Shashi Aggarwal - Profile on Academia.edu (original) (raw)

Papers by Shashi Aggarwal

Fully Fuzzy Multi-Choice Multi-Objective Linear Programming Solution via Deviation Degree

The purpose of this paper is to study fully fuzzy multi-choice multi- objective linear programmin... more The purpose of this paper is to study fully fuzzy multi-choice multi- objective linear programming problem (FFMMOLPP), in which, right hand side of each constraint has two choices. With the help of ranking function, deviation distance and deviation degree between two fuzzy numbers are defined. A new method is proposed to find the  - fuzzy pareto optimal solution of FFMMOLPP which is defuzzified by using deviation degree and ranking function. Furthermore, a comparative study of the existing methods in the literature and proposed method is conducted for the particular case of FFMMOLPP. Hereafter, a real world problem is presented to illustrate the efficiency of proposed method.

Duality in Multiple Right Hand Choice Linear Fractional Problems

Journal of Information and Optimization Sciences, 1991

Abstract In this paper we study a multiple right hand choice linear fractional programming proble... more Abstract In this paper we study a multiple right hand choice linear fractional programming problem of the form Min , where B is a finite subset of R n . A dual has been introduced to the above problem, weak and strong duality results are proved. Certain duality results have been studied for linear fractional programming problem with multiple right hand choice and multiple objective functions.

European Journal of Operational Research, 1992

Necessary and sufficient conditions are derived for nonlinear nonsmooth multiobjective programmin... more Necessary and sufficient conditions are derived for nonlinear nonsmooth multiobjective programming problems. A dual is introduced and certain duality results are established.

BI - level programming

In this paper, bi-level linear programming problem with multiple objectives at each level in intu... more In this paper, bi-level linear programming problem with multiple objectives at each level in intuitionistic fuzzy environment is studied and solved.

In this paper, a new ranking method for generalized trapezoidal intuitionistic fuzzy number (GTRI... more In this paper, a new ranking method for generalized trapezoidal intuitionistic fuzzy number (GTRIFN) is introduced to overcome the limitations of the existing methods. Further, we have considered a transportation problem in intuitionistic fuzzy environment. In this problem, costs are represented by GTRIFNs. An algorithm is proposed to evaluate the initial basic feasible and optimal solution of intuitionistic fuzzy transportation problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed methods. 2010 AMS Classification: 90C70, 90C05, 90C08

Bi-Level Multi-Objective Linear Programming under Intuitionistic Fuzzy Environment

In this paper, bi-level linear programming problem with multiple objectives at each level in intu... more In this paper, bi-level linear programming problem with multiple objectives at each level in intuitionistic fuzzy environment is studied and solved. In this problem, technological coefficients and res ources are characterized by intuitionistic fuzzy numbers having linear membersh ip and non-membership function. Intuitionistic fuzzy efficient solution is computed for the upper level by the proposed model. Finally, intuitionistic fuzzy o ptimization technique is used to obtain the satisfying solution of the given prob lem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed approach.

Solving Intuitionistic Fuzzy Solid Transportation Problem Via New Ranking Method Based on Signed Distance

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper, signed distance of Symmetrical Intuitionistic Fuzzy Numbers (SIFNs) is introduced.... more In this paper, signed distance of Symmetrical Intuitionistic Fuzzy Numbers (SIFNs) is introduced. Based on this signed distance and the crisp ranking system on real numbers, a new ranking system for SIFNs is defined, which seems to be very realistic. To illustrate the applicability and suitability of the proposed ranking method and to deal with ambiguity and imprecision, one of the vital mathematical programming problem viz. Solid Transportation Problem (STP) is formulated in intuitionistic fuzzy environment. A new method has been proposed to compute initial basic feasible solution for the same. Also the significance of the proposed approach over existing methods is illustrated. Finally numerical examples are solved to demonstrate the efficiency of the proposed methods.

