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Bi-matrix game in bifuzzy environment

Journal of Uncertainty Analysis and Applications 2013年第1期1卷 1-17页

作者： Sankar Kumar Roy Prasanta Mula Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India ISRO Satellite Centre Bangalore India

In this paper, a new concept of bifuzzy bi-matrix game is introduced where all elements of the payoff matrices are characterized by bifuzzy variables. The uncertainties of entries of payoff matrices (bifuzzy variables) are measured by bifuzzy measure known as Chance measure. Combining the bifuzzy set theory and bi-matrix game theory, the solution concept of bifuzzy bi-matrix game theory is introduced. The quadratic programming problem plays the major role to solve bifuzzy bi-matrix game. In order to show the applicability and feasibility of our proposed method, a real-life bi-matrix game problem is considered and solved.

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Three-layer supply chain in an imperfect production inventory model with two storage facilities under fuzzy rough environment

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Journal of Uncertainty Analysis and Applications 2014年第1期2卷 1-31页

作者： Amalesh Kumar Manna Jayanta Kumar Dey Shyamal Kumar Mondal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India Department of Mathematics Mahishadal Raj College Mahishadal India

This article focuses on an imperfect production inventory model considering product reliability and reworking of imperfect items in three-layer supply chain under fuzzy rough environment. In the model, the supplier receives the raw materials, all are not of perfect quality, in a lot and delivers the items of superior quality to the manufacturer and the inferior quality items are sold at a reduced price in a single batch by the end of the cent percent screening process. The manufacturer produces a mixture of perfect and imperfect quality items. A portion of the imperfect items is transformed into perfect quality items after rework. Another portion of imperfect items, termed as `less perfect quality items', is sold at a reduced price to the retailer, and the portion which cannot be either transformed to the perfect quality items or sold at a reduce price is being rejected. Here, retailer purchases both the perfect and imperfect quality items from the manufacturer to sell the items to the customers through his/her respective showrooms of finite capacities. A secondary warehouse of infinite capacity is hired by the retailer on rental basis to store the excess quantity of perfect quality items. This model considers the impact of business strategies such as optimal order size of raw materials, production rate, and unit production cost in different sectors in a collaborating marketing system that can be used in the industry, like textile, footwear, and electronics goods. An analytical method has been used to optimize the production rate and raw material order size for maximization of the average profit of the integrated model. Finally, a numerical example is given to illustrate the model.

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A novel reduction method for type-2 uncertain normal critical values and its applications on 4D profit transportation problem involving damageable and substitute items

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International Journal of applied and Computational mathematics 2021年第4期7卷 1-30页

作者： Sahoo, Palash Jana, Dipak Kumar Pramanik, Sutapa Panigrahi, Goutam Department of Mathematics National Institute of Technology Durgapur Durgapur 713209 West Bengal India School of Applied Sciences & Humanities Haldia Institute of Technology Haldia Purba Midnapur 721657 West Bengal India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 West Bengal India

In this paper, we developed and investigated some four-dimensional profit maximization transportation problems considering damageablity and substitutability, where the parameters are of a type-2 normal uncertain variable in nature. Here, unit transportation cost, distances of the paths, fixed charges, rate of breakability, availability, demands, capacities of conveyances, the unit selling price, unit purchasing cost, unit procurement cost are regarded as type-2 normal uncertain variables. Two models are formulated based on two separate criteria of the substitution items. We use a critical value-based reduction method to reduce type-2 normal uncertain variables into type-1 normal uncertain variables and then apply some properties of uncertainty theory to convert the profit transportation parameters into deterministic form. The two deterministic models are solved using the optimization software named LINGO -18.0. A real-life numerical example and optimal results are presented here to show the application of the proposed model and the proposed reduction method. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Critical value Four dimensional profit transportation problem Reduction method Type-2 normal uncertain variables

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An EOQ Model for Time Dependent Backlogging Over Idle Time: A Step Order Fuzzy Approach

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International Journal of applied and Computational mathematics 2015年第2期1卷 171-185页

作者： Das, Prasenjit Kumar De, Sujit Sana, Shib Sankar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Paschim Medinipur 721102 West Bengal India Department of Mathematics Midnapore College Paschim Medinipur 721101 West Bengal India Department of Mathematics Bhangar Mahavidyalaya C.U. 24-Parganas Kolkata West Bengal India

The present article deals with a backorder Economic Order Quantity (EOQ) model for natural leisure/closing time system where the demand rate depends upon the total shortage period and the seasonal effect. A cost minimization problem is developed by trading off setup cost, inventory cost, cost for idle time and shortage cost. The intuitionistic step order fuzzy number for optimization has been developed, assuming all parameters as fuzzy numbers. Ranking is done by employing score function, accuracy value on the centre of gravity and Euclidean distance function over the objective function. Finally numerical examples are considered to justify the model. © 2014, Springer India Pvt. Ltd.

