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intuitionistic fuzzy programming Models for Matrix Games with Payoffs of Trapezoidal intuitionistic fuzzy Numbers

INTERNATIONAL JOURNAL OF fuzzy SYSTEMS 2014年第4期16卷 444-456页

作者： Nan, Jiang-Xia Zhang, Mao-Jun Li, Deng-Feng Guilin Univ Elect Technol Guangxi Coll & Univ Key Lab Data Anal & Computat Sch Math & Computat Sci Guangxi 541004 Guilin Peoples R China Fuzhou Univ Sch Management Fuzhou 350108 Fujian Peoples R China

The aim of this paper is to develop a methodology for solving matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs). In this methodology, the concepts of TrIFNs and solutions for matrix games with payoffs of TrIFNs are defined. Two new auxiliary intuitionistic fuzzy nonlinear programming models are hereby constructed to solve matrix games with payoffs of TrIFNs. Using a new ranking method based on the value and ambiguity of TrIFNs, the auxiliary intuitionistic fuzzy nonlinear programming models are transformed into the bi-objective parameterized nonlinear programming models, which are further integrated into the parameterized linear programming models, which are used to obtain solutions of matrix games with payoffs of TrIFNs. The validity and applicability of the proposed methodology in this paper are illustrated with a numerical example.

关键词： intuitionistic fuzzy set matrix game intuitionistic fuzzy programming ranking method

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Generalized intuitionistic fuzzy programming for non-linear multiobjective optimization using t-norms and t-conorms

Generalized intuitionistic fuzzy programming for non-linear ...

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IEEE International Conference on fuzzy Systems (FUZZ-IEEE)

作者： Chauhan, Abhishek Mahajan, Sumati Deemed Be Univ Dept Math Punjab Engn Coll Chandigarh India

ISBN: (纸本)9798350319552;9798350319545

In real-world scenarios, decision-makers are often faced with the problem of optimizing several conflicting objectives governed by non-linear functions. In such cases, non-linear multi-objective programming problems are an important tool. However, as such, these cannot incorporate the underlying imprecision and vagueness of data. Therefore, to better accommodate the associated ambiguity of realistic circumstances, uncertain non-linear multiobjective programming problems are used. To optimize multiple objectives together, a compromise or Pareto-optimal solution is obtained using intuitionistic fuzzy programming (IFP). Through this article, we attempt to extend this widely used technique by utilizing t-norms and t-conorms of fuzzy sets. The proposed method generalizes the prevalent IFP and provides a decision-maker-friendly approach. Afterwards, a numerical illustration is presented using the proposed methodology with various t-norms and t-conorms and then the results are compared amongst themselves as well as with several predominant studies.

关键词： intuitionistic fuzzy programming Multiobjective problems t-norms and t-conorms Non-linear optimization

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The Relationship Between intuitionistic fuzzy programming and Goal programming 6th

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6th International Conference on Soft Computing for Problem Solving (SocProS)

作者： Kumar, Sandeep Chaudhary Charan Singh Univ Dept Math Meerut 250004 Uttar Pradesh India

ISBN: (纸本)9789811033223;9789811033216

One of the generalizations of fuzzy programming (FP) is intuitionistic fuzzy programming (IFP). IFP and goal programming (GP) are two important techniques for determining the solution (optimal) of multi-objective optimization problem by transforming it to a single objective one. The main purpose of this article is to introduce the similarities between IFP and GP. In this work, the max and min-operator are considered to transform the IFP to a deterministic program. One example is given to show the applicability of the proposed theory.

关键词： fuzzy programming Multi-objective problem intuitionistic fuzzy programming Goal programming

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Multiobjective Multi-Product Production Planning Problem Using intuitionistic and Neutrosophic fuzzy programming

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IEEE ACCESS 2021年 9卷 37466-37486页

作者： Khan, Mohammad Faisal Haq, Ahteshamul Ahmed, Aquil Ali, Irfan Saudi Elect Univ Coll Sci & Theoret Studies Dept Basic Sci Riyadh 11673 Saudi Arabia Aligarh Muslim Univ Dept Stat & Operat Res Aligarh 202002 Uttar Pradesh India

In this article, a multiobjective multiproduct production planning (MOMPP) problem discussed for a hardware firm. The hardware firm produces various types of hardware locks and other items in a production run. The firm manager's objectives are minimizing the production cost and inventory holding cost while maximizing the net profit subject to some system constraints. The multiproduct production planning is solved with the last production run information precisely known to the decision-maker, and finally, the model is solved using the intuitionistic and neutrosophic programming approaches, respectively. Also, the multiproduct production planning problem is discussed for situations when the product information is vague. The interval-valued trapezoidal neutrosophic numbers used to define this Vagueness. The multiobjective multiproduct production planning problem under fuzziness is solved using the neutrosophic compromise programming. The stepwise solution procedures are discussed using the case study.