Sensitivity Analysis of Intuitionistic Fuzzy Solid Transportation Problem

International Journal of Fuzzy Systems

This paper focuses on sensitivity analysis of intuitionistic fuzzy solid transportation problem (... more This paper focuses on sensitivity analysis of intuitionistic fuzzy solid transportation problem (IFSTP). In real-world situation, IFSTP seems to be more realistic than solid transportation problem (STP) as available information is uncertain. Due to degeneracy of IFSTP or that of STP, Type I sensitivity analysis seems to be impractical. Hence , in this paper, a new algorithm is proposed to determine the Type II sensitivity ranges to overcome this problem. A numerical example is illustrated to demonstrate the feasibility of the proposed algorithm and the efficiency of recommended method over existing method.

Solving Fully Fuzzy Multi-objective Linear Programming Problem Using Nearest Interval Approximation of Fuzzy Number and Interval Programming

International Journal of Fuzzy Systems

AbstractThis paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in ... more AbstractThis paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in which all the coefficients and decision variables are LR flat fuzzy numbers, the more generalized version of fuzzy numbers and all the constraints are fuzzy inequalities. A new algorithm is proposed for solving FFMOLP problem which first converts it into the Multi-Objective Interval Linear Programming (MOILP) problem. Further, taking the help of fuzzy slack variable, fuzzy surplus variables, nearest interval approximation of fuzzy numbers and scalarization technique, MOILP is then converted into the Crisp Linear Programming (CLP) problem. It is shown that the optimal solution of CLP problem is the fuzzy Pareto optimal solution of FFMOLP problem. The main advantage of the proposed algorithm is that it transforms FFMOLP problem into Crisp Linear Programming problem. Moreover, to apply algorithm, only the knowledge of arithmetic operations of LR flat fuzzy numbers, centre and width of the closed intervals are required. At the end, to illustrate the proposed method and its effectiveness over the existing method, numerical examples are solved and compared.

Implementing deviation degree of two closed intervals to decode fully fuzzy multiobjective linear programming problem

Journal of Intelligent & Fuzzy Systems, 2016

In this paper, a new concept of deviation distance and deviation degree between two closed interv... more In this paper, a new concept of deviation distance and deviation degree between two closed intervals is being intro- duced. A new algorithm has been proposed to solve a Fully Fuzzy Multiobjective Linear Programming (FFMOLP) problem with all the constraints as fuzzy inequalities. In the algorithm, the FFMOLP problem is transformed into Crisp Nonlinear Programming (CNLP) problem by using the proposed concept of deviation degree, fuzzy nearest interval approximation, and goal programming (GP) technique. Then, it is proved that the δ-optimal solution of the CNLP problem is the fuzzy Pareto optimal solution of FFMOLP problem. Finally, to illustrate our method and to show its effectiveness, numerical examples are solved and are compared with the existing methods.

In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introdu... more In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introduced. A new ranking method is introduced for p - norm generalized trapezoidal intuitionistic fuzzy numbers. Also we consider linear programming problem in intuitionistic fuzzy environment. In this problem, all the coefficients and variables are represented by p - norm generalized trapezoidal intuitionistic fuzzy numbers. To overcome the limitations of the existing methods, a new method is proposed to compute the intuitionistic fuzzy optimal solution for intuitionistic fuzzy linear programming problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed approach.

In this paper, a new ranking method for generalized trapezoidal intuitionistic fuzzy number (GTRI... more In this paper, a new ranking method for generalized trapezoidal intuitionistic fuzzy number (GTRIFN) is introduced to overcome the limitations of existing methods. Also we consider transportation problem in intuitionistic fuzzy environment. In this transportation problem, costs are represented by GTRIFNs. An algorithm is proposed to evaluate the initial basic feasible and optimal solution of intuitionistic fuzzy transportation problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed methods.

Sensitive Analysis in intuitionistic Fuzzy Solid Transportation Problem

In this paper, bi-level linear programming problem with multiple objectives at each level in intu... more In this paper, bi-level linear programming problem with multiple objectives at each level in intuitionistic fuzzy environment is studied and solved.

