Pythagorean fuzzy set (PFS) is a significant soft computing tool for tackling embedded fuzziness in decision-making. Many computing methods have been studied to facilitate the application of PFS in modeling practical problems, among which the concept of correlation coefficient is very important. This article proposes some novel methods of computing correlation between PFSs via the three characteristic parameters of PFS by incorporating the ideas of Pythagorean fuzzy deviation, variance, and covariance. These novel methods evaluate the magnitude of relationship, show the potency of correlation between the PFSs, and also indicate whether the PFSs are related in either negative or positive sense. The proposed techniques are substantiated together with some theoretical results and numerically validated to be superior in terms of reliability and accuracy compared to some similar existing techniques. Decision-making processes involving pattern recognition and career placement problems are determined using the proposed techniques.

This article studies the positivity and stability of homogeneous coupled differential-difference equations with time-varying delays. First, a sufficient positivity condition is proposed for the nonlinear coupled differential-difference equations with delays. Then, based on this positivity condition, we present necessary and sufficient conditions ensuring the exponential stability and bounding the decay rate for time-delay homogeneous coupled differential-difference equations with homogeneity of degree one. Furthermore, the necessary and sufficient condition is extended to the global polynomial stability analysis of homogeneous coupled differential-difference equations when the degree of homogeneity is greater than one, and the decay rate is also investigated. Two numerical examples are employed to show the effectiveness of the obtained results.

In this article, we study the discrete-time decentralized optimization problems of multiagent systems by an event-triggering interaction scheme, in which each agent privately knows its local convex cost function, and collectively minimizes the total cost functions. The underlying interaction and the corresponding weight matrix are required to be undirected connected and doubly stochastic, respectively. To resolve this optimization problem collaboratively, we propose a decentralized event-triggering algorithm (DETA) that is based on the consensus theory and inexact gradient tracking technique. DETA involves each agent interacting with its neighboring agents only at some independent event-triggering sampling time instants. Under the assumptions that the global convex cost function is coercive and has Lipschitz continuous gradient, we prove that DETA steers all agents' states to an optimal solution even with nonuniform constant step sizes. Moreover, our analysis also shows that DETA converges at a rate of O(1/√t) if the step sizes are uniform and do not exceed some upper bounds. We illustrate the effectiveness of DETA on a canonical simple decentralized parameter estimation problem.

This work focuses on the stability analysis of positive Takagi–Sugeno (T–S) fuzzy descriptor systems with time-varying delays. An equivalent augmented system is constructed to investigate the positivity and stability of T–S fuzzy descriptor time-delay systems. By using this transformed system, a necessary and sufficient positivity condition is first derived for systems, which can be verified by linear programming (LP). Then, based on the positivity of T–S fuzzy descriptor systems, a sufficient condition is put forward for the asymptotic stability of systems with bounded and unbounded time-varying delays. Finally, several examples are provided to show the effectiveness of the obtained results.