First a new notion of the random exponential Hanson-Antczak type [Formula: see text]-V-invexity is introduced, which generalizes most of the existing notions in the literature, second a random function [Formula: see text] of the second order is defined, and finally a class of asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming is established. ...

Fractional Erbium:Glass 1550nm laser is a fractional photothemolysis (FP) laser with high effectiveness in atrophic acne scars treatment. Recently, fractional bipolar radiofrequency (RF) has been introduced to improve the efficacy and reduce side effects of the FP. Objective: The objective of the study was to compare the effectiveness and side effects of fractional bipolar radiofrequency with f...

Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of...

Fractional delay FIR filters design method based on the differential evolution algorithm is presented. Differential evolution is an evolutionary algorithm for solving a global optimization problems in the continuous search space. In the proposed approach, an evolutionary algorithm is used to determine the coefficients of a fractional delay FIR filter based on the Farrow structure. Basic differe...

Optimization of the ratio of two functions is called fractional programming or ratio optimization problem. If one can optimize simultaneously collection of fractional objective functions then the problem is called multi-objective fractional programming. This paper presents a survey on fractional programming problems. In contrast, this survey excludes many of the technical details and provides a...

We introduce a weight update formula that is expressed only in terms of firing rates and their derivatives and that results in changes consistent with those associated with spike-timing dependent plasticity (STDP) rules and biological observations, even though the explicit timing of spikes is not needed. The new rule changes a synaptic weight in proportion to the product of the presynaptic firi...

The design of the optimal fuzzy fractional-order PID controller is addressed in this work. A multi-objective genetic algorithm is proposed to design rule base and membership functions of the fuzzy logic systems. Three conflicting objective functions in both time and frequency domains have been used in Pareto design of the fuzzy fractional-order PID controller. The simulation results reveal the ...

We present an algorithm to solve a bi-level multi-objective fractional integer programming problem involving fuzzy numbers in the right-hand side of the constraints. The suggested algorithm combine the method of Taylor series together with the Kuhn Tucker conditions to solve fuzzy bi-level multi-objective fractional integer programming problem (FBLMOFIPP) then Gomory cuts are added till the int...