Mathematics and Statistics Vol. 11(4), pp. 710 - 725
DOI: 10.13189/ms.2023.110413
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To Enhance New Interval Arithmetic Operations in Solving Linear Programming Problem Using Interval-valued Trapezoidal Neutrosophic Numbers

S Sinika , G Ramesh ^*
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, 603203, India

ABSTRACT

Now in real-life scenarios, indeterminacy arises everywhere in various fields, including physics, mathematics, economics, philosophy, social sciences, etc. It occurs whenever prediction is difficult, when we didn't get a predetermined outcome or obtain fixed or multiple possible outcomes etc. Overcoming indeterminacy is one of the most prominent duties for everyone to lead a confusion-less society. Hence a neutrosophic concept came into force to analyze indeterminacy explicitly. In contrast, a fuzzy set assigns only membership grade, and an intuitionistic set allocates membership and non-membership to elements. Decision-makers can use neutrosophic settings to model uncertainty and ambiguity in complex systems for flexible analysis. The neutrosophic environment with interval numbers makes one handle the situations efficiently. Hence we utilize interval-valued trapezoidal neutrosophic numbers for more flexibility. Trapezoidal number together with interval truth, interval indeterminacy, and interval falsity are the parameters of these neutrosophic numbers. Considering a de-neutrosophication technique in crisp numbers again leads to vagueness in real-life circumstances. Hence our primary goal is to develop a new de-neutrosophication strategy in the form of an interval number instead of the crisp number. This paper provides an overview of the de-neutrosophication and a new ranking technique based on an interval number, and some extended neutrosophic linear programming theorems. Further, an interval version of simplex and Robust Two-Step method (RTSM) are used to answer an interval-valued trapezoidal neutrosophic linear programming problem. Finally, this paper highlights the limitations and advantages of the proposed technique to improve problem-solving in a wide range of fields.

KEYWORDS
Simplex Method, Neutrosophic Linear Programming Problem, Interval-valued Trapezoidal Neutrosophic Number, Interval Numbers

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] S Sinika , G Ramesh , "To Enhance New Interval Arithmetic Operations in Solving Linear Programming Problem Using Interval-valued Trapezoidal Neutrosophic Numbers," Mathematics and Statistics, Vol. 11, No. 4, pp. 710 - 725, 2023. DOI: 10.13189/ms.2023.110413.

(b). APA Format:
S Sinika , G Ramesh (2023). To Enhance New Interval Arithmetic Operations in Solving Linear Programming Problem Using Interval-valued Trapezoidal Neutrosophic Numbers. Mathematics and Statistics, 11(4), 710 - 725. DOI: 10.13189/ms.2023.110413.