques are compared. The FCP-II technique appears to provide a relatively simple approach at hierarchical or multilevel multiple objective decision-making, where uncertainty is described by fuzziness. (KEY TERMS: compromise programming; fuzzy arithmetic; fuzzy sets; hierarchical criteria; karstic aquifer; l_p, norms; mining; multiple objectives; thermal springs.)