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Journal articles on the topic 'Interval neutrosophic set (INS)'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Broumi, Said, and Florentin Smarandache. "Correlation Coefficient of Interval Neutrosophic Set." Applied Mechanics and Materials 436 (October 2013): 511–17. http://dx.doi.org/10.4028/www.scientific.net/amm.436.511.

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2

Yang, Han, Xiaoman Wang, and Keyun Qin. "New Similarity and Entropy Measures of Interval Neutrosophic Sets with Applications in Multi-Attribute Decision-Making." Symmetry 11, no. 3 (2019): 370. http://dx.doi.org/10.3390/sym11030370.

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Information measures play an important role in the interval neutrosophic sets (INS) theory. The main purpose of this paper is to study the similarity and entropy of INS and its application in multi-attribute decision-making. We propose a new inclusion relation between interval neutrosophic sets where the importance of the three membership functions may be different. Then, we propose the axiomatic definitions of the similarity measure and entropy of the interval neutrosophic set (INS) based on the new inclusion relation. Based on the Hamming distance, cosine function and cotangent function, som

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3

Yang, Hai-Long, Yan-Ling Bao, and Zhi-Lian Guo. "Generalized interval neutrosophic rough sets and its application in multi-attribute decision making." Filomat 32, no. 1 (2018): 11–33. http://dx.doi.org/10.2298/fil1801011y.

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Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues. In this paper, we put forward generalized interval neutrosophic rough sets based on interval neutrosophic relations by combining interval neutrosophic sets with rough sets. We explore the hybrid model through constructive approach as well as axiomatic approach.

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4

Rosli, Siti Nur Idara, and Mohammad Izat Emir Zulkifly Zulkifly. "Interval Neutrosophic Cubic Bézier Curve Approximation Model for Complex Data." Malaysian Journal of Fundamental and Applied Sciences 20, no. 2 (2024): 336–46. http://dx.doi.org/10.11113/mjfas.v20n2.3240.

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Complex data is defined as data that has the qualities of huge data, a lack of data information, and uncertainty. This paper discussed constructing the interval neutrosophic cubic Bézier curve (INCBC) approximation model for complex data. To construct the interval neutrosophic data point (INDP) based on the definition of interval neutrosophic set (INS), interval neutrosophic relation (INR) and interval neutrosophic point (INP). Next is the introduction of an interval neutrosophic control point (INCP) that blends with the theory of interval neutrosophic set and the Bernstein basis function. Lat

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Khan, Qaisar, Rashad A. R. Bantan, and Mohammed Elgarhy. "Applications of Hesitant Interval Neutrosophic Linguistic Schweizer-Sklar Power Aggregation Operators to MADM." Journal of Function Spaces 2022 (March 19, 2022): 1–30. http://dx.doi.org/10.1155/2022/1654820.

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Hesitant interval neutrosophic linguistic sets (HINLSs) are one of the core generalization of various sets, such as neutrosophic set (NS), interval neutrosophic set (INS), and interval neutrosophic linguistic set (INLS). HINLS can represent the uncertainty, inconsistency, and reluctance of assessment specialists by expressing qualitative and quantitative information. The goal of this article is to introduce a novel MADM technique that can account for changes in the semantic environment as well as negative consequences of experts’ excessive evaluation values. First, several innovative operation

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Aiyared, Aiyared, S. Sahaya Jude Dhas, T. T. Raman, and Aiyared Iampan. "New approach towards (g1, g2, g3) neutrosophic normal interval valued set applied to sin trigonometric aggregating operator and its generalization." International Journal of Neutrosophic Science 24, no. 2 (2024): 147–62. http://dx.doi.org/10.54216/ijns.240213.

