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 lp 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; lp, norms; mining; multiple objectives; thermal springs.)

Fuzzy composite programming to combine remote sensing and crop models for decision support in precision crop management

“…The x-axis in Figs. 6 and 7 is the fuzzy distance towards the ideal solution (Bardossy and Duckstein, 1992). A value of 1 on the x-axis would indicate that the ideal solution has been achieved.…”

“…The best and worst values for the ®rst level indicators are determined by the user and are detailed in Table 4. Bardossy and Duckstein (1992) noted that the best and worst values might be crisp or fuzzy. For this example, the best and worst values are assumed to be crisp.…”

“…The addition of fuzzy set theory (Zadeh, 1965) to compromise programming is used to represent uncertainties of the indicators. In a manner similar to the composite programming extension, fuzzy compromise programming can be extended to a normalized multi-level distance-based methodology to account for uncertainties, also known as FCP (Bardossy and Duckstein, 1992). Zadeh (1965) proposed the use of fuzzy set theory (FST) to describe relationships that are best characterized by compliance to a collection of attributes.…”

“…FCP is a distance-based multi-objective optimization problem that uses fuzzy representation of uncertainty (Bardossy and Duckstein, 1992). Examples of FCP methodology include management of a karstic aquifer (Bardossy and Duckstein), nitrate risk management (Lee et al, 1992), management of dredged material (Lee et al, 1991) and land®ll hazard ranking (Hagemeister et al, 1996).…”

Stochastic-fuzzy multi criteria decision making for robust water resources management

“…More recently, Triantaphyllou and Lin (1996) evaluated five fuzzy MCDM methods: fuzzy Simple Additive Weighting (SAW) model, fuzzy weighted product model, fuzzy AHP, revised fuzzy AHP and fuzzy TOPSIS. Bardossy and Duckstein (1992) applied fuzzy Compromise Programming (CP) to a special water resource management problem. Chen (2000) extended the fuzzy TOPSIS method into group decision making when the evaluations of the alternatives versus the criteria are linguistic variables.…”