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Picture fuzzy -tolerance competition graphs with its application

Journal of Ambient Intelligence and Humanized Computing 2024年第1期15卷 547-559页

作者： Das, Sankar Poulik, Soumitra Ghorai, Ganesh Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore721102 India Department of Mathematics Kharagpur College West Bengal Kharagpur721305 India

In this study, the notions of picture fuzzy -tolerance competition graphs are exhibited adding more uncertainties to the fuzzy -tolerance competition graphs. Taking as max, min and sum functions three special types of picture fuzzy -tolerance competition graphs are introduced and few interesting properties of them are studied. The operations of Cartesian product, composition and union between two picture fuzzy digraphs are studied. Also, few hereditary properties of picture fuzzy -tolerance competition graphs under these operations are illustrated. Two real life applications in railway network and medical science are modeled using picture fuzzy min-tolerance competition graph. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.

关键词： Graphic methods

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Lagrange’s Interpolating Polynomial Approach to Solve Multi-choice Transportation Problem

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International Journal of applied and Computational mathematics 2015年第4期1卷 639-649页

作者： Roy, Sankar Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 West Bengal India

This paper deals with the multi-choice transportation problem (TP) in which the parameters of the TP such as the cost coefficients of the objective function, supplies and demands of the constraints are all followed multi-choice parameters. The main aim of this paper is to select an appropriate choice from the multi-choices for the cost coefficients of the objective function, supplies and demands of the constraints in TP by introducing Lagrange’s interpolating polynomial in such a way that the total cost is minimum. Finally, a non-linear mathematical model has been formulated. Using LINGO software, the optimal solution of the proposed problem is obtained. A real-life problem on multi-choice TP is considered to illustrate the proposed method in this paper. © 2015, Springer India Pvt. Ltd.

关键词： Lagrange’s interpolating polynomial Multi-choice programming Transportation problem

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Bi-level programming for Stackelberg Game with Intuitionistic Fuzzy Number: a Ranking Approach

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Journal of the Operations Research Society of China 2021年第1期9卷 131-149页

作者： Sumit Kumar Maiti Sankar Kumar Roy School of Applied Sciences and Humanities Haldia Institute of TechnologyPurba MidnaporeWB 721657India Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeWB 721102India

This paper introduces a ranking function procedure on a bi-level programming for Stackelberg game involving intuitionistic fuzzy *** fuzzy num-ber is considered in many real-life situations,so it makes perfect sense to address decision-making problem by using some specified intuitionistic fuzzy *** this paper,intuitionistic fuzziness is characterized by a normal generalized triangular intuitionistic fuzzy number.A defuzzification method is introduced based on the pro-portional probability density function associated with the corresponding membership function,as well as the complement of non-membership *** the proposed ranking technique,a methodology is presented for solving bi-level programming for Stackelberg *** application example is provided to demonstrate the applica-bility of the proposed methodology,and the achieved results are compared with the existing methods.

关键词： Bi-levelprogramming Triangular intuitionistic fuzz ynumber Ranking function Nonlinear programming Optimal solution

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Analyzing a Two-Staged Multi-objective Transportation Problem Under Quantity Dependent Credit Period Policy Using q-fuzzy Number

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International Journal of applied and Computational mathematics 2020年第5期6卷 1-33页

作者： Bera, Raj Kumar Mondal, Shyamal Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 W.B. India

Recently, the inclusion of a credit period policy becomes a beneficial strategy to improve a transportation business from the point of views of source and destination. In this regard, this study addresses a two-staged multi-objective transportation problem to transport the products from a production house to some retailers through some distributors by minimizing total transportation cost of retailers and by maximizing total profit of distributors simultaneously. Here, distributors offer a quantity dependent credit period policy to the retailers to induce them to procure the items from that distributors. Under this policy, those retailers who collect the materials more than a threshold value, would get this facility. Ideally, to assign a value of the credit period, there is no specific rule. It is totally the own strategy of the distributors with uncertainty. So, it takes different amounts at different times depending on the market situations. In that sense, it has been considered as q-fuzzy number, which is a combination of linear and non-linear memberships. To simplify the model, some arithmetic operations on q-fuzzy number and its defuzzification procedure have been introduced. Finally, two examples have been considered to examine the feasibility for both the cases (crisp and fuzzy) of the model and a non-elitist multi-objective genetic algorithm has been used to find the optimal solution. © 2020, Springer Nature India Private Limited.

关键词： Multi-objective transportation problem Non-elitist multi-objective genetic algorithm q-fuzzy number Quantity dependent credit period

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One machine multiple-product problem with production-inventory system under fuzzy inequality constraint

One machine multiple-product problem with production-invento...

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作者： Maity, Amit Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

This paper presents a one machine multiple-product problem with bounded production rate to minimize the total linear cost of inventory under imprecise space constraint. The demand is dependent on time and known. Also the production is a control variable and unknown. The net discount rate of inflation is fuzzy in nature. At first defined the expected value of fuzzy number, then the system is transferred to the fuzzy expected value model. The model is formulated as an optimal control problem and then reduced to an equivalent deterministic model and solved for optimum production function using Pontryagin's Optimal Control policy, the Kuhn-Tucker conditions and generalized reduced gradient (GRG) technique. The model is illustrated numerically and values of demand, optimal production and stock level are presented in both tabular and pictorial forms. © 2009 Elsevier B.V. All rights reserved.

