Reliability estimation using interval-valued neutrosophic number for multi-criteria decision making problems

Supriya; Suneel Kumar; Deepak Kumar

Authors

Supriya Department of Mathematics ; D.S.B. Campus, Kumaun University, Nainital–263002, India;
Suneel Kumar Department of Mathematics; D.S.B. Campus, Kumaun University, Nainital–263002, India;
Deepak Kumar Dr. Deepak Kumar, Department of Mathematics ; D.S.B. Campus, Kumaun University Nainital–263002, India ;

Keywords:

: Interval-valued neutrosophic number (IVNN); reliability estimation; normalized reliability measure; multi-criteria decision-making (MCDM); hamming distance; score function; aggregation operator

Abstract

Neutrosophic sets have garnered significant attention in recent years for their ability to handle
imprecise, indeterminate, and inconsistent information, making them particularly effective in solving complex
decision-making problems. Among their various extensions, Interval-Valued Neutrosophic Sets (IVNS) provide
a more expressive framework than classical fuzzy or intuitionistic fuzzy systems by introducing three independent membership intervals: truth, indeterminacy, and falsity. By incorporating this enhanced structure,
decision-making processes can better capture practical situations involving ambiguity, indecision, and missing
data, especially in MCDM contexts. However, traditional reliability assessment methods in the IVNS environment often lead to logically inconsistent outcomes, sometimes resulting in negative reliability values—an
issue that directly impacts the reliability of decision-making processes. To overcome this critical limitation, the
present study proposes a normalized reliability function that ensures all reliability estimates are strictly confined
within the [0, 1] range, thereby maintaining both logical consistency and interpretability. For instance, take the
interval-valued neutrosophic number x = <(0.5, 0.9), (0.1, 0.2), (0.2, 0.3)>. Traditional reliability computations
produce results in the range (0.27, 0.50). In contrast, the new method adjusts this estimation to (0.37, 0.42),
providing outcomes that are both more consistent and practically meaningful. In addition to the normalized
reliability function, the study incorporates score functions, average vector strategies, and the Hamming distance
measure to further improve decision-making accuracy under the IVNS framework. The effectiveness and practicality of the proposed methodology are demonstrated through a real-world case study in which a customer
selects the most suitable agent from three alternatives based on four decision criteria, showcasing the model’s
robustness and potential for application in complex MCDM scenarios.