Informatica

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.

As the tourism and mobile internet develop, car sharing is becoming more and more popular. How to select an appropriate car sharing platform is an important issue to tourists. The car sharing platform selection can be regarded as a kind of multi-attribute group decision making (MAGDM) problems. The probabilistic linguistic term set (PLTS) is a powerful tool to express tourists’ evaluations in the car sharing platform selection. This paper develops a probabilistic linguistic group decision making method for selecting a suitable car sharing platform. First, two aggregation operators of PLTSs are proposed. Subsequently, a fuzzy entropy and a hesitancy entropy of a PLTS are developed to measure the fuzziness and hesitancy of a PLTS, respectively. Combining the fuzzy entropy and hesitancy entropy, a total entropy of a PLTS is generated. Furthermore, a cross entropy between PLTSs is proposed as well. Using the total entropy and cross entropy, DMs’ weights and attribute weights are determined, respectively. By defining preference functions with PLTSs, an improved PL-PROMETHEE approach is developed to rank alternatives. Thereby, a novel method is proposed for solving MAGDM with PLTSs. A car sharing platform selection is examined at length to show the application and superiority of the proposed method.

Generating sequences of random numbers or bits is a necessity in many situations (cryptography, modeling, simulations, etc…). Those sequences must be random in the sense that their behavior should be unpredictable. For example, the security of many cryptographic systems depends on the generation of unpredictable values to be used as keys. Since randomness is related to the unpredictable property, it can be described in probabilistic terms, studying the randomness of a sequence by means of a hypothesis test. A new statistical test for randomness of bit sequences is proposed in the paper. The created test is focused on determining the number of different fixed length patterns that appear along the binary sequence. When ‘few’ distinct patterns appear in the sequence, the hypothesis of randomness is rejected. On the contrary, when ‘many’ different patterns appear in the sequence, the hypothesis of randomness is accepted.

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.