关键词： Fuzzy rules

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Double-averaged Turbulence Characteristics Over Hemispherical Rough Bed 1

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26th International Conference on Hydraulics, Water Resources and Coastal Engineering, HYDRO 2021

作者： Shounda, Jaynata Barman, Krishnendu Department of Applied Mathematics With Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore721102 India

ISBN: (数字)9789811991516

ISBN: (纸本)9789811991509

This study characterized the double-averaged (time and space) turbulence parameters and local flow distributions through the experimental measurement over fully submerged artificially made hemispherical rough bed. Three different directional components of velocity data were collected by 3D micro-acoustic Doppler velocimeter (ADV) with a Reynolds number 62000. The changes of spatially averaged mean velocity profiles into specific flow layers on this rough bed were discussed corresponding with the smooth bed data. In the bottom wall region, double-averaged negative velocity components indicate the flow separation and strong recirculation zone. However, results from the double-averaged turbulent-kinetic-energy (TKE) flux and form-induced TKE flux were shown the upward and downward TKE transport throughout the flow depth. Also, TKE budgets terms turbulence production, diffusion and dissipation attain their peaks at the interfacial sub-layer of this rough bed flow. The production and dissipation rates of TKE have reached their maximum points at just above the lower extremity of form-induced sub-layer and within the interfacial sub-layer, respectively. The interfacial sub-layer has been treated as the losing zone of TKE pressure energy distribution and the zone of turbulence spreading. Moreover, the lower boundary of form-induced sub-layer shows as the energy access region. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Turbulence

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L(0, 1)-Labelling of Trapezoid Graphs

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International Journal of applied and Computational mathematics 2017年第1期3卷 599-610页

作者： Paul, Satyabrata Pal, Madhumangal Pal, Anita Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India Department of Mathematics National Institute of Technology Durgapur Durgapur 713209 India

L(0, 1)-labelling of a graph G= (V, E) is a function f from the vertex set V(G) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The L(0, 1)-labelling number denoted by λ _{0 , 1} (G) of G is the minimum range of labels over all such labelling. In this article, it is shown that, for a trapezoid graph G with maximum vertex degree Δ , the upper bound of λ _{0 , 1} (G) is Δ - 1. © 2017, Springer (India) Private Ltd.

关键词： Frequency assignment L(0 , 1) -labelling Trapezoid graphs

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Two-stage multi-item 4-dimensional transportation problem with fuzzy risk and substitution

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Journal of Ambient Intelligence and Humanized Computing 2023年第7期14卷 9469-9496页

作者： Devnath, Sudeshna De, Manoranjan Mondal, Seema Sarkar Maiti, Manoranjan Department of Mathematics National Institute of Technology Durgapur Durgapur713209 India Department of Mathematics Mugberia Gangadhar Mahavidyalaya West Bengal Purba Medinipur India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore721102 India

With the worldwide transport infrastructural development, there are several connecting roads between the cities for transportation. Some of these roads are smooth, and some are very rough, which invites some risks during transportation. For public distribution of some commodities, Govts. of developing countries collect those from the open markets, transport those to some warehouses for temporary storage, and from there, again transport to the fair-price shops for public distribution. With these facts, in this investigation, Govt.’s above scheme is modelled as two-stage four-dimensional transportation problems with different choices of conveyances and routes. There are some path and conveyance-wise uncertain travel risks. In fair-price shops, substitutable essential items (say rice and wheat) are sold with the necessary ones (say, mustard oil, etc.), which are sold by push-sale against some concession in an essential item (say, more rice, etc.). Thus, there is a trade-off between the ‘push-sale’ and ‘concession’, and hence an optimum decision is derived. Several models are developed depending on management’s and customers’ decisions, substitutability, push-sale, and environments. For road risk, a two-parameter (road’s roughness and distance) Mamdani-type fuzzy logic is implemented. The system’s profits for different models are maximised in both crisp and fuzzy environments and illustrated numerically using Generalised Reduced Gradient method through Lingo software. Here, the Govt.’s policy of introducing new products (termed as necessary item) among the public against a concession in an essential item has been introduced and analysed. This push-sale is effective up to a certain level, and after that, profit goes down. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

关键词： Fuzzy logic

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Two-Level Supply Chain Inventory Model for Perishable Goods with Fuzzy Lead-Time and Shortages

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International Journal of applied and Computational mathematics 2021年第5期7卷 1-18页

作者： Mallick, Rabin Kumar Manna, Amalesh Kumar Shaikh, Ali Akbar Mondal, Shyamal Kumar Department of Applied Mathematics With Oceanology and Computer Programming Vidyasagar University Midnapore 721102 West Bengal India Department of Mathematics The University of Burdwan Burdwan 713104 India

This study deals with a supplier-retailer supply chain system for perishable goods under fuzzy lead-time and fully backlogged shortages. In this proposed model, a supplier collects the deteriorating goods and fulfills the retailer's demand. Also, two different cases are considered. In the first case, retailer's fully backlogged shortages are incorporated whereas in the second case, retailer's shortages are not allowed. Lead-time of the system is considered as fuzzy in nature. In the first case, the integrated average profit of the supply chain system is obtained in fuzzy nature and the centroid method is used for defuzzification. The aim of this study is to maximize the integrated average profit by optimizing retailer's reorder level and business period. Three numerical examples are considered and solved for justification of the proposed model. Finally, the sensitivity analyses are performed with respect to the values of different system parameters. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Fuzzy lead-time Perishable goods Shortages Supply chain

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L(0,1)-labelling of Permutation Graphs

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Journal of Mathematical Modelling and Algorithms in Operations Research 2015年第4期14卷 469-479页

L(0,1)-labelling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The goal of L(0,1)-labelling problem is to produce a legal labelling that minimize the largest label used. In this article, it is shown that, for a permutation graph G with maximum vertex degree Δ, the upper bound of λ_0,1(G) is Δ−1. Finally, we prove that the result is exact for bipartite permutation graph. © 2015, Springer Science+Business Media Dordrecht.

关键词： Frequency assignment problem L(0,1)-labelling Permutation graph

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