A Computational Procedure for Solving a Non-Convex Multi-Objective Quadratic Programming Under Fuzzy Environment

International Journal of Pure and Apllied Mathematics, 2013

Fully Fuzzy Multi-Choice Multi-Objective Linear Programming Solution via Deviation Degree

The purpose of this paper is to study fully fuzzy multi-choice multi- objective linear programmin... more The purpose of this paper is to study fully fuzzy multi-choice multi- objective linear programming problem (FFMMOLPP), in which, right hand side of each constraint has two choices. With the help of ranking function, deviation distance and deviation degree between two fuzzy numbers are defined. A new method is proposed to find the  - fuzzy pareto optimal solution of FFMMOLPP which is defuzzified by using deviation degree and ranking function. Furthermore, a comparative study of the existing methods in the literature and proposed method is conducted for the particular case of FFMMOLPP. Hereafter, a real world problem is presented to illustrate the efficiency of proposed method.

Duality in Multiple Right Hand Choice Linear Fractional Problems

Journal of Information and Optimization Sciences, 1991

Abstract In this paper we study a multiple right hand choice linear fractional programming proble... more Abstract In this paper we study a multiple right hand choice linear fractional programming problem of the form Min , where B is a finite subset of R n . A dual has been introduced to the above problem, weak and strong duality results are proved. Certain duality results have been studied for linear fractional programming problem with multiple right hand choice and multiple objective functions.

European Journal of Operational Research, 1992

Necessary and sufficient conditions are derived for nonlinear nonsmooth multiobjective programmin... more Necessary and sufficient conditions are derived for nonlinear nonsmooth multiobjective programming problems. A dual is introduced and certain duality results are established.

BI - level programming

In this paper, bi-level linear programming problem with multiple objectives at each level in intu... more In this paper, bi-level linear programming problem with multiple objectives at each level in intuitionistic fuzzy environment is studied and solved.

In this paper, a new ranking method for generalized trapezoidal intuitionistic fuzzy number (GTRI... more In this paper, a new ranking method for generalized trapezoidal intuitionistic fuzzy number (GTRIFN) is introduced to overcome the limitations of the existing methods. Further, we have considered a transportation problem in intuitionistic fuzzy environment. In this problem, costs are represented by GTRIFNs. An algorithm is proposed to evaluate the initial basic feasible and optimal solution of intuitionistic fuzzy transportation problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed methods. 2010 AMS Classification: 90C70, 90C05, 90C08

Bi-Level Multi-Objective Linear Programming under Intuitionistic Fuzzy Environment

In this paper, bi-level linear programming problem with multiple objectives at each level in intu... more In this paper, bi-level linear programming problem with multiple objectives at each level in intuitionistic fuzzy environment is studied and solved. In this problem, technological coefficients and res ources are characterized by intuitionistic fuzzy numbers having linear membersh ip and non-membership function. Intuitionistic fuzzy efficient solution is computed for the upper level by the proposed model. Finally, intuitionistic fuzzy o ptimization technique is used to obtain the satisfying solution of the given prob lem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed approach.

Solving Intuitionistic Fuzzy Solid Transportation Problem Via New Ranking Method Based on Signed Distance

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper, signed distance of Symmetrical Intuitionistic Fuzzy Numbers (SIFNs) is introduced.... more In this paper, signed distance of Symmetrical Intuitionistic Fuzzy Numbers (SIFNs) is introduced. Based on this signed distance and the crisp ranking system on real numbers, a new ranking system for SIFNs is defined, which seems to be very realistic. To illustrate the applicability and suitability of the proposed ranking method and to deal with ambiguity and imprecision, one of the vital mathematical programming problem viz. Solid Transportation Problem (STP) is formulated in intuitionistic fuzzy environment. A new method has been proposed to compute initial basic feasible solution for the same. Also the significance of the proposed approach over existing methods is illustrated. Finally numerical examples are solved to demonstrate the efficiency of the proposed methods.

