A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem-Reference-Cited by-同舟云学术

A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

Published:2017-09-01 Issue:3 Volume:27 Page:563-573
ISSN:2083-8492
Container-title:International Journal of Applied Mathematics and Computer Science
language:en
Short-container-title:

Author:

Vidhya Rajendran¹²,Irene Hepzibah Rajkumar³⁴

Affiliation:

1. Research Scholar, Bharathiar University , Coimbatore 641046 , Tamil Nadu, India

2. Department of Mathematics , AS-SALAM College of Engineering and Technology , Aduthurai , Tamil Nadu, India

3. Research and Development Centre , Bharathiar University , Coimbatore 641046 , Tamil Nadu, India

4. Department of Mathematics , AVC College of Engineering , Mayiladuthurai , Tamil Nadu, India

Abstract

Abstract In a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming different α and β cut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference21 articles.

1. Atanassov, K.T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems20(1): 87–96.10.1016/S0165-0114(86)80034-3

2. Atanassov, K.T. and Gargov, G. (1989). Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems31(3): 343–349.10.1016/0165-0114(89)90205-4

3. Ben Aicha, F., Bouani, F. and Ksouri, M. (2013). A multivariable multiobjective predictive controller, International Journal of Applied Mathematics and Computer Science23(1): 35–45, DOI: 10.2478/amcs-2013-0004.10.2478/amcs-2013-0004

4. Chanas, S. and Kuchta, D. (1996). Multi objective programming in optimization of interval objective functions—A generalized approach, European Journal of Operational Research94(3): 594–598.10.1016/0377-2217(95)00055-0

5. Chinneck, J.W. and Ramadan, K. (2000). Linear programming with interval coefficients, Journal of the Operational Research Society51(2): 209–220.10.1057/palgrave.jors.2600891

Cited by 8 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On Comparison of Crisp, Fuzzy, Intuitionistic Fuzzy Unconstrained Optimization Problems Using Newton’s Method;Communications in Mathematics and Applications;2022-12-25

2. A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem;Complex & Intelligent Systems;2022-02-20

3. Intuitionistic Fuzzy Sets and Dynamic Programming for Multi-objective Non-linear Programming Problems;International Journal of Fuzzy Systems;2021-02-06

4. The New Definitions of Intuitionistic and Belief-Plausibility Based Local Criteria With Interval and Fuzzy Inputs Applied to the Multiple Criteria Problem of a Raw Material Supplier Selection;IEEE Access;2021

5. Gradual interval arithmetic and fuzzy interval arithmetic;Granular Computing;2019-11-07