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New methods for fuzzy linear programming problem based on heptadecagonal fuzzy number

Life Cycle Reliability and Safety Engineering 2024年第1期13卷 25-32页

作者： Bala, Vipin Kumar, Jitender Kadyan, M.S. Department of Statistics and Operational Research Kurukshetra University Kurukshetra India

In this paper, three new methods for fuzzy linear programming problem (FLPP) based on heptadecagonal fuzzy number are proposed. The cost coefficients in the objective function, coefficients of decision variables, and right-hand side coefficients of constraints in linear programming problem are considered as heptadecagonal fuzzy number. These proposed new methods are used to convert fuzzy linear programming problem into a crisp valued problem. The simplex method is used to find the optimal solution for FLPP with inequality constraints, occurring in real-life situations. The proposed methods are illustrated with numerical examples and the comparisons of the proposed methods are also discussed. © The Author(s), under exclusive licence to Society for Reliability and Safety (SRESA) 2024.

关键词： fuzzy linear programming problem Heptadecagonal fuzzy number Ranking function Simplex method

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New Computational Technique for Solving linear programming problem Subjected to fuzzy Uncertainty

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NEW MATHEMATICS AND NATURAL COMPUTATION 2024年第1期20卷 13-25页

作者： Xavier, Dennis Xavier, Santhi Dennis Behera, Diptiranjan Stat Univ Technol Sch Math Jama 237 Old Hope Rd Kingston 6 Jamaica M Univ Coll Dept Math 1 Marescauex Rd Kingston 5 Jamaica Univ West Indies Dept Math Mona Campus Kingston 7 Jamaica

This paper proposes two new computational methods for solving linear programming problem under trapezoidal and triangular fuzzy uncertainties with equality constraints. The coefficients of the constraints and the objective functions are assumed to be crisp. However, the decision variables and the right-hand side vector of the constraints are considered as uncertain in nature. The concepts of fuzzy addition and subtraction have been used to develop the proposed methods. In the first method, the coefficients are considered as non-negative, whereas mixed coefficients (i.e. both negative and non-negative) are considered in the second method. The obtained results are compared with Behera et al. [D. Behera, K. Peters and S. A. Edalatpanah, Alternative methods for linear programming problem under triangular fuzzy uncertainty, Journal of Statistics and Management Systems, 25 (2022) 521-539;D. Behera, K. Peters, S. A. Edalatpanah and D. Qiu, New methods for solving imprecisely defined linear programming problem under trapezoidal fuzzy uncertainty, Journal of Information and Optimization Sciences, 42 (2021) 603-629], and Saati et al. [S. Saati, M. Tavana, A. Hatami-Marbini and E. Hajiakhondi, A fuzzy linear programming model with fuzzy parameters and decision variables, International Journal of Information and Decision Sciences, 7 (2015) 312-333.] for the validation.

关键词： fuzzy linear programming problem fuzzy number a-cut fuzzy arithmetic

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Solving Multi-Objective linear programming problem by Statistical Averaging Method with the Help of fuzzy programming Method

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American Journal of Operations Research 2023年第2期13卷 19-32页

作者： Samsun Nahar Marin Akter Md. Abdul Alim Department of Basic Sciences and Humanities University of Asia Pacific Dhaka Bangladesh General Education Department City University Dhaka Bangladesh Department of Mathematics Bangladesh University of Engineering and Technology Dhaka Bangladesh

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

关键词： fuzzy programming Method fuzzy linear programming problem Multi-Objective linear programming problem Statistical Averaging Method New Statistical Averaging Method

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Alternative methods for linear programming problem under triangular fuzzy uncertainty

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JOURNAL OF STATISTICS AND MANAGEMENT SYSTEMS 2022年第3期25卷 521-539页

作者： Behera, Diptiranjan Peters, Konor Edalatpanah, S. A. Univ West Indies Dept Math Kingston 7 Jamaica Ayandegan Inst Higher Educ Dept Ind Engn Tonekabon *** Mazandaran Iran

In this paper, linear programming problem under triangular fuzzy uncertainty has been taken into consideration. Accordingly, here the coefficient matrix of the constraints and coefficients of the objective functions are assumed as crisp. However, decision variables and the right-hand side vector of the constraints are assumed as uncertain. Two new methods have been developed here using the concept of a fuzzy centre, core and radius for the solution. In first method, coefficients are considered as non-negative in nature, whereas both non-negative and negative coefficients are considered for the second method. Obtained results are compared with Nasseri (2008) and Lone et al. (2017) for validation.

