Environmental impact assessment (EIA) is usually evaluated by many factors influenced by various kinds of uncertainty or fuzziness. As a result, the key issues of EIA problem are to represent and deal with the uncertain or fuzzy information. D numbers theory, as the extension of Dempster-Shafer theory of evidence, is a desirable tool that can express uncertainty and fuzziness, both complete and incomplete, quantitative or qualitative. However, some shortcomings do exist in D numbers combination process, the commutative property is not well considered when multiple D numbers are combined. Though some attempts have made to solve this problem, the previous method is not appropriate and convenience as more information about the given evaluations represented by D numbers are needed. In this paper, a data-driven D numbers combination rule is proposed, commutative property is well considered in the proposed method. In the combination process, there does not require any new information except the original D numbers. An illustrative example is provided to demonstrate the effectiveness of the method.
This article considers applications of the formalism of subjective modeling proposed in 36], based on modeling of uncertainty reflecting unreliability of subjective information and fuzziness common of its content. A subjective model of probabilistic randomness is defined and studied. It is shown that a researcher-modeler (RM) defines a subjective model of a discrete probability space as a space with plausibility and believability that de facto turns out to be a subjective model of the class of subjectively equivalent probability spaces that model an arbitrary evolving stochastic object, and the same space with plausibility and believability is its subjective model. This enables us to empirically recover a subjective model of an evolving stochastic object accurately and using a finite number of event observations, while its probabilistic model cannot be empirically recovered. A similar connection is established between equivalence classes of plausibility and believability distributions and classes of subjectively equivalent absolutely continuous probability densities. For two versions of plausibility and believability measures, entropies of plausibility and believability distributions of the values of an uncertain element (UCE) that model RM's subjective judgments as characteristics of the information content and uncertainty of his judgments are considered. It is shown that in the first version entropies have properties that are formally similar to those of Shannon entropy but due to absence of the law of large numbers (LLN) their interpretation fundamentally differs from the interpretation of Shannon entropy. In the third version there is an analog of the LLN, and its connection to the Shannon entropy was obtained for the expected value of subjective informational content/uncertainty. A subjective model M( )=(Omega,3(Omega), P (zeta,I degrees) (center dot,center dot; ), N (zeta,I degrees) (center dot,center dot; ) of an uncertain fuzzy element is considered, and an
In this paper, cartographic and architectural methodologies are compared, showing their congruency and contrasts, butalso reversions of concepts: cartography deals with the depiction of spatial objects and phenomena; architecture startswith a conceptual idea which is then implemented in a real physical object. Architectural projects begin with sketches at asynoptic scale, which are gradually converted into detailed plans. Maps are generalized from detailed geographic data.Cartographers make intentional use of 'subjective' methods; however, they try to avoid too high a degree of subjectivityduring the map design process by applying predefined design rules. The architectural designing process is influenced by thepersonal interpretation of the architect for the building task. The process then becomes more and more objective, takingregulations, structures, building technologies, etc., into account. Evidently, both cartography and architecture deal withcontrary levels of scale and precision. Reversing scale and precision leads to a paradox. Two examples of architecture andlandscape architecture demonstrate this outcome.
mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x a X of the model M(x) of a research object is defined by the researcher-modeler as a space(1) (X, p(X), , ) with plausibility and believability measures, where x is an uncertain element taking values in X that models researcher-modeler's uncertain propositions about an unknown x a X, measures , model modalities of a researcher-modeler's subjective judgments on the validity of each x a X: the value of determines how relatively plausible, in his opinion, the equality is, while the value of determines how the inequality should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, aEuro cent enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model , and if the data on observations of a research object is available, then it: aEuro cent enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research object.