关键词： programming Production planning Production Optimization Linear programming Aggregates Planning Interval-valued trapezoidal neutrosophic numbers intuitionistic fuzzy programming multiobjective optimization multiproduct production planning neutrosophic programming

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On optimistic, pessimistic and mixed fuzzy-programming based approaches to solve multi-objective fully intuitionistic fuzzy linear fractional programming problems

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ANNALS OF OPERATIONS RESEARCH 2025年第2期346卷 1399-1443页

作者： Malik, Manisha Gupta, S. K. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttarakhand India

A decision-maker often encounters a state of uncertainty as well as hesitancy due to various unpredictable factors while solving real-world optimization problems. Due to ambiguity in the decision-making process, the parameters and decision variables of an optimization model generally fail to have the exact values. To deal with such realistic uncertain conditions, the concept of intuitionistic fuzzy numbers has been employed widely. In this article, a model of the linear fractional programming problem having multiple objectives with all the parameters and decision variables expressed as intuitionistic fuzzy numbers has been presented. To solve the problem, we first linearize the fractional model using appropriate transformations, and thereafter utilizing the accuracy function and intuitionistic fuzzy programming, the equivalent optimization model is obtained. The conflicting nature of the multiple objectives in the linearized model has been handled using the linear and exponential membership/non-membership functions applying normal, optimistic, pessimistic, and mixed approaches. Moreover, to validate the various equivalent constructions of the original problem, the underlying theorems are also proved at the relevant places. In last, a practical application related to production process in the textile industry has been constructed and solved using the proposed algorithm, and further, a comparison is drawn among various approaches to establish the efficacy of the proposed modelling and developed algorithm.

关键词： Multi-objective optimization intuitionistic fuzzy numbers Membership functions Linear fractional optimization intuitionistic fuzzy programming Optimistic and pessimistic approaches

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New approach for solving intuitionistic fuzzy multi-objective transportation problem

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2018年第1期43卷 1-12页

作者： Roy, Sankar Kumar Ebrahimnejad, Ali Luis Verdegay, Jose Das, Sukumar Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 India Islamic Azad Univ Qaemshahr Branch Dept Math Qaemshahr *** Iran Univ Granada Dept Comp Sci & Artificial Intelligence E-18014 Granada Spain

Multi-objective transportation problem (MOTP) under intuitionistic fuzzy (IF) environment is analysed in this paper. Due to the fluctuation of market scenario, we assume that the transportation cost, the supply and the demand parameters are not always precise. Hence, the parameters are imprecise, i.e., they are IF numbers. Considering the specific cut interval, the IF transportation cost matrix is converted to interval cost matrix in our proposed problem. Again, using the same concept, the IF supply and the IF demand of the MOTP are reduced to the interval form. Then the proposed MOTP is changed into the deterministic MOTP, which includes interval form of the objective functions. Two approaches, namely intuitionistic fuzzy programming and goal programming, are used to derive the optimal solutions of our proposed problem, and then the optimal solutions are compared. A numerical example is included to illustrate the feasibility and the applicability of the proposed problem. Finally, we present the conclusions with the future scopes of our study.

关键词： Transportation problem multi-objective decision making intuitionistic fuzzy programming interval programming goal programming

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A trapezoidal intuitionistic fuzzy optimization approach for crashing a budget constrained project

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AIN SHAMS ENGINEERING JOURNAL 2024年第4期15卷

作者： Kasimoglu, Fatih Bayeg, Selami Pinar, Adem Utku, Durdu Hakan Univ Turkish Aeronaut Assoc Dept Ind Engn TR-06790 Ankara Turkiye Shenandoah Univ Sch Business 1460 Univ Dr Winchester VA 22601 USA Univ Turkish Aeronaut Assoc Dept Mechatron Okul Sk 11 TR-06790 Ankara Turkiye

While the classical fuzzy applications have gained popularity in many different areas, intuitionistic fuzzy set theory emerged as an advancement to better identify various complex circumstances such as the hesitancy of a decision maker under uncertainty. In this study, we propose a project scheduling model in which the allocated budget for crashing is treated as an intuitionistic fuzzy number. With the intuitionistic fuzzy approach, the uncertainty inherent in the project completion time as well as the hesitancy of a decision maker in using the budget amount are integrated into decision making process. The proposed model numerically provides more information than that of the classical ones and better represents the complexity of decision making related to time and cost in project management. Decision makers are provided not only with an optimal schedule but also with a determined degree of satisfaction/dissatisfaction related to the budget and project completion time. Our experimental results show that the decision makers can substantially save money with some delays in the project completion time. Thus, a broader perspective encompassing the satisfaction/dissatisfaction level of a decision maker is presented to schedule a project under uncertain conditions.

