Sharif Digital Repository

Type-2 fuzzy sets are generalisations of ordinary fuzzy sets in which the membership grades are characterised by fuzzy membership functions. Here, we consider the problem of finding the distance between two interval type-2 fuzzy sets (IT2-FSs). We define the formulation of calculating the distance between two IT2-FSs based on a new definition of centroid for an IT2-FS and explain an algorithm for obtaining it. Then, based on our proposed distance formulation, we present a method to deal with fuzzy multiple attributes group decision-making (FMAGDM) problems. We also use two examples to illustrate the FMAGDM process of the proposed method. The method provides us with a useful way to deal with... 

Similarity measures are very important concepts in fuzzy sets theory. There are several definitions for similarity measures in both type-1 and interval type-2 fuzzy sets (IT2-FSs). Here, the problem of finding similarity between two IT2-FSs is considered. A new similarity measure is proposed and its performance is compared with existing approaches in literature. Furthermore, an application of this measure in multiple criteria group decision making problem is given. Based on the proposed similarity measure, the satisfaction degree for different alternatives are established which then are used to rank alternatives in multiple criteria group decision making. Finally, a case study concerning the... 

Group working has an important role in cellular manufacturing systems (CMS) as they can affect the work environment and job executions on machines. The most important factors affecting human resources are aspects of ability and interactional interest among workers in workshops. Here, we present a simple and efficient method considering these two aspects to deal with the assignment of workers to cells. We use interval type-2 fuzzy interactional interest among workers and the capability of working on machines to develop a new concept of cell formation in CMS. By using a multidepot multiple travelling salesman problem (MDmTSP) model, we assign workers to cells and then propose a mathematical... 

Supplier selection is a decision-making process to identify and evaluate suppliers for making contracts. Here, we use interval type-2 fuzzy values to show the decision makers' preferences and also introduce a new formula to compute the distance between two interval type-2 fuzzy sets. The performance of the proposed distance formula in comparison with the normalized Hamming, normalized Hamming based on the Hausdorff metric, normalized Euclidean and the signed distances is evaluated. The results show that the signed distance has the same trend as our method, but the other three methods are not appropriate for interval type-2 fuzzy sets. Using this approach, we propose a hierarchical... 

We consider a multi-objective linear programming model with type-2 fuzzy objectives. The considered model has the flexibility for the user to specify the more general membership functions for objectives to reflect the inherent fuzziness, while being simple and practical. We develop two solution strategies with reasonable computing costs. The additional cost, as compared to the type-1 fuzzy model, is indeed insignificant. These two algorithms compute Pareto optimal solutions of the type-2 problems, one being based on a maxmin approach and the other on aggregating the objectives. Finally, applying the proposed algorithms, we work out two illustrative examples  

Wind power is a promising source of electric power generation since it has tremendous environmental and social benefits. The generation scheduling (GS) problem encounters several uncertainties in terms of the system's parameters such as load, reserve and available wind power generation. The modeling of those uncertainties is an important issue in power system scheduling. A fuzzy based modeling approach can be used to develop the generation schedule under an uncertain environment. In this paper, the type-2 fuzzy membership function (MF) is implemented to model the linguistic uncertainty of type-1 MF of available wind power generation which stems from opinions of different experts. The...