Informatica

In our daily life, we could be confronted with numerous multiple attribute group decision making (MAGDM) problems. For such problems we designed a model which employs probabilistic linguistic MABAC (multi-attributive border approximation area comparison) based on the cumulative prospect theory (CPT-PL-MABAC) method to solve the MAGDM. The CPT-PL-MABAC method can take experts’ psychological behaviour and preferences into consideration. Furthermore, we utilize the combined weight consisting of subjective weight and objective weight. The objective weight is acquired by the entropy method. Additionally, the concrete calculating steps of CPT-PL-MABAC method are proposed to solve the MAGDM for selecting the optimal location of express distribution centre. Also, a numerical example for location selection of express distribution centre is given as the justification of the usefulness of the designed method. Finally, we compare the designed model with the other three existing models, and summarize the advantages and shortcomings.

Picture fuzzy sets (PFSs) utilize the positive, neutral, negative and refusal membership degrees to describe the behaviours of decision-makers in more detail. In this article, we expound the application of extended TODIM based on cumulative prospect theory under picture fuzzy multiple attribute group decision making (MAGDM). In addition, we adopt Information Entropy, which is used to ascertain the weighting vector of attributes to improve the availability of the TODIM method. At last, we exercise the improved TODIM into a numerical case for super market location and testify the effectiveness of this new method by comparing its results with other methods’ results.

For this article, we shall expand the TODIM model to the MADM with the picture fuzzy numbers (PFNs). Firstly, the concept, comparative method and distance of PFNs are introduced and the traditional TODIM model is presented. Then, the expanded TODIM model is developed to solve MADM problems with PFNs. Finally, a numerical example is given to verify the proposed approach.

Heronian mean (HM) has the characteristic of capturing the correlations of the aggregated arguments and the neutrosophic set can express the incomplete, indeterminate and inconsistent information, in this paper, we applied the Heronian mean to the neutrosophic set, and proposed some Heronian mean operators. Firstly, we presented some operational laws and their properties of single valued neutrosophic numbers (SVNNs), and analyzed the shortcomings of the existing weighted HM operators which have not idempotency, then we propose the improved generalized weighted Heronian mean (IGWHM) operator and improved generalized weighted geometric Heronian mean (IGWGHM) operator based on crisp numbers, and prove that they can satisfy some desirable properties, such as reducibility, idempotency, monotonicity and boundedness Further, we proposed the single valued neutrosophic number improved generalized weighted Heronian mean (NNIGWHM) operator and single valued the neutrosophic number improved generalized weighted geometric Heronian mean (NNIGWGHM) operator, and some desirable properties and special cases of them are discussed. Moreover, with respect to multiple attribute group decision making (MAGDM) problems in which attribute values take the form of SVNNs, the decision making approaches based on the proposed operators are developed. Finally, an application example has been given to show the decision making steps and to discuss the influence of different parameter values on the decision-making results.