关键词： fuzzy center fuzzy linear programming problem fuzzy radius theta-cut Triangular fuzzy number

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Solving fuzzy Multi-Objective linear programming problem by Applying Statistical Method

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American Journal of Operations Research 2022年第6期12卷 293-309页

In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.

关键词： fuzzy Multi-Objective linear programming problem fuzzy linear programming problem Chandra Sen’s Method Statistical Averaging Method New Statistical Averaging Method

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New methods for solving imprecisely defined linear programming problem under trapezoidal fuzzy uncertainty

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JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2021年第3期42卷 603-629页

作者： Behera, Diptiranjan Peters, Konor Edalatpanah, S. A. Qiu, Dong Univ West Indies Dept Math Kingston 7 Jamaica Ayandegan Inst Higher Educ Dept Ind Engn Tonekabon *** Mazandaran Iran Chongqing Univ Posts & Telecommun Coll Math & Phys Chongqing 400065 Peoples R China

In this paper, imprecisely defined linear programming problem under fuzzy uncertainty has taken into consideration for the analysis. Accordingly, in the considered problem, elements of the coefficient matrix of the constraints and coefficients of the objective functions are assumed as crisp. However, decision variables and the right-hand side vector of the constraints are anticipated as uncertain in nature. Uncertainty presents in the problem are modelled through convex normalized trapezoidal fuzzy sets. In this regard, two new methods have been proposed for the solution using the concept of fuzzy centre and radius. For the first method, coefficients are considered as non-negative, whereas mixed i.e., both non-negative and negative coefficients are considered for the second method. The advantages of the proposed methods over some existing methods such as Mahdavi-Amiri and Nasseri (2007) and Saati et al. (2015), are discussed. In special cases, the results are compared with some the mentioned methods and some numerical examples are given.

关键词： fuzzy linear programming problem Trapezoidal fuzzy number r-cut fuzzy centre fuzzy radius

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Epistemic uncertainty based linear programming problem and its solution

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2024年第6期15卷 2337-2346页

作者： Behera, Diptiranjan Thomas, Romane Univ West Indies Dept Math Kingston 7 Jamaica

Epistemic uncertainty such as fuzzy based linear programming problem with equality constraints has been considered here. Fuzziness presents in system parameters are modelled using Trapezoidal fuzzy Number (TrFN). In the considered problem the coefficients are defined as crisp while the decision variables as well as the right-hand side of the constraints are taken as fuzzy. Accordingly, a new method to solve the problem based on the fuzzy centre and radius has been proposed here. First the problem is solved for fuzzy centre and next the bounds of the fuzzy variable are replaced in terms of fuzzy centre and radius. Then using the obtained fuzzy centre solution there one can have the radius of the solution. Finally using the results for centre and radius one can get the final solution. For the implementation of this proposed methodology LINGO 18.0 software has been used. Consequently, optimal fuzzy feasible solution has been obtained to get the optimal value (maximum/minimum) of the fuzzy objective function. Moreover, various numerical examples have been solved using the proposed method and the obtained solutions are compared with the solution of existing methods for validation. Moreover, it has been observed that present methods overcome the limitations of Maleki (Maleki in Far East J Math Sci 4:283-301, 2002), Nasseri (Nasseri in Appl Math Sci 2:2473-2480, 2008), Mahdavi-Amiri and Nasseri (Mahdavi-Amiri and Nasseri in fuzzy Sets Syst 158:1961-1978, 2007) and Saati et al. (Saati et al. in Int J Inf Decis Sci 7:312-333, 2015), and clearly the advantages of the proposed method are discussed in conclusion section.

关键词： fuzzy optimization fuzzy linear programming problem fuzzy feasible solution fuzzy objective function Trapezoidal fuzzy number r-cut fuzzy centre fuzzy radius

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Solving epistemic uncertainty based optimization problem with crisp coefficients

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2024年第6期15卷 2130-2140页

作者： Behera, Diptiranjan Univ West Indies Dept Math Kingston 7 Jamaica

Optimization problem such as linear programming problem under epistemic uncertainty for instance fuzzy has been studied in this paper. Here, coefficients are assumed as crisp however, decision variables and the right-hand side vector of the constraints are presumed as uncertain in nature for the considered problem. Using the concept of fuzzy centre and fuzzy arithmetic a new method for the solution has been developed. First, solution of fuzzy centre for r = 0 has been obtained. And then as the upper bound of the solution can be expressed in term of fuzzy centre and lower bound, then using this an equivalent crisp system is solved to obtain the lower bound of the solution. Next again using the solution of lower bound and centre upper bound has been computed. Similarly lower and upper bounds for r = 1 have been obtained. Finally using these solutions fuzzy feasible optimal solution can be obtained. Various example problem has been solved using the proposed method and obtained results are compared with the existing results to show the advantage and validation.