Sensitivity Analysis of Intuitionistic Fuzzy Solid Transportation Problem

International Journal of Fuzzy Systems

This paper focuses on sensitivity analysis of intuitionistic fuzzy solid transportation problem (... more This paper focuses on sensitivity analysis of intuitionistic fuzzy solid transportation problem (IFSTP). In real-world situation, IFSTP seems to be more realistic than solid transportation problem (STP) as available information is uncertain. Due to degeneracy of IFSTP or that of STP, Type I sensitivity analysis seems to be impractical. Hence , in this paper, a new algorithm is proposed to determine the Type II sensitivity ranges to overcome this problem. A numerical example is illustrated to demonstrate the feasibility of the proposed algorithm and the efficiency of recommended method over existing method.

Solving Fully Fuzzy Multi-objective Linear Programming Problem Using Nearest Interval Approximation of Fuzzy Number and Interval Programming

International Journal of Fuzzy Systems

AbstractThis paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in ... more AbstractThis paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in which all the coefficients and decision variables are LR flat fuzzy numbers, the more generalized version of fuzzy numbers and all the constraints are fuzzy inequalities. A new algorithm is proposed for solving FFMOLP problem which first converts it into the Multi-Objective Interval Linear Programming (MOILP) problem. Further, taking the help of fuzzy slack variable, fuzzy surplus variables, nearest interval approximation of fuzzy numbers and scalarization technique, MOILP is then converted into the Crisp Linear Programming (CLP) problem. It is shown that the optimal solution of CLP problem is the fuzzy Pareto optimal solution of FFMOLP problem. The main advantage of the proposed algorithm is that it transforms FFMOLP problem into Crisp Linear Programming problem. Moreover, to apply algorithm, only the knowledge of arithmetic operations of LR flat fuzzy numbers, centre and width of the closed intervals are required. At the end, to illustrate the proposed method and its effectiveness over the existing method, numerical examples are solved and compared.

Implementing deviation degree of two closed intervals to decode fully fuzzy multiobjective linear programming problem

Journal of Intelligent & Fuzzy Systems, 2016

In this paper, a new concept of deviation distance and deviation degree between two closed interv... more In this paper, a new concept of deviation distance and deviation degree between two closed intervals is being intro- duced. A new algorithm has been proposed to solve a Fully Fuzzy Multiobjective Linear Programming (FFMOLP) problem with all the constraints as fuzzy inequalities. In the algorithm, the FFMOLP problem is transformed into Crisp Nonlinear Programming (CNLP) problem by using the proposed concept of deviation degree, fuzzy nearest interval approximation, and goal programming (GP) technique. Then, it is proved that the δ-optimal solution of the CNLP problem is the fuzzy Pareto optimal solution of FFMOLP problem. Finally, to illustrate our method and to show its effectiveness, numerical examples are solved and are compared with the existing methods.

In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introdu... more In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introduced. A new ranking method is introduced for p - norm generalized trapezoidal intuitionistic fuzzy numbers. Also we consider linear programming problem in intuitionistic fuzzy environment. In this problem, all the coefficients and variables are represented by p - norm generalized trapezoidal intuitionistic fuzzy numbers. To overcome the limitations of the existing methods, a new method is proposed to compute the intuitionistic fuzzy optimal solution for intuitionistic fuzzy linear programming problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed approach.

In this paper, a new ranking method for generalized trapezoidal intuitionistic fuzzy number (GTRI... more In this paper, a new ranking method for generalized trapezoidal intuitionistic fuzzy number (GTRIFN) is introduced to overcome the limitations of existing methods. Also we consider transportation problem in intuitionistic fuzzy environment. In this transportation problem, costs are represented by GTRIFNs. An algorithm is proposed to evaluate the initial basic feasible and optimal solution of intuitionistic fuzzy transportation problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed methods.

Sensitive Analysis in intuitionistic Fuzzy Solid Transportation Problem

In this paper, bi-level linear programming problem with multiple objectives at each level in intu... more In this paper, bi-level linear programming problem with multiple objectives at each level in intuitionistic fuzzy environment is studied and solved.

A Computational Procedure for Solving a Non-Convex Multi-Objective Quadratic Programming Under Fuzzy Environment

International Journal of Pure and Apllied Mathematics, 2013