An Enhanced Multi-Criteria Decision-Making Model Using Prospect Theory Under Interval-Valued Intuitionistic Quadri-Partitioned Neutrosophic Soft Set Environment

P Sai Anu; A Arulselvam

doi:10.22342/jims.v32i2.2226

P Sai Anu ⁽¹⁾ , A Arulselvam ⁽²⁾

(1) Department of Mathematics, Bharath Institute of Higher Education and Research, India,

(2) Department of Mathematics, Bharath Institute of Higher Education and Research, India

https://doi.org/10.22342/jims.v32i2.2226

Issue
Vol. 32 No. 2 (2026): JUNE

Submitted
September 3, 2025

Accepted
May 20, 2026

Published
June 18, 2026

Keywords:

Intuitionistic fuzzy, neutrosophic soft set, quadri-partitioned, MCDM

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Abstract

This paper presents a novel framework for addressing complex multi-criteria decision analysis (MCDA) problems by integrating Prospect Theory with the recently developed interval-valued intuitionistic quadri-partitioned neutrosophic soft set (IVIQPNSS) structure. The proposed model effectively incorporates both subjective preferences and objective criteria weights by leveraging Prospect Decision Theory, which models human behavior under risk and uncertainty based on gains and losses relative to a reference point. A newly formulated score function (SF) is introduced to transform the quadri-partitioned interval-valued neutrosophic information—comprising truth, indeterminacy, contradiction, and falsity—into precise numerical measures. This enables a refined ranking mechanism among alternatives. The proposed methodology merges expert judgment with data-driven insights, offering a robust algorithmic structure for decision-makers. The practical efficiency and reliability of the approach are demonstrated through a real-world application, ma\-king it a promising tool in the context of uncertain and ambiguous decision-making environments.

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References

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Authors

P Sai Anu

Department of Mathematics, Bharath Institute of Higher Education and Research

A Arulselvam

Department of Mathematics, Bharath Institute of Higher Education and Research

arulselvam.a91@gmail.com (Primary Contact)

Sai Anu, P., & Arulselvam, A. (2026). An Enhanced Multi-Criteria Decision-Making Model Using Prospect Theory Under Interval-Valued Intuitionistic Quadri-Partitioned Neutrosophic Soft Set Environment. Journal of the Indonesian Mathematical Society, 32(2), 2226. https://doi.org/10.22342/jims.v32i2.2226

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The proposed methodology merges expert judgment with data-driven insights, offering a robust algorithmic structure for decision-makers. The practical efficiency and reliability of the approach are demonstrated through a real-world application, making it a promising tool in the context of uncertain and ambiguous decision-making environments.

1. INTRODUCTION

To better capture uncertainty, hesitation, and contradictory information in real-world decision-making, Smarandache[1]introduced Neutrosophic Set (NS) theory. This framework addresses the limitations of classical fuzzy sets[2], intuitionistic fuzzy sets[3], and other hybrid models [4,5] by permitting an independent assessment of truth, indeterminacy, and falsity. To enhance practicality, Wang et al.[6]introduced Single-Valued Neutrosophic Sets (SVNS), later extended to Interval-Valued Neutrosophic Sets (IVNS)[7], which represent membership degrees as intervals for greater flexibility in handling imprecise evaluations in Multi-Criteria Decision Analysis (MCDA). Subsequent research by Chinnadurai et al. [8,9] and Jun et al. [10,11] explored IVNS applications in algebraic structures and parameter-based rankings. Scholars such as Ridvan[12], Liu[13], and Garg[14]further developed aggregation operators and score functions (SFs) for MCDA within neutrosophic environments. Despite these advances, traditional IVNS frameworks, constrained by their tri-partitioned structure (truth, indeterminacy, falsity), remain limited in representing complex judgment scenarios involving multidimensional uncertainty and conflicting information.

