Variable precision multigranulation rough fuzzy set approach to multiple attribute group decision-making based on λ-similarity relation

Abstract This study proposes a fuzzy multigranulation rough set approach to the problem of multiple attribute group decision-making with uncertainty. Based on the classical Pawlak rough set theory, we define the λ - similarity ( 0 ⩽ λ ≤ 1 ) relation classes over the universe of discourse by introducing a distance measure to all alternatives with respect to attribute set. Subsequently, we present the α ( 0.5 α ≤ 1 ) rough approximation of a crisp decision-making object and a fuzzy decision-making object under the framework of multigranulation rough set theory, respectively. That is, we establish the variable precision multigranulation rough set model and variable precision multigranulation rough fuzzy set model based on λ - similarity relation, respectively. Meanwhile, we discuss the interrelationship between the proposed multigranulation rough fuzzy set model and the existing generalized rough set models. After that, we construct a new approach to multiple attribute group decision-making problems based on variable precision multigranulation rough fuzzy set theory. The decision-making procedure and the methodology as well as the algorithm of the proposed method are given and a detailed comparison of the traditional methods to multiple attribute group decision-making problems illustrates the advantages and limitations. Finally, an example of handling multiple criteria group decision-making problem of evaluation of emergency plans for unconventional emergency events illustrates this approach. The main contribution of this paper is twofold. One is to provide a new way to construct multigranulation rough set model with the fuzzy environment. Another is to try making a new way to handle multiple criteria group decision-making problems based on generalized rough set theory and methodologies.