International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this treatise, we define statistically pre-Cauchy sequences of complex uncertain variable for five cases of uncertainty viz., in mean, in measure, in distribution, in almost surely and in uniformly almost surely and we confine our study to statistically pre-Cauchy sequence in mean, in measure and in distribution only. Furthermore, we establish the relationship between statistically pre-Cauchy and statistically convergent sequence by using complex uncertain variables. Finally, we initiate the study of statistically pre-Cauchy sequences of complex uncertain variables via Orlicz functions also.

In evaluation and decision making frequently we need to consider and then well model the subjective preferences and behaviors of decision makers. This study firstly defines literally three types of conformities, namely, the Bounded Conformity, Extreme Conformity and Bounded Extreme Conformity. Then, we define two types of value-dependent preference aggregation operators, s-t-A extreme operators and Level dependent Preferences Ordered Weighted Averaging operators, to specifically model Extreme Conformity and Bounded Extreme Conformity, respectively. Some related mathematical properties and simple numerical examples are also presented.

In this paper, we are mainly to solve the functional equations given by the modularity condition. Modularity condition between disjunctive (resp. conjunctive) uni-nullnorms and some most studied classes of binary aggregation operators (i.e., t-norms, t-conorms, uninorms and semi-t-operators) are discussed. Both positive and negative results of modularity condition for uni-nullnorms are obtained. Since uni-nullnorms are an extension of nullnorms and uninorms, previous results about modularity condition for nullnorms and uninorms in ${{𝒰}}_{max}$ and ${{𝒰}}_{min}$ can be obtained as simple corollaries.

The conditional distributivity of aggregation operators has always been the focus of research because it is crucial for various areas including integration theory, utility theory and so on. Therefore, this article is mainly devoted to dealing with the conditional distributivity of a uni-nullnorm over a uninorm with the continuous underlying operators and also gives the full characterization of each pair $(F,U)$ satisfying this property. Moreover, it extends the previous research results since they are now on a much wider class of uninorms.

In social media, the data-sharing activities have turned out to be more pervasive; individuals and companies have comprehended the significance of promoting info by social media network. However, these individuals and companies face more challenges with the issue of “how to obtain the full benefit that the platforms provide”. Therefore, social media policies to improve the online promotion are turning out to be more significant. The popularization of social media contents are related to public attention and interest of users, thus the popularity fore cast of online contents has considered being the major task in social media analytic and it facilitates several appliances in diverse domain as well. This paper intends to introduce a popularity forecast approach that derives and combines the richest data of “text content encoder, user encoder, time series encoder, and user sentiment analysis”. The extracted features are then predicted via Long Short Term Memory (LSTM). Particularly, to enhance the prediction accuracy of the LSTM, the weights are fine-tuned via Self Adaptive Rain optimization (SA-RO).

This paper discusses a nonlinear optimization problem with the system of max-Archimedean bipolar fuzzy relation equations as constraints. Some results related to the structure of the solution set of max-Archimedean bipolar fuzzy relation equations are proved. Using these results, a genetic algorithm is proposed to solve the problem for obtaining optimal or converging solutions. The effectiveness of the algorithm is also compared with other methods found in the literature. The previous methods require conversion of the problem into 0-1 mixed integer optimization problem solvable by some nonlinear optimization solvers and thereby, the computational work may increase with the size of the problem. Some test problems are developed to evaluate the performance of the proposed algorithm.

Process control is the interested domain of interest as the industrial high-order applications require an effective control mechanism with higher robustness. Since the conventional method of proportional integral derivative (PID) controller remains inadequate for the higher-order processes, this research concentrates on the fuzzy fractional-order controllers, that more and more attention nowadays in various research areas of science and engineering specifically, on the areas of tuning, design, implementation, and analysis of these controllers. Accordingly, this research marks a milestone for the control industry through introducing a robust controller, fuzzy fractional-order (FO) PI${}^{\lambda }$D${}^{\mu }$ (fuzzy FOPID) for higher-order applications with dead time. The fractional-order controller requires the fractional orders for the derivative term $\mu$ and integral term $\lambda$. The results of the proposed fuzzy FOPID controller is analyzed and compared with the comparative methods, such as a proportional integral derivative (PID) controller and fractional order PID controller (FOPID). Accordingly, the time-domain specifications are evaluated in the presence/absence of the disturbances is analyzed and in addition, the time domain optimal integral metrics are determined. Simulations are carried out using MATLAB/SIMULINK.