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International Conference on Nonlinear applied Analysis and Optimization, ICNAAO-2021

作者： Ganguly, Sanchari Das, Pritha Maiti, Manoranjan Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur WB Howrah711103 India Department of Applied Mathematics Oceanology and Computer Programming Vidyasagar University WB Midnapore721102 India

ISBN: (纸本)9789819905966

Fairness concern behavior, a well-known cognitive bias, refers to a person’s attitude of dissatisfaction for unequal pay-offs in someone’s favor. Against environmental pollution, many firms are focused on green manufacturing to maintain sustainable development. The adoption of online shopping by customers around the globe has altered the dynamics of competitiveness in the retail supply chain (SC). Considering the above facts, the effect of fairness concern on optimal prices and channel members’ profits in a two-level dual channel SC is investigated. Here, we consider an SC comprising a green manufacturer and a fair-minded retailer where the manufacturer produces and sells the green product through both offline and online channels to consumers. Due to uncertainty in the real world, the fuzziness is associated with market demand, price elasticity, and the coefficient of greenness. The fuzzy objectives and constraints are reduced to crisp ones using expectation and possibility measures, respectively. Both centralized and decentralized models (with and without cognitive bias) are formulated and solved by the Stackelberg game for the optimal prices and product greenness level. The models’ optimal solutions are analyzed and compared with the deterministic models numerically. The effects of the fairness concern coefficient on the optimal prices, product greenness level, and channel members’ profits are investigated. The sensitivity analyses are presented to study the effects of the fuzzy degree of customers’ sensitivity toward greenness on channel members’ profits. Retailer’s fairness is harmful to the manufacturer but beneficial for her own profit. Finally, some conclusions and managerial insights are presented. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Game theory

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Some results on generalized interval-valued intuitionistic fuzzy sets

Some results on generalized interval-valued intuitionistic f...

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作者： Bhowmik, Monoranjan Pal, Madhumangal Department of Mathematics V.T.T. College Midnapore West Bengal-721101 India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

In this paper, we define some results on generalized interval-valued intuitionistic fuzzy sets (GIVIFSs). In fact, all interval-valued intuitionistic fuzzy sets (IVIFSs) are GIVIFSs but all GIVIFSs are not IVIFSs. We define two composite relations, four types of reflexivity and irreflexivity of GIVIFSs with some of their properties. We define generalized interval-valued intuitionistic fuzzy relation (GIVIFR) with some results. Also we define two operators C and I with some properties over GIVIFSs. Finally, an illustrative example is given to using GIVIFSs in a decision making problem. © 2012 TFSA.

关键词： Decision making

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A study on pentagonal fuzzy number and its corresponding matrices

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Pacific Science Review B: Humanities and Social Sciences 2015年第3期1卷 131-139页

作者： Apurba Panda Madhumangal Pal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India

In this article, the notion of pentagonal fuzzy number (PFN) is introduced in a generalized way. A few articles have been published based on this topic, but they have some ambiguities in defining this type of fuzzy number. Here, we proposed the logical definition in developing a pentagonal fuzzy number, along with its arithmetic operations. Based on PFN, the structure of pentagonal fuzzy matrices (PFMs) is studied, together with their basic properties. Some special type of PFMs and their algebraic natures (trace of PFM, adjoint of PFM, determinant of PFM, etc.) are discussed in this article. Finally, the notion of nilpotent PFM, comparable PFM, and constant PFMs, with their many properties, are highlighted in this article.

关键词： Pentagonal fuzzy number Arithmetic of pentagonal fuzzy number Pentagonal fuzzy matrices Pentagonal fuzzy determinant Nilpotent pentagonal fuzzy matrices

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Generalised multi-fuzzy soft set and its application in decision making

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Pacific Science Review A: Natural Science and Engineering 2015年第1期17卷 23-28页

作者： Asit Dey Madhumangal Pal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India

The aim of this paper is to introduce the concept of generalised multi-fuzzy soft set. We also define several generalised multi-fuzzy soft set operations and study their properties, and applications of generalised mul... 详细信息

关键词： Soft sets Fuzzy soft sets Multi-fuzzy sets Multi-fuzzy soft sets Generalised multi-fuzzy soft sets Decision making

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Analysis of pricing decision for substitutable and complementary products with a common retailer

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Pacific Science Review A: Natural Science and Engineering 2016年第3期18卷 190-202页

作者： Raghu Nandan Giri Shyamal Kumar Mondal Manoranjan Maiti Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India

In this paper, a competition of selling two substitutable products and one complementary product has been studied in two-echelon supply chain systems in which one of these three products is produced by one manufacturer separately, and all produced items are sold through a common retailer in the market. The demand of each product depends linearly on prices of these three products as per their nature. In this study, four different decision scenarios are developed mathematically under the game theory framework to maximize the profit function of each participant of the supply chain, and a number of pricing strategies are subsequently worked out for manufacturers and retailer. Finally, the model under different scenarios is illustrated with numerical data to study the feasibility of the model exploring the managerial insights, as well. Different marketing policies are predicted for maximum individual and system profits.

