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Qualitative models of complex sustainability systems using integrations of equations and equationless knowledge items generated by several experts

机译：使用多个专家生成的方程式和无方程式知识项的集成，构建复杂的可持续性系统的定性模型

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Highly non-linear, partially subjective, inconsistent, vague and multidimensional sustainability systems are often prohibitively difficult to study using numerical and/or verbal and consequently fuzzy quantifiers. Oversimplified or highly specific quantitative models are sometimes obtained and their practical applicability is therefore limited. Moreover, definitions of some ecological and consequently sustainability indicators are unclear and difficult to quantify by their very nature. This is the reason why the least information intensive descriptions must be incorporated into sustainability models developments. Time trends, e.g. increasing, are such information non-intensive descriptors. There are just three trend/qualitative values used to quantify variables and their derivatives: plus/increasing; zero/constant; negative/decreasing. The qualitative quantifiers are the key elements of qualitative models. Qualitative sustainability knowledge items are available in forms of equations with unknown numerical values of relevant constants and in equationless forms such as heuristics. For example - the unsteady state behaviour of a temperature is described by a dumped oscillation equation, however, the relevant equation's constants are not known; return on equity is increasing more and more rapidly. A qualitative model must be developed when the relevant complex quantitative model must be heavily simplified. The key information input in sustainability analysis is expert knowledge. A consensus among experts is often not reached because of substantial subjectivity of experts' knowledge. Qualitative model solutions are discrete sets of scenarios. Different unions U and intersections boolean AND of sets of qualitative solutions can be used to model unachievable consensuses among experts to identify a meaningful compromise. The case study presents a model generated by one expert. It is based on integration of one qualitative equation and 23 equationless relations using 13 variables e.g. return on equity, consumption of renewable energy, productivity of labour. The result is represented by 7 scenarios and 8 transitions among them. A set of five modifications of the sustainability model is studied. (C) 2015 Elsevier Ltd. All rights reserved.
机译：高度非线性的，部分主观的，不一致的，模糊的和多维的可持续性系统通常难以使​​用数字和/或口头的，因此模糊的量词来研究。有时会获得过于简化或高度特定的定量模型，因此其实用性受到限制。此外，一些生态指标的定义尚不清楚，因此很难根据其本质进行量化。这就是为什么必须将信息最少的描述纳入可持续性模型开发的原因。时间趋势，例如这些信息非密集描述符的数量在增加。只有三个趋势/定性值用于量化变量及其导数：加/增；零/常数负/递减。定性量词是定性模型的关键要素。定性的可持续性知识项目可以以方程式的形式获得，这些方程式的相关常数的数值未知，而无方程式的形式（如启发式）。例如-温度的非稳态行为由一个振荡方程描述，但是相关方程的常数未知；股本回报率越来越快。当必须大大简化相关的复杂定量模型时，必须开发定性模型。可持续性分析中输入的关键信息是专家知识。由于专家知识的实质性主观性，常常无法在专家之间达成共识。定性模型解决方案是场景的离散集合。定性解集的不同并集U和交集布尔AND可以用来为专家之间无法达成的共识建模，以找出有意义的折衷方案。案例研究提供了一个专家生成的模型。它基于一个定性方程和使用13个变量的23个无方程关系的积分。股本回报率，可再生能源的消耗，劳动生产率。结果由7个场景和其中的8个过渡表示。研究了对可持续性模型的五种修改。 （C）2015 Elsevier Ltd.保留所有权利。

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