A fuzzy logic approach for evaluating ecosystem sustainability
Introduction
Human activities have adverse impacts on ecosystems. The most significant impacts are climate change due to increasing concentrations of carbon dioxide in the atmosphere from the burning of fossil fuels, nonpoint source water pollution from increased fixation of nitrogen through the production of industrial fertilizer, and loss and fragmentation of wildlife habitats from human-induced landscape change (Hansson and Wachernagel, 1999). Such impacts have prompted many natural resource managers to change the focus of their management from resource extraction and exploitation to socially and ecologically sustainable management (National Research Council, 1992, Williams et al., 1997). This paradigm shift is embodied in the concept of ecosystem management, which involves “… managing … [ecosystem] patterns and processes in a holistic manner to provide for sustained character and function, as well as for benefits and commodities for humans” (Diaz and Bell, 1997).
Ecosystem management incorporates larger spatial scales, longer time periods and more variables than commodity-based resource management (Thomas, 1997), and strives for sustainable productivity of the whole ecosystem (Franklin, 1997, Schowalter et al., 1997) by focusing on achieving and sustaining a balance between producing consumer goods and services and ecological goods and services (MacKenzie, 1996). Ecological goods include timber, biomass fuels (coal, oil and natural gas) and natural fiber, and ecological services include air and water purification, mitigation of floods and drought, detoxification and decomposition of wastes, generation and renewal of soil, maintenance of biodiversity and partial stabilization of climate (Daily, 1997, Prato, 1998). The ecosystem manager attempts to maintain the long-term sustainability of the ecosystem (Franklin, 1997), or its capacity “to produce the same quantity and quality of goods and services in perpetuity” (Franklin, 1993).
Although fuzzy logic has been used to evaluate many biophysical issues (Silvert, 1997, Mackinson, 2000, Metternicht, 2001, Chen and Mynett, 2003, Svoray et al., 2004), this paper is unique in describing a fuzzy logic method for assessing the strong sustainability of an ecosystem. Strong sustainability requires all forms of capital (human, reproducible, and natural) to be non-decreasing over time (Pearce et al., 1990, Prato, 1999, Prato, 2000). Human capital includes people and their knowledge and skills, reproducible capital is the stock of human-made capital, such as automobiles, buildings and equipment, and natural capital is the stock of natural resources, such as soil, forests, water, and wildlife. Although there is relatively good information on human and reproducible capital, this is not the case for natural capital. For this reason, it is easier to evaluate strong sustainability of an ecosystem in terms of the flow of goods and services provided by human, reproducible, and natural capital.
For simplicity of exposition, consider an ecosystem manager that wants to determine whether an ecosystem is strongly sustainable based on three attributes or indicators of sustainability: regional income (I), biodiversity (B), and water quality (W). While these three attributes do not to envelop all aspects of ecosystem sustainability, they are sufficient to describe the fuzzy logic method proposed here. Determining strong sustainability involves two decisions. First, what are the values of the attributes? This is an empirical issue that requires measuring the attributes. Second, do particular values of the attributes imply the ecosystem is strongly sustainable? This is a conceptual issue. The conventional way to make the second decision is to declare an ecosystem strongly sustainable when It ≥ I*, Bt ≥ B*, and Wt ≥ W* for all t, where I*, B*, and W* are threshold values and t refers to time periods. These conditions for strong sustainability involve crisp sets for the attributes, which imply the manager can make a sharp, unambiguous distinction between when the ecosystem is strongly sustainable and when it is not. Defining strong sustainability in terms of crisp sets allows for knife-edge conclusions in which values of the attributes slightly above the thresholds imply the ecosystem is strongly sustainable, whereas values slightly below the thresholds imply the ecosystem is not strongly sustainable. A major drawback of knife-edge conclusions is that they run counter to the uncertainties inherent in ecosystem assessments.
This paper proposes an alternative for assessing the strong sustainability of an ecosystem that employs fuzzy sets and fuzzy logic. The alternative approach requires the ecosystem manager to develop fuzzy propositions about ecosystem attributes and strong sustainability. Four kinds of propositions can be developed and evaluated using fuzzy sets and fuzzy logic: (1) unconditional and unqualified; (2) unconditional and qualified; (3) conditional and unqualified; and (4) conditional and qualified (Klir and Yuan, 1995). Conditional propositions are stated in terms of conditional probabilities, and unconditional propositions are not. Qualified propositions have fuzzy probability qualifiers attached to them, and unqualified propositions do not. Only two of the four types of fuzzy propositions are considered here; unconditional and qualified propositions in Section 3, and conditional and qualified propositions in Section 4. Unqualified propositions are too limiting given the numerous uncertainties surrounding ecosystem management. Conditional and qualified propositions allow for a more comprehensive treatment of ecosystem uncertainties than unconditional and qualified propositions.
Section snippets
Fuzzy representation of ecosystem attributes
Evaluating fuzzy propositions about ecosystem sustainability requires the manager to define fuzzy sets for attributes and probability qualifiers, and to apply fuzzy logic to those propositions to reach a conclusion about the strong sustainability of an ecosystem. This section describes how to define fuzzy sets for variables, using I as an example. Suppose the manager defines four fuzzy sets for I on the universal set X = {0, 1, …, 10}, namely: I is very low (around 2); I is moderately low (around
Unconditional and qualified propositions
Consider the following unconditional and qualified propositions about attributes I, B and W:for i = 1, 2, 3, 4. A1I, A2I, A3I and A4I are fuzzy set for I, A1B, A2B, A3B and A4B are fuzzy sets for B, and A1W, A2W, A3W and A4W are fuzzy sets for W. Very low values of an attribute are represented by fuzzy sets A1I, A1B and A1W, moderately low values by sets A2I, A2B and A2W, moderately high values by sets A3I, A3B and A3W, and very
Conditional and qualified propositions
Consider the following conditional and qualified propositions about strong sustainability:where θ is defined on the universal set Y = {0, 1}, θS is a fuzzy set defined on Y that represents strong sustainability, g is a variable defined on G that represents combinations of values for I, B and W, Gf is a fuzzy set defined on G, and Pr(θ is θS|g is Gf) is a conditional probability. If each attribute takes on 11 values, as illustrated for I in
Conclusions
The conventional approach for assessing the strong sustainability of an ecosystem requires the manager to establish sustainability thresholds for attributes, measure the attributes, and determine whether measured attributes are above or below the thresholds, which involves crisp sets. An approach based on crisp sets for the attributes implies the ecosystem manager can make a sharp, unambiguous distinction between ecosystems that are and are not strongly sustainable. Knife-edge conclusions
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