关键词： Centre of gravity Euclidean distance Intuitionistic fuzzy set Inventory Natural idle time Optimization Shortage

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Connectivity index of m-polar fuzzy graph with application

Research Square

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Research Square 2021年

作者： Mandal, Sonia Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India

This paper brings in connectivity index of a m-polar fuzzy graph (mPFG) with its boundedness. We investigate how the connectivity index of a mPFG changes when a vertex or an edge is deleted. Some special types of vertices include m-polar fuzzy connectivity enhancing node(mPFCEN), m-polar fuzzy connectivity neutral node (mPFCNN), m-polar fuzzy connectivity reducing node (mPFCRN) with their properties are discussed. © 2021, CC BY.

关键词： Fuzzy sets

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<i>L</i>(0, 1)-Labelling of Cactus Graphs

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Communications and Network 2012年第1期4卷 18-29页

作者： Nasreen Khan Madhumangal Pal Anita Pal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India Department of Mathematics National Institute of Technology Durgapur Durgapur India

An L(0,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference between the labels assigned to any two vertices which are at distance two is at least one. The span of an L(0,1)-labelling is the maximum label number assigned to any vertex of G. The L(0,1)-labelling number of a graph G, denoted by λ0.1(G) is the least integer k such that G has an L(0,1)-labelling of span k. This labelling has an application to a computer code assignment problem. The task is to assign integer control codes to a network of computer stations with distance restrictions. A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we label the vertices of a cactus graph by L(0,1)-labelling and have shown that, △-1≤λ0.1(G)≤△ for a cactus graph, where △ is the degree of the graph G.

关键词： Graph Labelling Code Assignment L(0 1)-Labelling Cactus Graph

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An investigation on m-polar fuzzy saturation graph and its application

Research Square

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Research Square 2021年

作者： Mahapatra, Tanmoy Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore721102 India

The saturation graph is a well-defined topic. But, saturation in a fuzzy graph was defined recently and investigated many properties. In a fuzzy saturation graph, only one saturation is considered for every vertex. In a m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining saturation for mPFG is not easy and needs some new ideas. By considering m saturation for each component out of m components of membership values of a vertex, we defined saturation in mPFG. α-saturation as well as β-saturation in mPFG is introduced here. Many interesting properties of it are also presented. α-vertex count and β-vertex count in mPFG are also studied and the upper bound on some well known mPFG is also found here. Finally, a real-life application using saturation in mPFG is also presented. © 2021, CC BY.

关键词： Graph theory

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Fuzzy Optimization, Decision-making and Operations Research 1

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1000年

作者： Chiranjibe Jana Madhumangal Pal Ghulam Muhiuddin Peide Liu

This book is aimed at experts and practitioners in the fields of fuzzy optimization, fuzzy decision-making, and fuzzy operation research.

ISBN: (数字)9783031356681

ISBN: (纸本)9783031356674;9783031356704

This book is aimed at experts and practitioners in the fields of fuzzy optimization, fuzzy decision-making, and fuzzy operation research.

关键词： Operations Research, Management Science Optimization Functional Analysis Operator Theory Statistics, general

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Fuzzy ϕ -tolerance competition graphs

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Soft Computing 2017年第13期21卷 3723-3734页

作者： Pramanik, Tarasankar Samanta, Sovan Sarkar, Biswajit Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India Department of Industrial & Management Engineering Hanyang University Ansan Gyeonggi-do 426 791 South Korea Department of Mathematics Joykrishnapur High School (H.S.) Tamluk 721649 India

In this paper, fuzzy ϕ-tolerance competition graphs are defined. Several interesting properties are investigated. Here ϕ is any real valued function. Particular cases of ϕ, viz. minimum, maximum and sum are considered. A daily life problem is modelled using fuzzy min-tolerance competition graph. Few properties are investigated for fuzzy tolerance graphs. © 2016, Springer-Verlag Berlin Heidelberg.

关键词： Fuzzy competition graphs Fuzzy tolerance graphs ϕ-tolerance competition graph

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Optimal Control of Dengue-Chikungunya Co-infection: A Mathematical Study 4th

Optimal Control of Dengue-Chikungunya Co-infection: A Mathem...

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4th IFIP TC 12 International Conference on Intelligence Science, ICIS 2020

作者： De, Anupam Maity, Kalipada Panigrahi, Goutam Maiti, Manoranjan Department of Applied Sciences Haldia Institute of Technology Haldia West Bengal India Department of Mathematics Mugberia Gangadhar Mahavidyalaya Bhupatinagar West Bengal India Department of Mathematics National Institute of Technology Durgapur Durgapur West Bengal India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore West Bengal India

ISBN: (纸本)9783030748258

In the present work, we developed a mathematical model for dengue-Chikungunya co-infection to analyze the disease transmission dynamics and interrelationship. We considered the essence of time dependent optimal control with the help of Pontryagin’s maximum principle. The result of diverse combinations of control measures is analyzed and shown graphically. © 2021, IFIP International Federation for Information Processing.

关键词： Co-infection Dengue-Chikungunya Optimal control

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