The current study presents a novel multi-criteria decision making (MCDM) approach to address decision analysis with T-spherical fuzzy data, whose weights of criteria are fully unknown. To serve the purpose, we design some generalized operational laws, namely Frank operational laws for T-spherical fuzzy numbers (T-SFNs) using Frank t-norm and t-conorm. Then, based on the proposed operations, a range of T-spherical fuzzy aggregation operators is developed to aggregate T-spherical fuzzy information efficiently. Also, discuss their particular cases and desirable properties are well proved. Next, we propound the T-spherical fuzzy entropy measure and its capability to fulfil the required properties. Then it is further used for criteria weight determination in the proposed aggregation based MCDM approach. In addition, a descriptive example is provided for viewing the applicability of the established approach. Lastly, the superiority and validity of this approach are highlighted by parameter analysis and comparative analysis.

In this study, a novel technique using a hyper chaotic dynamical system and DNA computing has been designed with high plaintext sensitivity. In order to reduce cost, a selection procedure using tent map has been employed for generating different key streams from the same chaotic data obtained from the iterations of chaotic dynamical system. After separating the three channels from the input color image, they are both confused and diffused. First of all, these channels are diffused on a decimal level. Then they are permuted. Further, DNA encoding is performed upon these channels. Moreover, DNA level diffusion is performed to further increase the degree of randomness in the image. Lastly, the DNA encoded image is converted into decimal to get the final cipher image. Both the experimental results and security analysis strongly demonstrate the robustness of the proposed scheme. A comparison of the proposed scheme has also been made with other recently developed schemes to show that this scheme outperforms the others in terms of computational cost, time and memory efficiency. Additionally, with the large key space, the proposed scheme can resist any brute force, plaintext and statistical attacks, therefore it is a good fit for the real world applications of the image security.

The preference of one alternative over another is a useful way to express the opinion of the decision-maker. In the process of group decision-making, preference relations are used in preference modeling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty and, in many scenarios of decision-making problems, the probabilities of different events affect the decision-making process directly. In order to deal with this issue, the hesitant probabilistic multiplicative preference relation (HPMPR) is defined in this paper. Furthermore, consistency of the HPMPR and consensus among decision makers are studied here. In this respect, many algorithms are developed to achieve consistency of HPMPRs, reasonable consensus between decision-makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision-making. Lastly, we present a case study with complete illustration of the proposed model and discuss the effects of probabilities on decision-making validating the importance of the introduction of probability in hesitant multiplicative preference relations.