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We introduce the concept of sine trigonometric (g1, g2, g3) neutrosophic normal interval valued set. An identifying sine trigonometric (g1, g2, g3)neutrosophic normal interval valued set is a combination of (g1, g2, g3) neutrosophic interval valued set and neutrosophic interval valued set. We communicate the new aggregating operator such as sine trigonometric (g1, g2, g3) neutrosophic normal interval valued weighted averaging, sine trigonometric (g1, g2, g3) neutrosophic normal interval valued weighted geometric, sine trigonometric generalized (g1, g2, g3) neutrosophic normal interval valued w

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7

Aiyared, Aiyared, M. Palanikumar, and M. S. Malchijah Raj. "Different algebraic structures and their properties setting logarithm operator applied to extended neutrosophic interval-valued set." International Journal of Neutrosophic Science 25, no. 3 (2025): 92–105. http://dx.doi.org/10.54216/ijns.250309.

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We present the neutrosophic interval-valued set applied to the q-rung logarithmic operator (q-RLOANIVS). One might develop a q-rung neutrosophic interval-valued set by extending the Pythagorean interval-valued fuzzy set (PIVFS) and neutrosophic set (NS). We discuss the q-Rlogarithimic operator applied neutrosophic interval-valued weighted averaging (q-RLOANIVWA), q-Rlogarithimic operator applied neutrosophic intervalvalued weighted geometric (q-RLOANIVWG), extended q-Rlogarithimic operator applied neutrosophic intervalvalued weighted averaging (q-RELOANIVWA) and extended q-Rlogarithimic operat

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8

Khan, Majid, Muhammad Gulistan, Mumtaz Ali, and Wathek Chammam. "The Generalized Neutrosophic Cubic Aggregation Operators and Their Application to Multi-Expert Decision-Making Method." Symmetry 12, no. 4 (2020): 496. http://dx.doi.org/10.3390/sym12040496.

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In the modern world, the computation of vague data is a challenging job. Different theories are presented to deal with such situations. Amongst them, fuzzy set theory and its extensions produced remarkable results. Samrandache extended the theory to a new horizon with the neutrosophic set (NS), which was further extended to interval neutrosophic set (INS). Neutrosophic cubic set (NCS) is the generalized version of NS and INS. This characteristic makes it an exceptional choice to deal with vague and imprecise data. Aggregation operators are key features of decision-making theory. In recent time

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9

Su, Limin, Tianze Wang, Lunyan Wang, Huimin Li, and Yongchao Cao. "Project Procurement Method Selection Using a Multi-Criteria Decision-Making Method with Interval Neutrosophic Sets." Information 10, no. 6 (2019): 201. http://dx.doi.org/10.3390/info10060201.

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Project procurement method (PPM) selection influences the efficiency of project implementation. Owners are presented with different options for project delivery. However, selecting the appropriate PPM poses great challenges to owners, given the existence of ambiguous information. The interval neutrosophic set (INS) shows power to handle imprecise and ambiguous information. This paper aims to develop a PPM selection model under an interval neutrosophic environment for owners. The main contributions of this paper are as follows: (1) The similarity measure is innovatively introduced with interval

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10

Zhang, Hong-yu, Jian-qiang Wang, and Xiao-hong Chen. "Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems." Scientific World Journal 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/645953.

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As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decision making method. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the r

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Palanikumar, M., K. Arulmozhi, and Aiyared Iampan. "Interval Valued Neutrosophic Subbisemirings of Bisemirings." International Journal of Neutrosophic Science 19, no. 1 (2022): 116–31. http://dx.doi.org/10.54216/ijns.190109.

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We introduce the notion of interval valued neutrosophic subbisemirings (IVNSBSs), level sets of IVNSBSs and interval valued neutrosophic normal subbisemirings (IVNNSBSs) of bisemirings. Also, we introduce an approach to (α , β)-IVNSBSs and IVNNSBSs over bisemirings. Let Ã be an interval valued neutrosophic set (IVN set) in a bisemiring S. We have proved that š = (sTA‚ sIA‚ sFA) is an IVNSBS of S if and only if all non-void level set S(T,S) is a subbisemiring of S for t, s ∈ [[0,1]]. Let Ã be an IVNSBS of a bisemiring S and V be the strongest interval valued neutrosophic relation (SIVNR) of S.

