**Abstract**

Multicriteria decision-making usually requires a set of experts to evaluate the importance of selected criteria and the adequacy of feasible alternatives according to the criteria. Uncertainty can arise in these evaluations, since experts can be hesitant about their responses due to the difficulty of quantifying human language or lack of required knowledge. The Methodology for Integrated Multicriteria Decision-making with Uncertainty (MIMDU) tackles both factors of uncertainty by using non-predefined fuzzy numbers that are continuously adapted taking into account the level of confidence of the experts' opinions. The methodology also offers useful and complementary information to lead to a robust decision-making. This chapter proposes a novel methodology and provides a sample use case to demonstrate its capability to model uncertainty during decision-making process. In particular, a sensitivity analysis is included, which demonstrates (i) how uncertainty is incorporated into alternatives evaluation, and (ii) that the integrated multicriteria decision-making with uncertainty can be more reliable for decision-makers. The methodology is applied to the robust selection of the most sustainable technology to improve agriculture efficiency in rural areas by means of a case study of a low-cost biogas digester in a small-scale farm in Colombia.

**Keywords:** multicriteria decision-making, MIMDU methodology, confidence, rural areas development, sustainable agriculture

## **1. Introduction**

Decision-making in industrial and service sectors usually requires selecting one of several feasible alternatives for a specific problem or situation. This selection is not an easy task, since different criteria (e.g., economic, technical, social, environmental, etc.) can be conflicting. Multicriteria decision-making is a suitable approach to handle such problems [1] and usually requires the participation of experts to weigh the criteria and to evaluate the feasible alternatives according to the selected criteria [2]. In particular, for decisions aiming at sustainable development, experts are required to take into account many conflicting criteria with very different nature. These criteria include but not limited to economic (e.g., implementation costs), technical (e.g., systems reliability, ease of maintenance), social (e.g., job creation, degree of acceptance over population), and environmental (e.g., particles emissions, waste generation). Thus, experts are required to evaluate alternatives across all the considered criteria requiring many different expertises. Uncertainties arise due to incomplete knowledge required from experts.

Indeed, experts' opinions are surrounded by two factors of uncertainty: (i) the potential lack of confidence when providing an answer [3], and (ii) the difficulty of quantifying the answer [4]. For example, one expert could hesitate on whether the importance of a criterion should be "high" or "low," and none of those answers has a clear and unequivocal quantification on a numeric scale. Literature has focused until now on the second factor, as proven by the wide use of Fuzzy Linguistic Scales (FLS) in many applications [5, 6]. With FLS, experts are required to choose from different terms (e.g., high or low importance of a criterion), which are quantified through fuzzy numbers (FN) equidistantly disposed along a numerical scale. As an example, **Figure 1** shows numerical scale from 0 to 5. Thus, the same fuzzy number is assigned to two experts considering the importance of a criterion should be, for example, "low," regardless of how confident they are with their answer (e.g., [8]). As it can be seen, such approach does not consider the potential lack of confidence of experts, who can be more informed about some criteria but less about others. Thus, the developed MIMDU presented in this chapter addresses a research gap by considering the lack of confidence in human opinions.

The proposed MIMDU methodology can be used to enhance the efficiency of rural agriculture. As an example, the technique is used to increase the quality of a biofertilizer in developing farm areas with biogas digesters. Such biogas digesters

**Figure 1.** *Usual modeling of FN in literature [7].*

degrade cattle manure in anaerobic conditions to produce biogas for cooking or heating and a liquid effluent called digestate [9]. Digestate can be used as a biofertilizer, but it needs to be posttreated for its safe and efficient application to agricultural soil [10].

Different low-tech and low-cost alternatives, coupled with the digesters, can be implemented to posttreat the digestate. In this chapter, the following common posttreatment alternatives are considered to be feasible in a rural context and to allow the stabilization of the organic matter and the reduction of pathogens concentration: (i) a degassing tank, (ii) a sand filter, (iii) a vermifilter, (iv) digestate recirculation in the digester, and (v) a facultative pond. Most of these posttreatment technologies have been studied mainly for the treatment of urban wastewater [11, 12], and only a few studies were carried out with digestates. In this case, a comparative study of alternatives for the posttreatment of digestate from low-tech digesters is missing.

In this context, the aim of this chapter is twofold. First, to demonstrate the novelty of MIMDU to robustly assist multicriteria decision-making considering hesitance in human responses. Second, to apply MIMDU to select the best alternative for digestate posttreatment before its sustainable use in agriculture to enhance crop production. Sesction 2 details the phases of MIMDU, Section 3 provides an example case for illustrative purposes, displays the results of the case study in Colombia, and Section 3 concludes the MIMDU work presented in this chapter.
