Avijit De - Academia.edu (original) (raw)
Papers by Avijit De
Research Square (Research Square), Jul 18, 2022
The domain principle of intuitive fuzzy set (IFS), interval-value intuitionistic fuzzy set (IVIFS... more The domain principle of intuitive fuzzy set (IFS), interval-value intuitionistic fuzzy set (IVIFS), Pythagorean fuzzy set (PFS), interval-valued Pythagorean fuzzy set (IVPFS) and q-rung orthopair fuzzy set (q-ROFS) have various real-life implementations in different fields. But researchers found some limitations to apply these concepts in much uncertain problems due to some issues related to membership and non-membership grads in above mention theories. In order to resolve the issues, firstly, we introduce the novel idea of the interval-valued intuitionistic linear Diophantine fuzzy set (IVILDFS) with the introduction of reference parameters. Next, we propose some score and accuracy functions for interval-valued intuitionistic linear Diophantine fuzzy numbers (IVILDFNs) and apply them in decision making paradigm. We also define interval-valued intuitionistic linear Diophantine fuzzy weighted geometric aggregation operator (IVILDFWGA) for decision making purpose. Then we present two algorithms to solve multiple attribute group decision making (MAGDM) problems using the propose score functions and IVILDFWGA operator. To illustrate the applicability of the proposed approach, we have used two numerical examples. Finally, we present a comparative study and sensitivity analysis to analyze the effectiveness of the proposed method with the existing approaches. The proposed study exhibits a useful way to solve fuzzy MAGDM problems in much efficient manner.
The domain principle of intuitive fuzzy set (IFS), interval-value intuitionistic fuzzy set (IVIFS... more The domain principle of intuitive fuzzy set (IFS), interval-value intuitionistic fuzzy set (IVIFS), Pythagorean fuzzy set (PFS), interval-valued Pythagorean fuzzy set (IVPFS) and q-rung orthopair fuzzy set (q-ROFS) have various real-life implementations in different fields. But researchers found some limitations to apply these concepts in much uncertain problems due to some issues related to membership and non-membership grads in above mention theories. In order to resolve the issues, firstly, we introduce the novel idea of the interval-valued intuitionistic linear Diophantine fuzzy set (IVILDFS) with the introduction of reference parameters. Next, we propose some score and accuracy functions for interval-valued intuitionistic linear Diophantine fuzzy numbers (IVILDFNs) and apply them in decision making paradigm. We also define interval-valued intuitionistic linear Diophantine fuzzy weighted geometric aggregation operator (IVILDFWGA) for decision making purpose. Then we present two ...
Computational and Applied Mathematics, 2020
This paper deals with a single period fuzzy production inventory model with the assortment items ... more This paper deals with a single period fuzzy production inventory model with the assortment items in a finite time horizon. Here, we tried to implement the preservation technology for decreasing the deterioration rate and control the preservation cost of the deteriorated products. In harmony with the real-life uncertain production inventory system, the decision variables and some of the parameters of the proposed model are assumed to be fuzzy variables. So a fuzzy dynamical system has been developed and solved for controlling the system. The optimality of the objective function in fuzzy optimal control has been derived and we have introduced a new approach, the granular differentiability for defuzzifying the system. Then the defuzzified optimal control problem is solved by using Pontryagin’s maximum principle. Here, we have used the Runge–Kutta forward–backward method of fourth-order through MATLAB software. The proposed model is illustrated through a numerical example to determine the optimality conditions and the results are shown both in tabular form and graphically.
Soft Computing - A Fusion of Foundations, Methodologies and Applications, Aug 21, 2019
Ranking of fuzzy numbers has become an important research direction for decision-making problems ... more Ranking of fuzzy numbers has become an important research direction for decision-making problems due to its role to find the best objects under uncertainty. In this paper, we propose a new approach to perform multiple attribute group decision-making (MAGDM) problems using the ranking of interval type-2 fuzzy sets. Initially, a new ranking method for interval type-2 fuzzy numbers based on centroid and rank index has been proposed. Next, we present a comparative study to analyze the ranking values of the proposed method with the existing approaches, where we explore the necessity of the proposed ranking method. After that, a new MAGDM approach has been developed using the proposed ranking procedure to solve uncertain MAGDM problems. Finally, the applicability of the proposed approach has been illustrated using two numerical examples and a case study related to car-sharing problems. The proposed study exhibits a useful way to solve fuzzy MAGDM problems with much efficient manner since it applies interval type-2 fuzzy sets compared to type-1 fuzzy sets to signify the evaluating values and weights of the attributes.
