Fish and broiler optimal harvesting models in imprecise environment

2017 ◽  
Vol 10 (08) ◽  
pp. 1750115 ◽  
Author(s):  
A. De ◽  
K. Maity ◽  
G. Panigrahi
Keyword(s):  
Mathematical Program ◽  
Equilibrium Points ◽  
Solution Procedure ◽  
Optimal Harvesting ◽  
Mathematical Software ◽  
Interval Numbers ◽  
Interval Mathematics ◽  
Different Characteristics ◽  
Interval Valued ◽  
Biological Equilibrium

In this paper, a two-species harvesting model has been considered and developed a solution procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parameters. This interval-valued problem is converted into an equivalent crisp model using interval mathematics. The main advantage of the proposed procedure is that different characteristics of the model can be presented in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.

Stability analysis of combined project of fish, broiler and ducks: Dynamical system in imprecise environment

2015 ◽  
Vol 08 (05) ◽  
pp. 1550067 ◽  
Author(s):  
A. De ◽  
K. Maity ◽  
M. Maiti
Keyword(s):  
Dynamical System ◽  
Mathematical Program ◽  
Equilibrium Points ◽  
Solution Procedure ◽  
Biological Parameters ◽  
Mathematical Software ◽  
Interval Numbers ◽  
Different Characteristics ◽  
Interval Valued ◽  
Biological Equilibrium

In this paper, we consider three species harvesting model and develop a solution procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parameters. This interval-valued problem is converted into equivalent crisp model using interval operations. The main advantage of the proposed procedure is that we can present different characteristics of the model in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.

scholarly journals An Algorithm for Solution of an Interval Valued EOQ Model

2012 ◽  
Vol 3 (1) ◽  
pp. 55-64 ◽  
Author(s):  
Susovan CHAKRABORTTY ◽  
Madhumangal PAL ◽  
Prasun Kumar NAYAK
Keyword(s):  
Lead Time ◽  
Solution Procedure ◽  
Lot Size ◽  
Setup Cost ◽  
Single Product ◽  
Interval Numbers ◽  
Eoq Model ◽  
Interval Valued ◽  
Total Average Cost ◽  
Total Average

This paper deals with the problem of determining the economic order quantity (EOQ)in the interval sense. A purchasing inventory model with shortages and lead time, whose carryingcost, shortage cost, setup cost, demand quantity and lead time are considered as interval numbers,instead of real numbers. First, a brief survey of the existing works on comparing and ranking anytwo interval numbers on the real line is presented. A common algorithm for the optimum productionquantity (Economic lot-size) per cycle of a single product (so as to minimize the total average cost) isdeveloped which works well on interval number optimization under consideration. A numerical exampleis presented for better understanding the solution procedure. Finally a sensitive analysis of the optimalsolution with respect to the parameters of the model is examined.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

scholarly journals On a predator-prey system interaction under fluctuating water level with nonselective harvesting

2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li
Keyword(s):  
Water Level ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fluctuating Water Level

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

Multi-criteria decision-making algorithm based on aggregation operators under the complex interval-valued q-rung orthopair uncertain linguistic information

2021 ◽  
pp. 1-30
Author(s):  
Harish Garg ◽  
Zeeshan Ali ◽  
Zaoli Yang ◽  
Tahir Mahmood ◽  
Sultan Aljahdali
Keyword(s):  
Decision Making ◽  
Brain Tumors ◽  
Score Function ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Linguistic Features ◽  
Interval Numbers ◽  
Fundamental Properties ◽  
Interval Valued

The paper aims to present a concept of a Complex interval-valued q-rung orthopair uncertain linguistic set (CIVQROULS) and investigated their properties. In the presented set, the membership grades are considered in terms of the interval numbers under the complex domain while the linguistic features are added to address the uncertainties in the data. To further discuss more, we have presented the operation laws and score function for CIVQROULS. In addition to them, we present some averaging and geometric operators to aggregate the different pairs of the CIVQROULS. Some fundamental properties of the proposed operators are stated. Afterward, an algorithm for solving the decision-making problems is addressed based on the proposed operator using the CIVQROULS features. The applicability of the algorithm is demonstrated through a case study related to brain tumors and their effectiveness is compared with the existing studies.

scholarly journals On Some Classes of Double Difference Sequences of Interval Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Kuldip Raj ◽  
Abdullah Alotaibi
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Double Difference ◽  
Difference Sequence ◽  
Topological Properties ◽  
Interval Numbers ◽  
Difference Sequences ◽  
Inclusion Relations ◽  
Interval Valued ◽  
Difference Sequence Spaces

The aim of this paper is to introduce some interval valued double difference sequence spaces by means of Musielak-Orlicz functionM=(Mij). We also determine some topological properties and inclusion relations between these double difference sequence spaces.

scholarly journals A Heterogeneous MCDM Framework for Sustainable Supplier Evaluation and Selection Based on the IVIF-TODIM Method