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12

Abdul Razak, Samsiah, Zahari Md. Rodzi, Noraini Ahmad, and Ghafur Ahmad. "Exploring The Boundaries of Uncertainty: Interval Valued Pythagorean Neutrosophic Set and Their Properties." Malaysian Journal of Fundamental and Applied Sciences 20, no. 4 (2024): 813–24. http://dx.doi.org/10.11113/mjfas.v20n4.3482.

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The interval-valued Pythagorean fuzzy set (IVPFS) presents a novel approach to tackling vagueness and uncertainty, while neutrosophic sets, a broader concept encompassing of fuzzy sets and intuitionistic fuzzy sets, are tailored to depict real-world data characterized by uncertainty, imprecision, inconsistency, and incompleteness. Additionally, the development of Interval Value Neutrosophic Sets (IVNS) enhances precision in handling problems involving a range of numbers within the real unit interval, rather than focusing solely on a single value. However, despite these advancements, there is a

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13

Aiyared, Aiyared, T. T. Raman, A. Swaminathan, and Aiyared Iampan. "Extension of arithmetic and geometric aggregating operators using new type interval-valued neutrosophic sets." International Journal of Neutrosophic Science 24, no. 3 (2024): 220–32. http://dx.doi.org/10.54216/ijns.240319.

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The purpose of this article is to present a novel approach to the (δ,ε) interval-valued neutrosophic set (IVNS). This is an extension of the IVNS. As a result of this article, we will discuss the concept of (δ,ε) interval valued neutrosophic weighted averaging (IVNWA), (δ,ε) interval-valued neutrosophic weighted geometric (IVNWG), (δ,ε) generalized interval-valued neutrosophic weighted averaging (GIVNWA) and (δ,ε) generalized interval-valued neutrosophic weighted geometric (GIVNWG). Additionally, the (δ,ε) IVNS approach is characterized by idempotency, boundedness, commutativity and monotonici

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14

Khan, Abdullah, Mahmood, Naeem, and Rashid. "MADM Based on Generalized Interval Neutrosophic Schweizer-Sklar Prioritized Aggregation Operators." Symmetry 11, no. 10 (2019): 1187. http://dx.doi.org/10.3390/sym11101187.

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The interval neutrosophic set (INS) can make it easier to articulate incomplete, indeterminate, and inconsistent information, and the Schweizer-Sklar (Sh-Sk) t-norm (tm) and t-conorm (tcm) can make the information aggregation process more flexible due to a variable parameter. To take full advantage of INS and Sh-Sk operations, in this article, we expanded the Sh-Sk and to IN numbers (INNs) in which the variable parameter takes values from , develop the Sh-Sk operational laws for INNs and discussed its desirable properties. After that, based on these newly developed operational laws, two types

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15

Aiyared, Aiyared, K. Arulmozhi, and Aiyared Iampan. "Cosine trigonometric rules applied to average and geometric aggregating operators using extension q-rung interval-valued neutrosophic set approach." International Journal of Neutrosophic Science 24, no. 3 (2024): 240–57. http://dx.doi.org/10.54216/ijns.240321.

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We introduce the concept of cosine trigonometric q-rung Diophantine neutrosophic interval-valued set (CosTq-rung DioNSIVS). The fact that CosTq-rung DioNSIVS combines q-rung neutrosophic interval-valued set, q-rung neutrosophic set and neutrosophic interval-valued set is one of its distinguishing characteristics. A new idea of CosTq-rung DioNSIVWA, CosTq-rung DioNSIVWG, GCosTq-rung DioNSIVWA and GCosTq-rung DioNSIVWG is proposed in this study. We also look at the idempotency, boundedness, commutativity, and monotonicity of the CosTq-rung DioNSIVS based on algebraic operations. We considered ne

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16

Khan, Qaisar, Nasruddin Hassan, and Tahir Mahmood. "Neutrosophic Cubic Power Muirhead Mean Operators with Uncertain Data for Multi-Attribute Decision-Making." Symmetry 10, no. 10 (2018): 444. http://dx.doi.org/10.3390/sym10100444.