OPSEARCH
Ranking of fuzzy numbers exhibits a significant role to solve the multiple attributes group decis... more Ranking of fuzzy numbers exhibits a significant role to solve the multiple attributes group decision making (MAGDM) problems. One of the commonly used indices for MAGDM problems is the correlation coefficient. Type-2 fuzzy numbers (T2FNs) are considered to be more effective than type-1 fuzzy numbers (T1FNs) to handle uncertainties in MAGDM problems. Moreover, T2FNs allow additional freedom to reflect uncertainty. In this paper, we propose a new approach to rank the interval type-2 fuzzy numbers (IT2FNs) using the correlation coefficient, where the correlation coefficient is obtained using the Mellin transform. Initially, we define the correlation coefficient for interval type-2 trapezoidal fuzzy numbers (IT2TrFNs) using Mellin transform and prove some of its major features. Then a new group decision-making method has been recommended using the proposed ranking concept. Eventually, three examples are given to demonstrate the usefulness of the suggested method. Finally, a comparative study is conducted to depict the feasibility of the developed ranking technique.
Journal of Intelligent & Fuzzy Systems
In general, inventory models consider unlimited capacity of warehouses. But in real inventory sit... more In general, inventory models consider unlimited capacity of warehouses. But in real inventory situations, the capacities of warehouses are limited. So in such cases, to deal with unlimited stocks, one requires additional warehouses. Here a two-warehouse inventory model has been developed for deteriorating items with ramp type demand. Also a corresponding fuzzy model has been developed by considering inventory costs (holding cost, setup cost) and deterioration cost. Subsequently the model has been solved by fuzzy ranking based approach. In both crisp and fuzzy cases, models are being numerically illustrated through examples through a gradient based nonlinear optimization technique (LINGO). Moreover, some sensitivity analysis has been done by taking into consideration the deterioration rate and cost parameters.
Research Square (Research Square), Jul 18, 2022
The domain principle of intuitive fuzzy set (IFS), interval-value intuitionistic fuzzy set (IVIFS... more The domain principle of intuitive fuzzy set (IFS), interval-value intuitionistic fuzzy set (IVIFS), Pythagorean fuzzy set (PFS), interval-valued Pythagorean fuzzy set (IVPFS) and q-rung orthopair fuzzy set (q-ROFS) have various real-life implementations in different fields. But researchers found some limitations to apply these concepts in much uncertain problems due to some issues related to membership and non-membership grads in above mention theories. In order to resolve the issues, firstly, we introduce the novel idea of the interval-valued intuitionistic linear Diophantine fuzzy set (IVILDFS) with the introduction of reference parameters. Next, we propose some score and accuracy functions for interval-valued intuitionistic linear Diophantine fuzzy numbers (IVILDFNs) and apply them in decision making paradigm. We also define interval-valued intuitionistic linear Diophantine fuzzy weighted geometric aggregation operator (IVILDFWGA) for decision making purpose. Then we present two algorithms to solve multiple attribute group decision making (MAGDM) problems using the propose score functions and IVILDFWGA operator. To illustrate the applicability of the proposed approach, we have used two numerical examples. Finally, we present a comparative study and sensitivity analysis to analyze the effectiveness of the proposed method with the existing approaches. The proposed study exhibits a useful way to solve fuzzy MAGDM problems in much efficient manner.
The domain principle of intuitive fuzzy set (IFS), interval-value intuitionistic fuzzy set (IVIFS... more The domain principle of intuitive fuzzy set (IFS), interval-value intuitionistic fuzzy set (IVIFS), Pythagorean fuzzy set (PFS), interval-valued Pythagorean fuzzy set (IVPFS) and q-rung orthopair fuzzy set (q-ROFS) have various real-life implementations in different fields. But researchers found some limitations to apply these concepts in much uncertain problems due to some issues related to membership and non-membership grads in above mention theories. In order to resolve the issues, firstly, we introduce the novel idea of the interval-valued intuitionistic linear Diophantine fuzzy set (IVILDFS) with the introduction of reference parameters. Next, we propose some score and accuracy functions for interval-valued intuitionistic linear Diophantine fuzzy numbers (IVILDFNs) and apply them in decision making paradigm. We also define interval-valued intuitionistic linear Diophantine fuzzy weighted geometric aggregation operator (IVILDFWGA) for decision making purpose. Then we present two ...
