Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment

Bharati, Shailendra Kumar; Singh, S. R.

doi:10.1007/s00500-018-3100-6

Cited by 39 publications

(13 citation statements)

References 21 publications

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“…Also, we apply the expected value operator on the IMOLP under uncertainty variables as follows. Indeed, the objective functions are the expected value of the interval objective functions of model (7). Also, we have:…”

Section: Expected Value Operator In the Imolpmentioning

confidence: 99%

“…Dechao et al [9] employed an admissible order and interval ordered weighted aggregation operator to transform a IMOLP problem into an interval weighted sum scalarization multiobjective optimization problem whose solution can be derived by solving several related real-valued programming problems, and the Pareto optimal solution of this IMOLP problem can likewise be obtained. Bharati and Singh developed a new method for obtaining the solution of the MOLP models based on intervalvalued intuitionistic fuzzy sets [7]. Uncertainty theory was founded by Liu in 2007, and a branch of mathematics for modelling under uncertainty was introduced [24].…”

Section: Introductionmentioning

confidence: 99%

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Finding efficient solutions in the interval multi-objective linear programming models

Batamiz

Allahdadi

2021

YUGOSLAV J OPERATION

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The aim of our paper is to obtain efficient solutions to the interval multi- objective linear programming (IMOLP) models. In this paper, we propose a new method to determine the efficient solutions in the IMOLP models by using the expected value and variance operators (EVV operators). First, we define concepts of the expected value, variance, and uncertainty distributions, and present some properties of the EVV operators. Then, we introduce the IMOLP model under these operators. An IMOLP model consist of separate ILPs, but using the EVV operators and the uncertainty distributions, it can be converted into the interval linear programming (ILP) models under the EVV operators (EVV-ILP model). We show that optimal solutions of the EEV-ILP model are the efficient solutions of IMOLP models with uncertainty variables. The proposed method, which is called EVV, is not hard to solve. Finally, Monte Carlo simulation is used to show its the performance assessment.

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Section: Expected Value Operator In the Imolpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finding efficient solutions in the interval multi-objective linear programming models

Batamiz

Allahdadi

2021

YUGOSLAV J OPERATION

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“…An IVIHFS involving interval-valued hesitant membership and non-membership degrees can be a fit tool. Bharati and Singh [ 5 ] studied interval-valued intuitionistic fuzzy sets and investigated new computational algorithm which is an extension of both fuzzy and intuitionistic fuzzy optimization techniques. And its validity and superiority are explained by an illustrative example, and a comparison with existing algorithms is tabulated.…”

Section: Literature Reviewmentioning

confidence: 99%

An Interval-Valued Intuitionistic Hesitant Fuzzy Methodology and Application

Bharati

2021

New Gener. Comput.

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Using advantages of interval-valued intuitionistic hesitant fuzzy sets (IVIHFS) for describing the hesitant and intuitionistic decisions of experts and identifying the limitations of previous research works about optimization techniques, this paper introduces a new optimization technique and provides a new computational algorithm, applicable in various real life multiobjective optimization problem (MOOP) of engineering and management sectors, and for this, a new operation between IVIHFSs is first introduced. On the basis of this concept, a stepwise computational algorithm is constructed, and it is an extension of both fuzzy and intuitionistic fuzzy optimization techniques. Finally, the proposed algorithm is illustrated using a production planning problem, and the obtained results are compared with the existing optimization techniques.

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“…Abhishekh and Nishad [29] proposed a novel ranking approach for solving fully LR-intuitionistic fuzzy transportation problem. Bharati and Singh [30] studied a method for the solution of multiobjective linear programming problems in intervalvalued intuitionistic fuzzy environments. Kabiraj et al [31] proposed another method for intuitionistic fuzzy linear programming problems.…”

Section: Introductionmentioning

confidence: 99%

Methods for Solving $L R$ -Type Pythagorean Fuzzy Linear Programming Problems with Mixed Constraints

Akram

Ullah

Alharbi

2021

Mathematical Problems in Engineering

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A Pythagorean fuzzy set is the superset of fuzzy and intuitionistic fuzzy sets, respectively. Yager proposed the concept of Pythagorean fuzzy sets in which he relaxed the condition that sum of square of both membership degree and nonmembership degree of an element of a set must not be greater than 1. This paper introduces two new techniques to solve L R -type fully Pythagorean fuzzy linear programming problems with mixed constraints having unrestricted L R -type Pythagorean fuzzy numbers as variables and parameters by introducing unknown variables and using a ranking function. Furthermore, we show the equivalence of both the proposed methods and compare the solutions obtained by the two techniques. Besides this, we solve an already existing practical model using proposed techniques and compare the result.

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Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment

Cited by 39 publications

References 21 publications

Finding efficient solutions in the interval multi-objective linear programming models

Finding efficient solutions in the interval multi-objective linear programming models

An Interval-Valued Intuitionistic Hesitant Fuzzy Methodology and Application

Methods for Solving $L R$ -Type Pythagorean Fuzzy Linear Programming Problems with Mixed Constraints

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Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment

Cited by 39 publications

References 21 publications

Finding efficient solutions in the interval multi-objective linear programming models

Finding efficient solutions in the interval multi-objective linear programming models

An Interval-Valued Intuitionistic Hesitant Fuzzy Methodology and Application

Methods for Solving L R -Type Pythagorean Fuzzy Linear Programming Problems with Mixed Constraints

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Methods for Solving $L R$ -Type Pythagorean Fuzzy Linear Programming Problems with Mixed Constraints