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The problem of expanding a meaningful entropic theory for fuzzy information cannot be thought of as being a mere (more or less formal) extension of Shannon theory. By using the information theory of deterministic functions, the present author had already obtained some results in this way, and he herein continues this approach. After a short background on the different entropies of deterministic functions and on membership entropy of fuzzy sets, successively mixed entropy of fuzzy sets, joint membership functions of independent fuzzy sets, and conditional entropy of fuzzy sets with respect to other fuzzy sets are considered; the problem of defining transinformation between fuzzy sets, as a generalisation of the well known Shannon concept, is then examined. One of the conclusions of the article is that it is possible to build up a meaningful information theory of fuzzy sets by using the entropy of deterministic functions.

A definition of entropy of maps which does not involve probability, but nevertheless is fully consistent with Shannon entropy can be derived using the informational equation H(X,Y) = H(X) + H(Y,X). This approach has been extended in order to obtain the “Shannon entropy” of distributed maps. The model that is obtained involves two parameters which characterise the scanning procedures normally used by the cortex in human vision. The results are then used to re‐define the entropy of a fuzzy set and to extract the value of a membership from a small sample of observed data. The measure of entropic distance between patterns without using probability is also considered.

The purpose of this paper is to investigate the effects of Ha and the Nanoparticles (NP) volume fraction over the irreversibility and heat transport in Darcy–Forchheimer nanofluid saturated lid-driven porous medium.

The present paper highlights entropy generation because of mixed convection for a lid-driven porous enclosure filled through a nanoliquid and submitted to a uniform magnetic field. The analysis is achieved using Darcy–Brinkman–Forchheimer technique. The set of partial differential equations governing the considered system was numerically solved using the finite element method.

The main observations are as follows. The results indicate that the movement of horizontal wall is an important factor for the entropy generation inside the porous cavity filled through Cu–water nanoliquid. The variation of the thermal entropy generation is linear through NPs volume fraction. The total entropy generation reduces when the Darcy, Hartmann and the nanoparticle volume fraction increase. The porous media and magnetic field effects reduce the total entropy generation.

Interest in studying thermal interactions by convective flow within a saturating porous medium has many fundamental considerations and has received extensive consideration in the literature because of its usefulness in a large variety of engineering applications, such as the energy storage and solar collectors, crystal growth, food processing, nuclear reactors and cooling of electronic devices, etc.

By examining the literature, the authors found that little attention has been paid to entropy generation encountered during convection of nanofluids. Hence, this work aims to numerically study entropy generation and heat transport in a lid-driven porous enclosure filled with a nanoliquid.

This study aims to analyze entropy generation and magnetohydrodynamic (MHD) natural convection of hybrid nanofluid in a square cavity, with a heated elliptical block placed at the center, in presence of a periodic-variable magnetic field.

In this paper, simulations were performed with a FORTRAN home code. The numerical methodology used to solve Navier–Stokes, energy and entropy generation equations with corresponding boundary conditions, is essentially based on the finite volume method and full multigrid acceleration.

The cavity is filled with Ag–Tio₂/Water hybrid nanofluid. The main objective of this investigation is to predict the effects of body’s size (6 cases), type of applied magnetic field (variable or uniform), the non-dimensional period number of the variable magnetic field (VMF) (0.2 ≤ Λ ≤ 0.8), the inclination angle of the VMF (0 ≤ χ ≤ 90), Rayleigh number (5 × 103 ≤ Ra ≥ 105) and Hartmann number (5 ≤ Ha ≥ 100) on thermal performance, heat transfer rate, entropy generation and flow patterns.

To the authors’ best knowledge, this paper is the first numerical investigation deals with the entropy generation and natural convection of hybrid nanofluid in a two-dimensional cavity, with specific thermal boundary conditions, containing an elliptical block under periodic-variable magnetic field. Different combinations between flow-governing parameters were made to find optimal thermal performance.

The study aims to investigate magnetohydrodynamics thermal convection energy transference and entropy production in an open chamber saturated with ferrofluid having an isothermal solid block.

Analysis of thermal convection phenomenon was performed for an open chamber saturated with a nanofluid having an isothermal solid unit placed inside the cavity with various aspect ratios. The left border temperature is kept at T_c. An external cooled nanofluid of fixed temperature T_c penetrates into the domain from the right open border. The nanofluid circulation is Newtonian, incompressible, and laminar. The uniform magnetic field of strength B at the tilted angle of γ is applied. The finite volume technique is used to work out the non-linear equations of liquid motion and energy transport. For Rayleigh number (Ra=1e+7), numerical simulations were executed for varying the solid volume fractions of the nanofluid (ϕ = 0.01–0.04), the aspect ratios of a solid body (A_s = 0.25–4), the Hartmann number (Ha = 0–100), the magnetic influence inclination angle (γ = 0–π/2) and the non-dimensional temperature drop (Ω = 0.001–0.1) on the liquid motion, heat transference and entropy production.

