In the previous chapter, the MIVES and MIVES – Monte Carlo methods were presented. MIVES is based on requirement trees, value functions, and the analytic hierarchy process. It helps integrate environmental, social, and economic sustainability indicators in a global sustainability index. Deterministic models can cause significant problems in terms of adequately managing the sustainability objective of a project. A method not only has to estimate the potential sustainability index at the end of the project. It also has to evaluate the degree of uncertainty that may make it difficult to achieve the sustainability objective. The MIVES – Monte Carlo method employs simulation to solve this problem. This chapter presents an alternative method, based on MIVES and fuzzy arithmetic. Different defuzzification parameters are proposed. An example of potential application related to heating and air conditioning systems in residential buildings is put forward. The advantages and drawbacks of using both methods are summarized.
TopFuzzy Arithmetic
Fuzzy sets were conceived as an extension of the crisp, conventional sets for constructing models that could embrace the imprecision or vagueness of many human concepts. The fuzzy sets theory can be applied to solve a broad range of problems. It was proposed by Lotfi Zadeh (1965) in the 1960s as a possible approach for dealing with uncertainty. Fuzzy sets led to the development of fuzzy logic, as well as possibility theory, for dealing with forms of uncertainty which are inherently non-statistical in nature.
Probability theory is based on principles of randomness, and there are specific characteristics of uncertainty not related to randomness (Dubois & Prade, 1988). On the other hand, some of the aspects covered by many uncertainty problems have a part related to randomness. Hybrid methods could be developed for treating each part of uncertainty with the most suitable techniques, but both techniques can really be applied to solve the vast majority of uncertainty problems. Each has specific advantages and disadvantages.
There are abundant publications dealing with fuzzy sets and their application to the analysis or control of processes and physical systems, in addition to decision making (Almeida Ribeiro, 1999; Cox, 1994; Dubois & Prade, 1980, 2000; Gil-Aluja, 2010; Juang, 1988; Kaufmann & Gupta, 1985, 1991; Lowen, 2010; Ross, 2010, Wadia-Fascetti & Smith, 1996; Zadeh et al., 1975; Zimmermann, 1991; for example).
As for project uncertainty, fuzzy sets have played a role in project selection; project financial analysis; time and cost estimation and control; contractor selection; and risk analysis (Abbasianjahromi & Rajaie, 2012; Carr & Tah, 2001; del Caño, 1992; Gil-Aluja, 2010; Kangari & Boyer, 1987; Kangari & Leland, 1989; Kaufmann & Gupta, 1985, 1991; Li et al., 2007; Nguyen, 1985; Pham & Valliappan, 1993; Singh & Tiong, 2005; Zadeh et al., 1975; among others).