Abstract
As one of the emerging renewable resources, the use of photovoltaic cells has become a promise for offering clean and plentiful energy. The selection of a best photovoltaic cell for a promoter plays a significant role in aspect of maximizing income, minimizing costs and conferring high maturity and reliability, which is a typical multiple attribute decision making (MADM) problem. Although many prominent MADM techniques have been developed, most of them are usually to select the optimal alternative under the hypothesis that the decision maker or expert is completely rational and the decision data are represented by crisp values. However, in the selecting processes of photovoltaic cells the decision maker is usually bounded rational and the ratings of alternatives are usually imprecise and vague. To address these kinds of complex and common issues, in this paper we develop a new interval-valued intuitionistic fuzzy behavioral MADM method. We employ interval-valued intuitionistic fuzzy numbers (IVIFNs) to express the imprecise ratings of alternatives; and we construct LINMAP-based nonlinear programming models to identify the reference points under IVIFNs contexts, which avoid the subjective randomness of selecting the reference points. Finally we develop a prospect theory-based ranking method to identify the optimal alternative, which takes fully into account the decision maker’s behavioral characteristics such as reference dependence, diminishing sensitivity and loss aversion in the decision making process.
Highlights
With natural resource scarcity and environmental protection, the use of renewable energy has become a promise for offering clean and plentiful energy source [1]
Many prominent decision making techniques have been developed for solving multiple attribute decision making (MADM) problems during the past decade years, such as Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) [2], the TOPSIS method [3], the VIKOR method [4,5], the ELECTRE method [6,7], the DEMATEL method [8], the WASPAS method [9], etc
Case 1: let A1 be an alternative, and let C1 be an attribute which the alternative A1 satisfies, the rating of the alternative A1 with respect to the attribute C1 is represented by interval-valued intuitionistic fuzzy numbers (IVIFNs) as C1 ( A1 ) = ([0.5, 0.6], [0.2, 0.3]), which can express the meaning that the alternative A1 is an excellent alternative for the decision maker (DM) on the attribute C1 with a chance between 50% and 60%, and simultaneously A1 is not an excellent choice with a chance between 20% and 30% [31]; and Case 2: given two alternatives A1 and A2, if the DM prefers A1 to A2 with IVIFN preference information
Summary
With natural resource scarcity and environmental protection, the use of renewable energy has become a promise for offering clean and plentiful energy source [1]. Energies 2016, 9, 835 fuzzy numbers [13,14], the decision environments of interval-valued intuitionistic fuzzy numbers (IVIFNs) [15], the decision contexts of grey [16], etc These aforementioned MADM techniques are derived from expected utility theory which is based on the strict assumption regarding complete rationality of the decision maker (DM), while many excellent papers involving behavioral experiments [17,18] have shown that the DM is usually bounded rational in real-life decision process.
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