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

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...

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Vydáno v:International journal of applied mathematics and computer science Ročník 27; číslo 3; s. 563 - 573
Hlavní autoři: Vidhya, Rajendran, Irene Hepzibah, Rajkumar
Médium: Journal Article
Jazyk:angličtina
Vydáno: Zielona Góra Sciendo 01.09.2017
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Témata:
Interval arithmetic
interval valued intuitionistic fuzzy arithmetic
interval valued intuitionistic fuzzy multi-objective linear programming problem
interval valued intuitionistic fuzzy number
Linear programming
Mathematical programming
modified interval valued intuitionistic fuzzy arithmetic
Multiple objective analysis
Pareto optimum
pentagonal intuitionistic fuzzy number
Preempting
ISSN:2083-8492, 1641-876X, 2083-8492
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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 and 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.
AbstractList 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 and 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.
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.
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.
Author Irene Hepzibah, Rajkumar
Vidhya, Rajendran
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Cites_doi 10.1016/S0165-0114(98)00407-2
10.1016/j.camwa.2010.06.039
10.14403/jcms.2013.26.2.297
10.1016/j.ejor.2005.12.042
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SubjectTerms Interval arithmetic
interval valued intuitionistic fuzzy arithmetic
interval valued intuitionistic fuzzy multi-objective linear programming problem
interval valued intuitionistic fuzzy number
Linear programming
Mathematical programming
modified interval valued intuitionistic fuzzy arithmetic
Multiple objective analysis
Pareto optimum
pentagonal intuitionistic fuzzy number
Preempting
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Title A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem
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