Improvement of Environmental Impact Assessment Using Dempster-Shafer Theory (Case Study: Binalud County, Khorasan Razavi)

Introduction
Environmental impact assessment is a systematic process to identify, predict and evaluate the environmental effects of proposed actions and projects. This process is applied prior to major decisions and commitments being made. Environment, social, cultural and health effects are considered as an integral part of EIA. Particular attention is paid to EIA practice for preventing, mitigating, and offsetting the significant adverse effects of proposed actions. Uncertainty is present when the knowledge about future conditions is incomplete or lacking and also the possibility to make precise decisions about these conditions is low. Using the theory of Dempster-Shafer is a novel methodology for decision-making under uncertain conditions in environmental assessment as we try to examine with insufficient, fuzzy and uncertain data. This theory provides a mathematical framework for describing incomplete and inadequate data.
 
Materials and Methods
The Dempster-Shafer theory has an advantage over the Bayesian probability theory. In Bayesian probability theory, only singleton hypotheses are recognized and assumed to be exhaustive. Thus, ignorance is not recognized, and lack of evidence for a hypothesis constitutes evidence against that hypothesis. These requirements and assumptions are often not warranted in real-world decision situations. In contrast to this, the logic of Dempster-Shafer theory can express the degree to which the state of one’s knowledge does not distinguish between the hypotheses. This is known as ignorance. Ignorance expresses the incompleteness of one’s knowledge as a measure of the degree to which we cannot distinguish between any of the hypotheses. The basic assumptions of Dempster-Shafer theory are that ignorance exists in the body of knowledge, and that belief for a hypothesis is not necessarily the complement of the belief for its negation. A belief function can be viewed as a generalized probability function and the belief and plausibility measures can be regarded as lower and upper bounds for the probability of an event. To express the concept in mathematical terms, let Θ = {H₁, H₂,…, H_N} be a collectively exhaustive and mutually exclusive set of hypotheses or propositions, which is called the frame of discernment. A basic probability assignment (bpa) is a function m: 2^Θ [0,1], which is called a mass function, satisfying:
m(Ф) = 0                                                                                                                                 (1)
and
where, Ф is an empty set, A is any subset of Θ, and 2^Θ is the power set of Θ, which consists of all the subsets of Θ, i.e.
 = {Ф, {H₁}, …, . , {},{H₁, H₂},{H₁, },…, }                                                             (2)
The assigned probability (also called probability mass) m(A) measures the belief exactly assigned to A and represents how strongly the evidence supports A. All the assigned probabilities sum to unity and there is no belief in the empty set (Ф). The assigned probability to, i.e. m(, is called the degree of ignorance. Each subset A such that m(A)> 0 is called a focal element of m. All the related focal elements are collectively called the body of evidence.
Associated with each bpa is the belief measure, Bel, and the plausibility measure, Pl, which are both functions:  [0, 1], and given by Bel(A) = and Pl(A) = , where A and B are subsets of . Bel(A) represents the exact support to A, i.e. the belief of the hypothesis A being true; Pl(A) represents the possible support to A, i.e. the total amount of belief that could be potentially placed in A. [Bel(A), Pl(A)] constitutes the interval of support to A and can be seen as the lower and upper bounds of the probability to which A is supported. The two functions are related to each other by Pl(A) = 1- Bel(Ā), where Ā denotes the complement of A. The difference between the belief and the plausibility of a set A describes the ignorance of the assessment for the set A.
Belief represents the total support for an hypothesis, and will be drawn from the BPAs for all subsets of that hypothesis, i.e.,:
BEL(X) = ∑ m(Y)           when       YX
In contrast to belief, plausibility represents the degree to which a hypothesis cannot be disbelieved. Unlike the case in Bayesian probability theory, disbelief is not automatically the complement of belief, but rather, represents the degree of support for all hypotheses that do not intersect with that hypothesis. Thus:
PL(X) = 1- BEL(X)    where X = not X
Thus,     PL(X) = ∑m(Y) when   Y∩X ≠ φ
Interpreting these constructs, we can say that while belief represents the degree of hard evidence in support of a hypothesis, plausibility indicates the degree to which the conditions appear to be right for that hypothesis, even though hard evidence is lacking. For each hypothesis, then, belief is the lower boundary of our commitment to that hypothesis, and plausibility represents the upper boundary. The range between the two is called the belief interval, and represents the degree of uncertainty in establishing the presence or absence of that hypothesis. As a result, areas with a high belief interval are those in which new evidence will supply the greatest degree of information. Dempster-Shafer is thus very useful in establishing the value of information and in designing a data gathering strategy that is most effective in reducing uncertainty. The Belief module can be used to implement the Dempster-Shafer logic. The Belief module has a wide variety of applications, as it can aggregate many different sources of information to predict the probability that any phenomenon might occur. Therefore, all assessment information, quantitative or qualitative, complete or incomplete, and precise or imprecise, can be modeled using a unified framework of a belief structure. Therefore, Dempster-Shafer Weight-of-Evidence modeling has been chosen as efficient method for the aggregation of data in tourism impact assessment. The tourism impact assessment by using Dempster-Shafer theory comprises multiple steps, in this research. In the first step, we identify the criteria for tourism impact assessment. Complex decision-making problems are usually modeled in terms of a number of decisive variables that are related hierarchically. Pieces of evidence are aggregated in a bottom-up way to determine the final decision goal. In the second step, we collect data from multiple information sources like human experts, questionnaire, models, etc. on the selected criteria for evaluation purposes. In the third step, the information from multiple data sources is combined using Dempster-Shafer theory and the impact assessment of Binalud region for tourism is estimated. Performing risk analysis can be a challenging task for complex systems due to the lack of data and insufficient understanding of the failure mechanisms. Thus, in this study the D-S Theory is used because of its ability to deal with ignorance and missing information which is very likely in realistic tourism development impact assessment and also its ability to deal with multiple decision makers and heterogeneous data types. Basically, the Dempster-Shafer theory is well-known for its usefulness to express uncertain judgments of experts. On the other hand, our evaluation about the information and land resources is basically based on the expert judgments.
 
Results and Discussion
Data and maps of important factors for tourism development in the present study were gathered and converted to raster format. Then, the fuzzy raster maps were treated for their ecological suitability or lack of suitability for recreation in the impact assessment of the suggested tourism and ecotourism for the area of study. In the next step, each map was introduced to the belief procedure. After entering all information, the process divided all the evidence based on the underlying hypotheses (appropriate, inappropriate, appropriate- inappropriate) and combined them to produce three images of belief, plausibility and belief interval. The image of the region recreational impact assessment using the fuzzy and multi-criteria evaluation method was also prepared and compared with the belief image.
 
Conclusions
The results showed that the belief procedure has produced a more reliable result for the tourism development and its impact assessment. The implementation of the theory in a region can present better results. The decision making process can be improved by Dempster-Shafer theory.