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The neutrosophic cubic set (NCS) is a hybrid structure, which consists of interval neutrosophic sets (INS) (associated with the undetermined part of information associated with entropy) and single-valued neutrosophic set (SVNS) (associated with the determined part of information). NCS is a better tool to handle complex decision-making (DM) problems with INS and SVNS. The main purpose of this article is to develop some new aggregation operators for cubic neutrosophic numbers (NCNs), which is a basic member of NCS. Taking the advantages of Muirhead mean (MM) operator and power average (PA) opera

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17

Palanikumar, M., and Said Broumi. "Multiple attribute decision making for square root diophantine neutrosophic interval-valued sets and their aggregated operators." International Journal of Neutrosophic Science 19, no. 4 (2022): 08–28. http://dx.doi.org/10.54216/ijns.190401.

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Square root Diophantine neutrosophic interval-valued set (SRDioNIVS) approaches to multiple attribute decisionmaking (MADM) problems. The square root neutrosophic sets, interval-valued Diophantine neutrosophic sets are both extensions of square root Diophantine neutrosophic sets. In this section, we discuss aggregating operations and how those interprtautions have evolved over time. The paper is focused on a novel idea known as square root neutrosophic interval-valued weighted averaging (SRDioNIVWA), square root neutrosophic interval-valued weighted geometric (SRDioNIVWG), generalized square r

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18

M., Surya, and P. Muralikrishna. "Application of MBJ - Neutrosophic Set on Filters of Incline Algebra." International Journal of Neutrosophic Science 19, no. 1 (2022): 60–67. http://dx.doi.org/10.54216/ijns.190104.

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The concept of fuzzy set has been generalized to many kinds and one among them is neutrosophic set which is a developed from intuitionistic fuzzy set by adding a components called indeterminate function between truth and falsity membership function. This neutrosophic set also moved a step forward and shows a variation in indeterminate function alone as an interval valued indeterminate function and other functions remains same and this is named as MBJ - neutrosophic set. Here, this work on the MBJ - neutrosophic set merged with incline algbera and introduces the idea of MBJ - neutrosophic filte

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Palanikumar, M., K. Arulmozhi, Aiyared Iampan, and Said Broumi. "New algebraic extension of interval valued Q-neutrosophic normal subbisemirings of bisemirings." International Journal of Neutrosophic Science 20, no. 1 (2023): 106–18. http://dx.doi.org/10.54216/ijns.200109.

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In this research article, we introduce the notions of interval valued Q-neutrosophic subbisemirings (IVQNSSBSs), level sets of an IVQNSSBS and interval valued Q-neutrosophic normal subbisemirings (IVQNSNSBSs) of bisemirings. Let Y ⃗ be an interval valued Q-neutrosophic set (IVQNS set) in a bisemiring 〆. Prove that Y ⃗ is an IVQNSSBS of S if and only if all nonempty level set Ξ(t,s) ⃗ is a subbisemiring (SBS) of S for t, s ∈ D[0, 1]. Let Y ⃗ be an IVQNSSBS of a bisemiring 〆 and V ⃗ be the strongest interval valued Qneutrosophic relation of 〆. Prove that Y ⃗ is an IVQNSSBS of S if and only if V

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20

Aiyared, Aiyared, G. Manikandan, T. T. Raman, K. Arulmozhi, and Aiyared Iampan. "Type-II q-rung neutrosophic interval valued soft sets." International Journal of Neutrosophic Science 23, no. 3 (2024): 318–28. http://dx.doi.org/10.54216/ijns.230326.