关键词： intuitionistic fuzzy programming intuitionistic fuzzy sets Linear programming Optimization Project scheduling

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Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment

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APPLIED INTELLIGENCE 2019年第10期49卷 3524-3538页

作者： Roy, Sankar Kumar Midya, Sudipta Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 W Bengal India

This paper analyzes multi-objective fixed-charge solid transportation problem with product blending in intuitionistic fuzzy environment. The parameters of multi-objective fixed-charge solid transportation problem may not be defined precisely because of globalization of the market and other unmanageable factors. So, we often hesitate in prediction of market demand and other parameters connected with transporting systems in a period. Based on these facts, the parameters of the formulated model are chosen as triangular intuitionistic fuzzy number. New ranking method is used to convert intuitionistic fuzzy multi-objective fixed-charge solid transportation problem with product blending to a deterministic form. New intuitionistic fuzzy technique for order preference by similarity to ideal solution (TOPSIS) is initiated to derive Pareto-optimal solution from the proposed model. Furthermore, we solve the formulated model using intuitionistic fuzzy programming;and a comparison is drawn between the obtained solutions extracted from the approaches. Finally, a practical (industrial) problem is incorporated to illustrate the applicability and feasibility of the proposed study. Conclusions with future research based on the paper are described at last.

关键词： Fixed-charge solid transportation problem Product blending Multi-objective optimization intuitionistic fuzzy programming Ranking method intuitionistic fuzzy TOPSIS

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Compromise optimum allocation in neutrosophic multi-character survey under stratified random sampling using neutrosophic fuzzy programming

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HELIYON 2024年第7期10卷 e28327页

作者： Ullah, Atta Shabbir, Javid Alomair, Abdullah Mohammed Alarfaj, Fawaz Khaled Quaid i Azam Univ Dept Stat Islamabad 45320 Pakistan COMSATS Univ Islamabad Dept Math Attock Campus Islamabad 43600 Pakistan Univ Wah Dept Stat Wah Cant 47040 Pakistan King Faisal Univ Sch Business Dept Quantitat Methods Al Hasa 31982 Saudi Arabia King Faisal Univ Sch Business Dept Management Informat Syst MIS Al Hasa 31982 Saudi Arabia

Survey sampling has wide range of applications in social and scientific investigation to draw inference about the unknown parameter of interest. In complex surveys, the sample information about the study variable cannot be expressed by a precise number under uncertain environment due fuzziness and indeterminacy. Therefore, this information is expressed by neutrosophic numbers rather than the classical numbers. The neutrosophic statistics, which is generalization of classical statistics, deals with the neutrosophic data that has some degree of indeterminacy and fuzziness. In this study, we investigate the compromise optimum allocation problem for estimating the population means of the neutrosophic study variables in a multi -character stratified random sampling under uncertain per unit measurement cost. We proposed the intuitionistic fuzzy cost function, modeling the fuzzy uncertainty in stratum per unit measurement cost. The compromise optimum allocation problem is formulated as a multi -objective intuitionistic fuzzy optimization problem. The solution methodology is suggested using neutrosophic fuzzy programming and intuitionistic fuzzy programming approaches. A numerical study includes the means estimation of atmospheric variables is presented to explore the real -life application, explain the mathematical formulation, and efficiency comparison with some existing methods. The results show that the suggested methods produce more precise estimates with less utilization of survey resources as compared to some existing methods. The Python is used for statistical analysis, graphical designing and numerical optimization problems are solved using GAMS.

关键词： Neutrosophic statistics Stratified sampling Cost function Optimum allocation intuitionistic fuzzy programming Neutrosophic fuzzy programming

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Neutrosophic fuzzy goal programming approach in selective maintenance allocation of system reliability

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COMPLEX & INTELLIGENT SYSTEMS 2021年第2期7卷 1045-1059页

作者： Kamal, Murshid Modibbo, Umar Muhammad AlArjani, Ali Ali, Irfan Aligarh Muslim Univ Dept Stat & Operat Res Aligarh 202002 Uttar Pradesh India Modibbo Adama Univ Technol Dept Stat & Operat Res PMB 2076 Yola 02002 Nigeria Prince Sattam Bin Abdulaziz Univ Coll Engn Al Kharj 16278 Saudi Arabia

Selective maintenance problem plays an essential role in reliability optimization decision-making problems. Systems are a configuration of several components, and there are situations the system needs small intervals or break for maintenance actions, during the intervals expert carried out the maintenance actions to replace or repair the deteriorated components of the systems. Because of the uncertainty associated with the component's operational time, failure, and next mission duration create a new challenge in determining optimal components allocation and evaluating future missions successfully. In this paper, a multi-objective selective maintenance allocation problem is formulated with fuzzy parameters under neutrosophic environment. A new defuzzification technique is introduced based on beta distribution to convert fuzzy parameters into crisp values. The neutrosophic goal programming technique is used to determine the compromise allocation of replaceable and repairable components based on the system reliability optimization. A numerical illustration is used to validate the model and ascertain its effectiveness. The result is compared with two other approaches and found to be better. The method is flexible and straightforward and can be solved using any available commercial packages. The extension of the concept can be useful to other complex system reliability optimization.

关键词： Reliability optimization Selective maintenance intuitionistic fuzzy programming Neutrosophic goal programming Defuzzification technique

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