Informatica

A complex spherical fuzzy set (CSFS) is a generalization of the spherical fuzzy set (SFS) to express the two-dimensional ambiguous information in which the range of positive, neutral and negative degrees occurs in the complex plane with the unit disk. Considering the vital importance of the concept of CSFSs which is gaining massive attention in the research area of two-dimensional uncertain information, we aim to establish a novel methodology for multi-criteria group decision-making (MCGDM). This methodology allows us to calculate both the weights of the decision-makers (DMs) and the weights of the criteria objectively. For this goal, we first introduce a new entropy measure function that measures the fuzziness degree associated with a CSFS to compute the unknown criteria weights in this methodology. Then, we present an innovative Complex Proportional Assessment (COPRAS) method based on the proposed entropy measure in the complex spherical fuzzy environment. Besides, we solve a strategic supplier selection problem which is very important to maximize the efficiency of the trading companies. Finally, we present some comparative analyses with some existing methods in different set theories, including the entropy measures, to show the feasibility and usefulness of the proposed method in the decision-making process.

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.

As an extension of intuitionistic fuzzy sets, picture fuzzy sets can deal with vague, uncertain, incomplete and inconsistent information. The similarity measure is an important technique to distinguish two objects. In this study, a similarity measure between picture fuzzy sets based on relationship matrix is proposed. The new similarity measure satisfies the axiomatic definition of similarity measure. It can be testified from a numerical experiment that the new similarity measure is more effective. Finally, we apply the proposed similarity measure to multiple-attribute decision making.

In this paper, we investigate green supplier evaluation and selection problems within the interval 2-tuple linguistic environment. Based on the operational laws and comparison rule of interval 2-tuple linguistic variables, we develop some new aggregation operators, such as the interval 2-tuple hybrid averaging (ITHA) operator, the interval 2-tuple ordered weighted averaging-weighted averaging (ITOWAWA) operator and the interval 2-tuple hybrid geometric (ITHG) operator. Then, an approach for green supplier evaluation and selection under the context of interval 2-tuple linguistic variables is proposed based on the developed interval 2-tuple linguistic hybrid aggregation operators. Finally, a practical application to the green supplier selection problem of an automobile manufacturer is presented to reveal the potentiality and aptness of the proposed green supplier selection approach. According to the findings, the supplier number ‘five’ got the highest rank, out of the five alternative green suppliers. The approach proposed in this paper may help managers and business professionals to evaluate and select the optimal green supplier by considering the importance degrees of both the given arguments and their ordered positions. Furthermore, it is able to take different scenarios into account and provide a more complete picture to the decision maker by using different hybrid aggregation operators.

In this paper, the main measure, an amount of information, of the information theory is analyzed and corrected. The three conceptions of the theory on the microstate, dissipation pathways, and self‐organization levels with a tight connection to the statistical physics are discussed. The concepts of restricted information were introduced as well as the proof of uniqueness of the entropy function, when the probabilities are rational numbers, is presented.