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Abstract: Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. By combining the multi-fuzzy set and soft set models, the purpose of this paper is to introduce the concept of multi-fuzzy soft sets. Some operations on a multi-fuzzy soft set are defined, such as complement operation, “AND” and “OR” operations, Union and Intersection operations. Then, the DeMorgan’s laws are proved. Finally, by means of level soft set, an algorithm is presented, and a decision problem is analyzed using multi-fuzzy soft set. [Copyright &y& Elsevier]

Group decision making is an important category of problem solving techniques for complicated problems, among which the Delphi method has been widely applied. In this paper an improved Delphi method based on Cloud model is proposed in order to deal with the fuzziness and uncertainty in experts' subjective judgments. The proposed Cloud Delphi Method (CDM) describes experts' opinions by Cloud model and we aggregate the experts' Cloud opinions by synthetic algorithm and weighted average algorithm. Another key point of CDM is to stabilize and accommodate the individual fuzzy estimates by the defined stability rules rather than having to force them to converge, or reduce. The Cloud opinions and aggregation results can be exhibited in a graphically way leading experts to judge intuitively and it can decrease the number of repetitive surveys and/or interviews. Moreover, it is more scientific and easier to represent experts' opinion base on Cloud model which can combine fuzziness and uncertainty well. A numerical example is examined to demonstrate applicability and implementation process of CDM. [ABSTRACT FROM AUTHOR]

Presenting a more efficient mathematical model for the problem of integrating lot sizing, loading, and scheduling in capacitated flexible flow shops with sequence-dependent setups is the main novelty of this paper. In comparison to the former model, fewer variables and constraints of the current model makes it easier to be solved. Comparison between this model and the former one shows the superiority of this model. To validate the new model, an efficient lower bound has been provided. Mixed integer programming-based algorithms have been used to solve this model. [ABSTRACT FROM AUTHOR]

Abstract: To tackle the problem of rough set on single-universe, we discuss the rough set model over dual-universes in aspect of building connection between single-universe model and dual-universes model. The rough set model over dual-universes denoted as RSMDU in this paper is built through inspecting the relation between the two universes. Firstly, we propose the RSMDU and study its property using character function and relation matrix. The algorithm for obtaining the lower and upper approximations is then presented. Secondly, we show that Pawlak rough set model can be induced using RSMDU. The theorem inferring the connection between Pawlak model induced by RSMDU and RSMDU is presented. Finally, the applications of RSMDU are studied. According to proposed model, we demonstrate that the existing models of rough set are special cases of RSMDU and that the set of conditional attribute and the set of decision attribute can be regarded as dual-universes in decision-making system, where the model can be utilized to handle decision processing. [Copyright &y& Elsevier]