关键词： Supply chain Substitutable products Complementary products Stackelberg game

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On hesitant multi-fuzzy soft topology

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Pacific Science Review B: Humanities and Social Sciences 2015年第3期1卷 124-130页

作者： Asit Dey Madhumangal Pal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India

The aim of this paper is to introduce and study the concept of hesitant multi-fuzzy soft topological space and some of its structural properties, such as the neighbourhood of hesitant multi-fuzzy soft sets and interior hesitant multi-fuzzy soft sets, the hesitant multi-fuzzy soft basis and hesitant multi-fuzzy soft subspace topology. Additionally, we introduce and define the hesitant multi-fuzzy soft cover, hesitant multi-fuzzy soft open cover, and hesitant multi-fuzzy soft compactness, and some important results on them are presented.

关键词： Hesitant multi-fuzzy soft basis Hesitant multi-fuzzy soft subspace topology Hesitant multi-fuzzy soft cover Hesitant multi-fuzzy soft open cover Hesitant multi-fuzzy soft compactness 54A05 54A40 03E72 54D30 54A10

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Partial Trade-Credit Policy of Retailer with Exponentially Deteriorating Items

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International Journal of applied and Computational mathematics 2015年第3期1卷 343-368页

作者： Sarkar, Biswajit Saren, Sharmila Department of Industrial & Management Engineering Hanyang University Ansan 426 791 Gyeonggi-do South Korea Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

This model considers the strategy that supplier offers retailer a full trade-credit policy whereas retailer offers their customers a partial trade-credit policy. For such assumption, retailer can earn more profits. In this supplier–retailer model, deterioration of products is assumed as exponential. The main purpose is to minimize the retailer’s annual total cost with finite replenishment rate. Graphical representations are given under different circumstances. The analytical derivation of the model is given to obtain the minimum cost. Some numerical examples for different cases are provided to illustrate the model. © 2014, Springer India Pvt. Ltd.

关键词： Inventory Trade-credit policy Variable deterioration

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α-Reliable Shortest Path Problem in Uncertain Time-Dependent Networks

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International Journal of applied and Computational mathematics 2022年第4期8卷 1-12页

作者： Biswal, Sagarika Ghorai, Ganesh Mohanty, S.P. Department of Mathematics Nimapara Autonomous College Nimapara Puri 752106 India Department of Applied Mathematics With Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore 721102 India Department of Mathematics Siksha ‘O’ Anusandhan University (SOA) Bhubaneswar 751030 India

In a congested road network, it is always desirable to find a reliable shortest path so far as travel time is concerned. Physical distance and travel time are invariably uncertain due to large-scale maintenance work, natural disaster, heavy accident, weather conditions, etc. Many researchers considered travel time to be stochastic where the Bellman’s principle of optimality is not preserved. Also, any sub-path of a shortest path is not necessarily shortest. Some researchers find non-dominated paths under different variants as a multi-objective optimization problem. Moreover, in the absence of sample data, probability theory cannot be used. In this work, the travel time is considered to be uncertain variable, where no sample data is required and it is established that Bellman’s principle of optimality is preserved. So, in contrast to the stochastic environment, classical dynamic approach can be used to find the α-reliable shortest path using uncertainty theory. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Dijkstra’s algorithm Non-dominated path Pre-trip planning Reliable shortest path Travel time Uncertain variable

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L(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 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 λ_0.1(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≤λ_0.1(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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Dynamics of a predator-prey model with stage-structure on both species and anti-predator behavior

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Informatics in Medicine Unlocked 2018年 10卷 50-57页

作者： Mortoja, Sk Golam Panja, Prabir Mondal, Shyamal Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 W.B. India Department of Applied Science Haldia Institute of Technology Purba Midnapore Haldia 721657 W.B. India

In this paper, we have formulated and studied a stage-structure predator-prey model. Here, we consider stage-structure on both prey as well as predator population which means that the prey population is divided into two sub populations such as juvenile prey and adult prey, on the other hand, the predator population is also divided into two sub populations such as juvenile predator and adult predator. It is assumed that only adult predator have the ability to predation and they consume both juvenile prey as well as adult prey. Here, it is also considered that the growth rate of juvenile prey depends upon the adult prey population i.e., the juvenile prey has no reproduction capability. Also, Holling II and Holling IV response function have been used for the consumption of juvenile prey and adult prey by adult predator respectively. It is also considered two types of factors such as anti-predator behavior and group defense to formulate our proposed model. Mathematically, we have analyzed the positivity and boundedness of solutions, existence of equilibria, stability of the proposed system around these equilibrium points and Hopf bifurcation of interior equilibrium point. Finally, some numerical simulations have been presented to validate our theoretical results. © 2017

关键词： Anti-predator behavior Group defense Holling IV response function Prey-predator model Stability analysis Stage-structure

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