Approach to solve multi-criteria group decision-making problems by exponential operational law in generalised spherical fuzzy environment

The construction of generalised spherical fuzzy number(GSFN)is a reliable philosophy to design and understanding of vagueness and impreciseness.In this study,at first,the authors have defined the generalised spherical fuzzy set and discussed its several properties.Then,a new score and accuracy functions have been introduced in the generalised spherical fuzzy environment which leads to a new method of conversion of fuzzy number into a crisp number.New exponential operational law has been defined for GSFNs where the bases are positive real numbers&components are GSFNs and its various algebraic properties have been studied explicitly.Using this exponential operational law,a generalised spherical weighted exponential averaging operator has been proposed,which is used to develop a multi-criteria group decision-making(MCGDM)method in the generalised spherical fuzzy environment.The newly developed MCGDM has been demonstrated through a real-life problem and its effectiveness and rationality have been shown through sensitivity analysis.

Cylindrical neutrosophic single-valued number and its application in networking problem, multi-criterion group decision-making problem and graph theory

In this study,the authors envisage the neutrosophic number from various distinct rational perspectives and viewpoints to give it a look of a conundrum.They focused and analysed neutrosophic fuzzy numbers when indeterminacy and falsity functions are dependent on each other,which serves an indispensable role for the uncertainty concept.Additionally,the idea of cylindrical neutrosophic single-valued number is focused here,when the indeterminacy and falsity functions are dependent to each other using an influx of different logical and innovative graphical representation.They also developed the score and accuracy function for this particular cylindrical neutrosophic single-valued number and analysed some real-life problems like networking critical path model problem and minimal spanning tree problem of operation research field when the numbers are in cylindrical neutrosophic ambiance.They also introduced a multi-criterion group decision-making problem in this cylindrical neutrosophic domain.This noble thought will help us to solve a plethora of daily life problems in the neutrosophic arena.

Dynamics of an autonomous food chain model and existence of global attractor of the associated non-autonomous system

In this paper,we have analyzed a tri-trophic food chain model consisting of phytoplankton,zooplankton and fish population in an aquatic environment.Here,the pelagic water column is divided into two layers namely,the upper layer and the lower layer.The zooplankton population makes a diel vertical migration(DVM)from lower portion to upper portion and vice-versa to trade-off between food source and fear from predator(Fish).Here,mathematical model has been developed and analyzed in a rigorous way.Apart from routine calculations like boundedness and positivity of the solution,local stability of the equilibrium points,we performed Hopf bifurcation analysis of the interior equilibrium point of our model system in a systematic way.It is observed that the migratory behavior of zooplankton plays a crucial role in the dynamics of the model system.Both the upward and downward migration rates of DVM leads the system into Hopf bifurcation.The upward migration rate of zooplankton deteriorates the stable coexistence of all the species in the system,whereas the downward migration rate enhance the stability of the system.FYirther,we analyze the non-autonomous version of the system to capture seasonal effect of environmental variations.We have shown that under certain parametric restrictions periodic coexistence of all the species of our system is possible.Finally,extensive numerical simulation has been performed to support our analytical findings.