In some Multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intu-itionistic fuzzy set on a real number set and have better capability to model ill-known quantities. Firstly, the weighted possibility means of membership and non-membership functions for TrIFNs are defined. Hereby, a new lexico-graphic ranking method for TrIFNs is presented. Then, a series of trapezoidal intuitionistic fuzzy prioritized aggregation operators are developed, including trapezoidal intuitionistic fuzzy prioritized score (TrIFPS) operator, trapezoidal intuitionistic fuzzy prioritized weighted average (TrIFPWA) operator, trape-zoidal intuitionistic fuzzy prioritized and (TrIFP-AND) operator and trape-zoidal intuitionistic fuzzy prioritized or (TrIFP-OR) operator. Some desirable properties of these operators are also discussed. By utilizing the TrIFPWA op-erator, the attribute values of alternatives are integrated into the overall ones, which are used to rank the alternatives. Thus, a new method is proposed for solving the prioritized MADM problems with TrIFNs. Finally, the applica-bility of the proposed method is illustrated with a supply chain collaboration example.

In recent years, the image retargeting (IR) problem has been discussed as one of the challenging topics in the field of image processing in different applied domains. In this paper, a Multi operators hybrid method is proposed (IRWCO2C) to improve performance of an IR system, which is performed in three sub-systems. Firstly, the identification precision of important regions is enhanced using a feature extraction technique based on wavelet coefficients (WC) then identified the saliency map of images. In second sub-system, this saliency map is used to improve performance of seam carving process instead of the saliency map identified by conventional methods. Finally, the act of operators selection is improved using metaheuristic techniques to optimize process of operators combination. Findings reveal that our method, IR-WCO2C provided the highest precision (0. 74) in the IR process. Also, IR-WCO2C provided an improvement of 20% over the previous methods in different stages of the IR.

Numerous studies published in the fi eld of cellular manufacturing system are based on the assumption that machines are reliable in the entire production line without any breakdown. Since such assumptions are not usually realistic, to contribute to closing this gap between assumption and reality, a new model was proposed that additionally considered machine reliability, alternative process routings, and workforce assignment in a dynamic environment. Given such considerations in this research, the modified problem was defined and formulated and an extended mixed integer Multi-period mathematical model was proposed. In order to evaluate the effectiveness and capability of the extended model, some hypothetical numerical instances were generated and computational experiments were carried out using GAMS optimization package. Experimental results demonstrated that the demand value could affect the machine breakdown rate, and a machine with a minimum breakdown rate was implemented more often than others. Moreover, the observed trade off between the workforce-related costs and cell-formation costs indicated that workforce related issues had a significant impact on the total efficiency of the system. The proposed model can be quite applicable to medium-and large-scale manufacturing companies.

The aim of this paper is to introduce an interval trapezoidal neutrosophic set, which is a combination of trapezoidal fuzzy numbers, and an interval neutrosophic set. This paper presents some operational rules and the score and accuracy functions of interval trapezoidal neutrosophic numbers. Then, some aggregation operators based on interval trapezoidal neutrosophic information are proposed: the Interval Trapezoidal Neutrosophic Number Weighted Arithmetic Averaging (ITNNWAA) operator and the Interval Trapezoidal Neutrosophic Number Weighted Geometric Averaging (ITNNWGA) operator; in addition, the properties of these operators are investigated in detail. Furthermore, a Multi-attribute decision-making method is developed based on the operators. Finally, a numerical example is presented to illustrate the applicability and e ectiveness of the proposed method.

The cubic uncertain fuzzy linguistic variable can easily express the fuzzy information, and the power average (PA) operator is a useful tool which provides more versatility in the information aggregation procedure. In this paper, we will combine the PA operator and Einstein operations to cubic uncertain linguistic environment and propose some new PA operators. Firstly, the definition and some basic operations of cubic uncertain linguistic number, power aggregation (PA) operator and Einstein operations are introduced. Then, we propose cubic uncertain linguistic fuzzy powered Einstein averaging operator, cubic uncertain linguistic fuzzy powered Einstein weighted (CULFPEWA) operator, cubic uncertain linguistic fuzzy Einstein geometric operator and cubic uncertain linguistic fuzzy Einstein weighted geometric (CULFPEWG) operator and discuss some properties of these in detail. Furthermore, we develop the decision-making methods for Multi-attribute group decision-making problems with cubic uncertain linguistic information and give the detail decision steps. At last, an illustrate example is given to show the process of decision making and the effectiveness of the proposed method.