2019 ◽  
Vol 11 (18) ◽  
pp. 5057 ◽  
Author(s):  
Ren-Jie Mao ◽  
Jian-Xin You ◽  
Chun-Yan Duan ◽  
Lu-Ning Shao
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Third Party ◽  
Multi Criteria Decision Making ◽  
Interval Numbers ◽  
Intuitionistic Fuzzy Numbers ◽  
Sustainability Performance ◽  
Intuitionistic Fuzzy ◽  
Relative Closeness ◽  
Interval Valued

The third-party platform named ECO system is used by many transnational companies to monitor the sustainability performance of their global suppliers because of its easiness and shareability. Nonetheless, methods used in this platform for evaluating and calculating the sustainability performance of the alternative suppliers are criticized for their lack of accuracy. In response to these problems, this paper presents a heterogeneous multi-criteria decision-making (MCDM) method based on interval-valued intuitionistic fuzzy--an acronym in Portuguese for interactive multi-criteria decision making (IVIF--TODIM) to improve the efficiency of the evaluation model. Considering the varying features of evaluation criteria, i.e., either quantitative or qualitative, the evaluation values under different criteria are expressed in their appropriate information types. In this paper, a general method based on the relative closeness to the technique for order preference by similarity to ideal solution (TOPSIS) method is applied for aggregating the heterogeneous assessment information, including crisp numbers, interval numbers, and triangular fuzzy numbers (TFNs), into interval-valued intuitionistic fuzzy numbers (IVIFNs). Then, the TODIM (an acronym in Portuguese for interactive multi-criteria decision making) is extended and employed to prioritize the alternative suppliers. Finally, the applicability and effectiveness of the proposed method is verified by a practical example of polymer manufacturing company and a comparison analysis with existing methods.

A Study of FCM Clustering Algorithm Based on Interval Multiple Attribute Information

2013 ◽  
Vol 444-445 ◽  
pp. 676-680
Author(s):  
Li Guo ◽  
Guo Feng Liu ◽  
Yu E Bao
Keyword(s):  
Clustering Algorithm ◽  
Distance Measure ◽  
Clustering Algorithms ◽  
Interval Numbers ◽  
Fuzzy Partition ◽  
Multiple Attribute ◽  
Attribute Information ◽  
Fcm Clustering ◽  
Attribute Clustering ◽  
Interval Valued

In multiple attribute clustering algorithms with uncertain interval numbers, most of the distances between the interval-valued vectors only consider the differences of each interval endpoint ignoring a lot of information. To solve this problem, according to the differences between corresponding points in each interval number, this paper gives a distance formula between interval-valued vectors, extends a FCM clustering algorithm based on interval multiple attribute information. Through an example, we prove the validity and rationality of the algorithm. Keywords: interval-valued vector; FCM clustering algorithm; distance measure; fuzzy partition

Stability and Bifurcation of a Fishery Model with Crowley–Martin Functional Response

2017 ◽  
Vol 27 (11) ◽  
pp. 1750174 ◽  
Author(s):  
Atasi Patra Maiti ◽  
B. Dubey
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Equilibrium Points ◽  
Control Variable ◽  
Dynamical Variable ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Fishery Model

To understand the dynamics of a fishery system, a nonlinear mathematical model is proposed and analyzed. In an aquatic environment, we considered two populations: one is prey and another is predator. Here both the fish populations grow logistically and interaction between them is of Crowley–Martin type functional response. It is assumed that both the populations are harvested and the harvesting effort is assumed to be dynamical variable and tax is considered as a control variable. The existence of equilibrium points and their local stability are examined. The existence of Hopf-bifurcation, stability and direction of Hopf-bifurcation are also analyzed with the help of Center Manifold theorem and normal form theory. The global stability behavior of the positive equilibrium point is also discussed. In order to find the value of optimal tax, the optimal harvesting policy is used. To verify our analytical findings, an extensive numerical simulation is carried out for this model system.

scholarly journals A Three Species Ecological Model with a Prey, Predator and Competitor to the Predator and Optimal Harvesting of the Prey

2012 ◽  
Vol 1 ◽  
pp. 21-32
Author(s):  
A.V. Papa Rao ◽  
K. Lakshmi Narayan ◽  
Shahnaz Bathul
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Single Species ◽  
Analytical Investigation ◽  
Optimal Harvesting ◽  
Stability Criteria ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Analytical Stability ◽  
The Stability

The present paper is devoted to an analytical investigation of three species ecological model with a Prey (N1), a predator (N2) and a competitor (N3) to the Predator without effecting the prey (N1). in addition to that, the species are provided with alternative food. The model is characterized by a set of first order non-linear ordinary differential equations. All the eight equilibrium points of the model are identified and local and global stabilitycriteria for the equilibrium states except fully washed out and single species existence are discussed. Further exact solutions of perturbed equations have been derived. The analytical stability criteria are supported by numerical simulations using mat lab. Further we discussed the effect of optimal harvesting on the stability.

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