关键词： fuzzy linear programming problem fuzzy set fuzzy number r-cut fuzzy centre fuzzy decision variables

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The combined study of improved fuzzy optimisation techniques with the analysis of the upgraded facility location centre for the Covid-19 vaccine by fuzzy clustering algorithms

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INTERNATIONAL JOURNAL OF NANOTECHNOLOGY 2023年第1-4期20卷 323-345页

作者： Kumar, Rakesh Dhiman, Gaurav Joshi, Varun Jhaveri, Rutvij H. Bhoi, Akash Kumar Lovely Profess Univ Sch Chem Engn & Phys Sci Dept Math Phagwara 144001 Punjab India Lebanese Amer Univ Dept Elect & Comp Engn Byblos Lebanon Chandigarh Univ Univ Ctr Res & Dev Dept Comp Sci & Engn Mohali 140413 India Graph Era Deemed Univ Dept Comp Sci & Engn Dehra Dun 248002 India Lovely Profess Univ Div Res & Dev Phagwara India Chitkara Univ Chitkara Univ Inst Engn & Technol Rajpura Punjab India Govt Bikram Coll Commerce Dept Comp Sci Patiala India Pandit Deendayal Energy Univ Dept Comp Sci & Engn Gandhinagar 382007 India KIET Grp Inst Ghaziabad 201206 Delhi NCR India Sikkim Manipal Univ Directorate Res Gangtok 737102 Sikkim India

With the latest production of vaccines at the conclusion of clinical trials in India, one of the next steps is to administer this vaccine to the consumer. The supply must be specifically positioned to ensure optimal distribution, and it also optimises the transportation cost. The significant concern of the location of facilities is a major logistic extent of decision-making for the vaccine distribution. How the material is passed to customers is one of the vital characteristics of a conversion process (manufacturing system). This fact involves deciding where the building or facility should be located. In this paper, the fuzzy cluster technology provides such optimised locations. Subsequently the optimal positions have been determined, the goal is to find the lowest transportation cost by FLLP. We report on experimental studies by taking artificial data from the current warehouse to prove feasibility and showing that the proposed solution is applicable.

关键词： Covid-19 facility location problem optimisation fuzzy clustering fuzzy linear programming problem

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An Advanced Optimization Technique for Smart Production Using α-Cut Based Quadrilateral fuzzy Number

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INTERNATIONAL JOURNAL OF fuzzy SYSTEMS 2021年第1期23卷 107-127页

作者： Kumar, Rakesh Chandrawat, Rajesh Kumar Sarkar, Biswajit Joshi, Varun Majumder, Arunava Lovely Profess Univ Dept Math Phagwara 144411 Punjab India Yonsei Univ Dept Ind Engn 50 Yonsei Ro Seoul 03722 South Korea

In the design phase of a new smart product, production costs are unpredictable due to location, transport, and engineering design. In these situations, consequently, cost optimization becomes ambiguous. This paper presents a methodology to obtain optimization through a fuzzy linear programming problem (FLPP) in which fuzzy numbers signify the right-side parameters. The comparative investigation of modeling and optimizing creation cost through a new alpha-cut based quadrilateral fuzzy number is proposed to solve the fuzzy linear programming and the necessary operations on the proposed number. Due to the probabilistic increase and decrease in the accessibility of the various constraints, the actual expected total cost fluctuates. In this respect, a unique situation of instability is incorporated, and reasonable models to reduce the cost of eradication in the creation process are presented. The main endeavor is made to look at the credibility of optimized cost utilizing the alpha-cut based quadrilateral FLPP models, and the outcome is contrasted with its augmentation. The data of the production cost of RCF Kapurthala is taken, and the creation expenses of various mentors from the year 2010-2011 are considered as input parameters. The aggregate cost is focused on the objective function. The least low, lower, upper, and most upper bounds are computed for each situation, and then systems of optimized fuzzy LPP are constructed. The credibility of quadrilateral fuzzy LPP concerning all situations is obtained and using this membership grade, the minimum, and highest minimum costs are illustrated.

关键词： Production planning Cost-effective analysis Uncertainty fuzzy number fuzzy linear programming problem

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