<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>α</italic> and <italic>β</italic> 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.</p></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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers...

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

Published Online: Sep 23, 2017

Page range: 563 - 573

Received: Aug 11, 2016

Accepted: May 02, 2017

DOI: https://doi.org/10.1515/amcs-2017-0040

Keywords
pentagonal intuitionistic fuzzy number, interval valued intuitionistic fuzzy number, interval valued intuitionistic fuzzy arithmetic, modified interval valued intuitionistic fuzzy arithmetic, interval valued intuitionistic fuzzy multi-objective linear programming problem

© 2017 Rajendran Vidhya et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Sep 23, 2017

Page range: 563 - 573

Received: Aug 11, 2016

Accepted: May 02, 2017

DOI: https://doi.org/10.1515/amcs-2017-0040

Keywordspentagonal intuitionistic fuzzy number, interval valued intuitionistic fuzzy number, interval valued intuitionistic fuzzy arithmetic, modified interval valued intuitionistic fuzzy arithmetic, interval valued intuitionistic fuzzy multi-objective linear programming problem

© 2017 Rajendran Vidhya et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
pentagonal intuitionistic fuzzy number, interval valued intuitionistic fuzzy number, interval valued intuitionistic fuzzy arithmetic, modified interval valued intuitionistic fuzzy arithmetic, interval valued intuitionistic fuzzy multi-objective linear programming problem