In parallel, Prospect Decision Theory (PDT)[15]has emerged as a robust psychological lens for modeling decisions under uncertainty, evaluating alternatives based on perceived gains and losses rather than absolute outcomes. The integration of PDT with fuzzy and neutrosophic sets has shown significant promise. Foundational work by[16]combined PDT with interval-valued intuitionistic fuzzy sets for stochastic MCDA, while[17]extended it to general fuzzy environments under risk. The incorporation of PDT into neutrosophic frameworks was advanced by[18]and[19], who developed algorithms for neutrosophic soft sets and single-valued neutrosophic sets, respectively, applied to group decision-making and physician selection. Further complexity was addressed by[20], who integrated cumulative prospect theory with interval neutrosophic sets using a generalized Shapley function. However, a critical limitation persists across these hybrid models: their reliance on tripartitioned structures prevents the explicit representation of contradiction where an element is simultaneously afirmed and denied. This is a common occurrence in expert judgments involving conflicting evidence or paradoxical data. To overcome this gap, we introduce a quadri-partitioned framework through Interval-Valued Intuitionistic Quadri-Partitioned Neutrosophic Soft Sets (IVIQNSS). By incorporating contradiction as a fourth independent component alongside truth, indeterminacy, and falsity, IVIQNSS provides a more nuanced and powerful ontological foundation. This structure enables a more expressive representation of decision-makers’ hesitation and conflicting assessments, allowing PDT to evaluate prospects not just under uncertainty, but under genuine cognitive conflict.

The key contributions of this work are as follows: The development of a reliable SF for IVIQNSS that efectively handles interval-based truth, indeterminacy, contradiction, and falsity. A hybrid model integrating PDT with IVIQNSS, combining objective weights (derived from data) and subjective weights (from expert opinions) to balance psychological and rational decision components. A structured algorithm for solving MCDA problems in an IVIQNSS-PDT environment, validated through a real-world case study and comparative analysis.

The remainder of this manuscript is organized as follows: Section 2 introduces essential definitions. Section 3 proposes the new SF for IVIQNSS and addresses ranking limitations. Section 4 details the integration of PDT with IVIQNSS and outlines the decision-making algorithm. Section 5 presents a practical application. Section 6 compares the proposed model with established methods to validate its performance. Section 7 concludes the paper and suggests future research directions.

2. Preliminaries

This section outlines the foundational concepts required for this study, including Neutrosophic Sets (NS), Single-Valued Neutrosophic Sets (SVNS), Interval-Valued Neutrosophic Sets (IVNS), and their corresponding SFs. Throughout this section, unless explicitly mentioned otherwise, \(X\)denotes a universal set.

Definition 2.1([1]).Let X be a universal set. A neutrosophic set (NS) on X is expressed as

where \(T _ { N } ^ { * } ( x ) , I _ { N } ^ { * } ( x )\), and \(F _ { N } ^ { * } ( x )\) denote the truth membership, indeterminacy membership, and falsity membership functions, respectively. These mappings are defined as \(T _ { N } ^ { * } ( x ) , I _ { N } ^ { * } ( x ) , F _ { N } ^ { * } ( x ) : X →] 0 ^ { - } , 1 ^ { + } [\). The sum of the three memberships satisfies the condition

Definition 2.2([6]).A single-valued neutrosophic set (SVNS) is a constrained form of NS, given by

where the functions \(T _ { N } ( x ) , I _ { N } ( x )\), and \(F _ { N } ( x )\) map each element \(x \in X\) to values within the closed interval \([0,1]\). These are referred to as the truth, indeterminacy,and falsity membership degrees, respectively. For all \(x \in X\), the following constraintmust hold:

Definition 2.3([7]).An interval-valued neutrosophic set (IVNS) extends the SVNS by allowing the membership values to be intervals rather than crisp numbers. It is formulated as

An Enhanced Multi-Criteria Decision-Making Model Using Prospect Theory Under Interval-Valued Intuitionistic Quadri-Partitioned Neutrosophic Soft Set Environment

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