Numerical outcomes are demonstrated by using isolines of temperature and stream function, profiles of mean Nusselt number and entropy generations. The results indicate that the entropy generation rate and mean Nu can be decreased with an increase in Ha. The inner solid block of A_s = 0.25 reflects the maximum heat transfer rate in comparison with other considered blocks. The addition of nano-sized particles results in a growth of energy transport and mean entropy generations.

An efficient computational technique has been developed to solve natural convection problem for an open chamber. The originality of this research is to scrutinize the convective transport and entropy production in an open domain with inner body. The outcomes would benefit scientists and engineers to become familiar with the investigation of convective energy transference and entropy generation in open chambers with inner bodies, and the way to predict the energy transference strength in the advanced engineering systems.

This study aims to numerically investigate the thermal-hydrodynamic performance of silicon oxide/water nanofluid laminar flow in the heat sink miniature channel with different fin cross-sections. The effect of the fin cross-section including semi-circular, rectangular and quadrant in two directions of flat and curved, and channel substrate materials of steel, aluminum, copper and titanium were examined. Finally, the analysis of thermal and frictional entropy generation in different channels is performed.

According to the numerical results, the highest heat transfer coefficients belong to the rectangular, quadrant 2, quadrant 1 and semi-circular fins compared to the channel without fin is 38.65%, 29.94%, 27.45% and 17.1%, respectively. Also, the highest performance evaluation criteria belong to the rectangular and quadrant 2 fins, which have 1.35 and 1.29, respectively. Based on the thermal conductivity of the substrate material, the best material is copper. According to the results of entropy analysis, the reduction of thermal irreversibility of the channel with rectangular, quadrant 1, quadrant 2 and semi-circular compared to non-finned channel is equal to 72%, 57%, 63% and 48%, respectively.

The rectangular and quadrant 2 fins are the best fins and the copper substrate material is the best material to reduce the entropy generation.

The silicon oxide/water nanofluid flow in the heat sink miniature channel with various fin shapes and the curvature angle against the fluid flow was simulated to increase the heat transfer performance. The whole test section is simulated in three-dimensional. Different channel materials have been investigated to find the best channel substrate material.

This paper proposes a fuzzy random multi-objective portfolio model with different entropy measures and designs a hybrid algorithm to solve the proposed model.

Because random uncertainty and fuzzy uncertainty are often combined in a real-world setting, the security returns are considered as fuzzy random numbers. In the model, the authors also consider the effects of different entropy measures, including Yager's entropy, Shannon's entropy and min-max entropy. During the process of solving the model, the authors use a ranking method to convert the expected return into a crisp number. To find the optimal solution efficiently, a fuzzy programming technique based on artificial bee colony (ABC) algorithm is also proposed.

(1) The return of optimal portfolio increases while the level of investor risk aversion increases. (2) The difference of the investment weights of the optimal portfolio obtained with Yager's entropy are much smaller than that of the min–max entropy. (3) The performance of the ABC algorithm on solving the proposed model is superior than other intelligent algorithms such as the genetic algorithm, differential evolution and particle swarm optimization.

To the best of the authors' knowledge, no effect has been made to consider a fuzzy random portfolio model with different entropy measures. Thus, the novelty of the research is constructing a fuzzy random multi-objective portfolio model with different entropy measures and designing a hybrid fuzzy programming-ABC algorithm to solve the proposed model.

This paper aims to innovatively propose to improve the efficiency of satellite observation and avoid the waste of satellite resources, a genetic algorithm with entropy operator (GAE) of synthetic aperture radar (SAR) satellites’ task planning algorithm.

The GAE abbreviated as GAE introduces the entropy value of each orbit task into the fitness calculation of the genetic algorithm, which makes the orbit with higher entropy value more likely to be selected and participate in the remaining process of the genetic algorithm.

The simulation result shows that in a condition of the same calculate ability, 85% of the orbital revisit time is unchanged or decreased and 30% is significantly reduced by using the GAE compared with traditional task planning genetic algorithm, which indicates that the GAE can improve the efficiency of satellites’ task planning.

The GAE is an optimization of the traditional genetic algorithm. It combines entropy in thermodynamics with task planning problems. The algorithm considers the whole lifecycle of task planning and gets the desired results. It can greatly improve the efficiency of task planning in observation satellites and shorten the entire task execution time. Then, using the GAE to complete SAR satellites’ task planning is of great significance in reducing satellite operating costs and emergency rescue, which brings certain economic and social benefits.