Computational and Applied Mathematics, 2020
This paper deals with a single period fuzzy production inventory model with the assortment items ... more This paper deals with a single period fuzzy production inventory model with the assortment items in a finite time horizon. Here, we tried to implement the preservation technology for decreasing the deterioration rate and control the preservation cost of the deteriorated products. In harmony with the real-life uncertain production inventory system, the decision variables and some of the parameters of the proposed model are assumed to be fuzzy variables. So a fuzzy dynamical system has been developed and solved for controlling the system. The optimality of the objective function in fuzzy optimal control has been derived and we have introduced a new approach, the granular differentiability for defuzzifying the system. Then the defuzzified optimal control problem is solved by using Pontryagin’s maximum principle. Here, we have used the Runge–Kutta forward–backward method of fourth-order through MATLAB software. The proposed model is illustrated through a numerical example to determine the optimality conditions and the results are shown both in tabular form and graphically.
Soft Computing - A Fusion of Foundations, Methodologies and Applications, Aug 21, 2019
Ranking of fuzzy numbers has become an important research direction for decision-making problems ... more Ranking of fuzzy numbers has become an important research direction for decision-making problems due to its role to find the best objects under uncertainty. In this paper, we propose a new approach to perform multiple attribute group decision-making (MAGDM) problems using the ranking of interval type-2 fuzzy sets. Initially, a new ranking method for interval type-2 fuzzy numbers based on centroid and rank index has been proposed. Next, we present a comparative study to analyze the ranking values of the proposed method with the existing approaches, where we explore the necessity of the proposed ranking method. After that, a new MAGDM approach has been developed using the proposed ranking procedure to solve uncertain MAGDM problems. Finally, the applicability of the proposed approach has been illustrated using two numerical examples and a case study related to car-sharing problems. The proposed study exhibits a useful way to solve fuzzy MAGDM problems with much efficient manner since it applies interval type-2 fuzzy sets compared to type-1 fuzzy sets to signify the evaluating values and weights of the attributes.
OPSEARCH
Ranking of fuzzy numbers exhibits a significant role to solve the multiple attributes group decis... more Ranking of fuzzy numbers exhibits a significant role to solve the multiple attributes group decision making (MAGDM) problems. One of the commonly used indices for MAGDM problems is the correlation coefficient. Type-2 fuzzy numbers (T2FNs) are considered to be more effective than type-1 fuzzy numbers (T1FNs) to handle uncertainties in MAGDM problems. Moreover, T2FNs allow additional freedom to reflect uncertainty. In this paper, we propose a new approach to rank the interval type-2 fuzzy numbers (IT2FNs) using the correlation coefficient, where the correlation coefficient is obtained using the Mellin transform. Initially, we define the correlation coefficient for interval type-2 trapezoidal fuzzy numbers (IT2TrFNs) using Mellin transform and prove some of its major features. Then a new group decision-making method has been recommended using the proposed ranking concept. Eventually, three examples are given to demonstrate the usefulness of the suggested method. Finally, a comparative study is conducted to depict the feasibility of the developed ranking technique.
Journal of Intelligent & Fuzzy Systems
In general, inventory models consider unlimited capacity of warehouses. But in real inventory sit... more In general, inventory models consider unlimited capacity of warehouses. But in real inventory situations, the capacities of warehouses are limited. So in such cases, to deal with unlimited stocks, one requires additional warehouses. Here a two-warehouse inventory model has been developed for deteriorating items with ramp type demand. Also a corresponding fuzzy model has been developed by considering inventory costs (holding cost, setup cost) and deterioration cost. Subsequently the model has been solved by fuzzy ranking based approach. In both crisp and fuzzy cases, models are being numerically illustrated through examples through a gradient based nonlinear optimization technique (LINGO). Moreover, some sensitivity analysis has been done by taking into consideration the deterioration rate and cost parameters.