Gradient flow systems provide effortless continuous time optimization. Such systems have inherent property that their solutions move in the direction of descent. This paper proposes a modified gradient flow technique to reach optimal point of an objective function within a priori chosen predefined time. A least square estimation problem and a quadratic programming problem are solved using the proposed continuous-time optimization approach. Simulation results of the aforementioned problems show the efficacy of the proposed method. Further, results obtained with predefined upper bound of settling time based approach are compared with the results using fixed-time stable gradient flow scheme.

This paper is the first to attempt the characterization of Nash equilibrium strategy in interval type-2 fuzzy environment. The payoffs of the matrix games are considered to be interval type-2 triangular fuzzy numbers. An ordering for interval type-2 fuzzy numbers is introduced and a model to investigate equilibrium strategies in this environment is proposed. Due to the uncertainty in payoffs, three types of equilibriums are given those are natural extensions of the Nash equilibrium from crisp games. The existence of these equilibrium strategies is studied and a method to obtain the equilibrium strategy by means of parametric bimatrix crisp game is also given. Finally, solutions to a few numerical examples of matrix games are explored using this new interval-valued fuzzy game framework.

This paper is the first which attempts to capture complete fuzzy non-dominated set of fuzzy multi-criteria optimization problems with fuzzy parameters. A proper mathematical formulation of fuzzy non-dominated set and its generation are primary aims of the proposed study. Present work is mainly focused on visualizing the considered problem from fuzzy geometrical viewpoint. Constraint set of a fuzzy multi-criteria optimization problem is viewed from two different spaces - decision space and criterion space. Fuzzy decision feasible region or the constraint set on decision space is formulated using the alpha-cuts of the parameters present in the problem. Under the assumption that fuzzy criteria are fuzzy number valued, it is shown that a fuzzy point will be obtained on the criterion space corresponding to each point on the decision feasible region. Union of all these fuzzy points determines fuzzy criteria feasible region or constraint set in the criterion space. To capture entire fuzzy non-dominated set of criteria feasible region, a method, hereby named fuzzy ideal cone method, has been proposed. The method essentially uses the cone of non-positive hyperoctant of the criteria space to generate complete fuzzy non-dominated set. Proposed methodology is supported by several numerical examples and pictorial illustrations.