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In this study, the theory of the Type-II q-rung neutrosophic interval valued soft set (Type-II q-rung NIVS) is introduced. We also define a few operations based on the Type-II q-rung NIVS set. Type-II q-rung NIVS sets are formed by extending neutrosophic interval valued soft (NIVS) sets and q-rung fuzzy soft sets. Type-II q-rung NIVS sets and their similarity measures. An illustrative example illustrates how they can be used to successfully address uncertainty-related problems.

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Palanikumar, M., Aiyared Iampan, Said Broumi, Lejo J. Manavalan, and K. Sundareswari. "Multi-criteria group decision making method in Pythagorean interval-valued neutrosophic fuzzy soft soft using VIKOR approach." International Journal of Neutrosophic Science 22, no. 1 (2023): 104–13. http://dx.doi.org/10.54216/ijns.220108.

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In contrast to the Pythagorean interval valued fuzzy soft set and the neutrosophic interval valued fuzzy soft set, the Pythagorean neutrosophic interval valued fuzzy soft set is a generalization of these sets. We discuss aggregating PyNIVFS decision matrixes by using aggregated operations. The VIKOR method, which is an extension of neutrosophic fuzzy soft sets, is a powerful method for evaluating multi-criteria group decision making. The score function in this approach is based on the aggregation of the VIKOR method to a PyNIVFSpositive and negative solution. Optimal alternatives are introduce

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22

Ibrahim, Ibrahim, Ali Al Al-Fayadh, Hassan H. Ebrahim, and Luma S. Abdalbaqi. "Implementation of the Neutrosophic Sets in Measurable Space with Respect to Neutrosophic Ring." International Journal of Neutrosophic Science 25, no. 3 (2025): 187–93. http://dx.doi.org/10.54216/ijns.250317.

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The generalization for interval fuzzy set name as neutrosophic set employed to construct a measurable space in this work. The measurable space with respect to a ring of sets that is closed under difference and union, is studied. The objective of this study is to extend the notion of a ring of sets by using neutrosophic sets. Neutrosophic set concept has gained popularity in various fields of mathematics, probability, and other sciences due to its many uses, especially when dealing with uncertainties. Several different properties of neutrosophic ring are studied. Examples and characterizations

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23

Cuauhtemoc, Cuauhtemoc, Cuauhtemoc Samaniego, Moustafa Mohamed Abouelnour, and Wael F. Ali. "Student Academic Performance Classification Using N-Valued Interval Neutrosophic Sets with Optimization Algorithms for Significant Feature Selection." International Journal of Neutrosophic Science 26, no. 1 (2025): 391–403. https://doi.org/10.54216/ijns.260131.

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The most effectual tools for demonstrating uncertainty in decision-making issues are the neutrosophic set (NS) and its additions, like interval NS (INS), complex NS (CNS), and interval complex NS (ICNS). NS delivers an effectual and precise method for defining an imbalance of information as per the data features. In present times, students’ academic performances have been evaluated on the base of regular examinations or memory-related tests and by equating their performances to recognize the features for forecasting their academic excellence. The prediction of student academic performance is i

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Sivakumar, C., Mowafaq Omar Al Al-Qadri, Abdallah shihadeh, et al. "q-rung square root interval-valued neutrosophic sets with respect to aggregated operators using multiple attribute decision making." International Journal of Neutrosophic Science 23, no. 3 (2024): 154–74. http://dx.doi.org/10.54216/ijns.230314.

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This paper introduces the concept of multiple attribute decision making (MADM) using q-rung square root interval valued neutrosophic sets (q-rung SRIVNS). The interval valued neutrosophic set (IVNS) and the q-rung square root neutrosophic set (q-rung SRNS) deals with the q-rung SRIVNS. The purpose of this article is to provide an analysis of several aggregating operations. In this article, we discuss a novel idea for the q-rung square root interval valued neutrosophic weighted averaging (q-rung SRIVNWA), q-rung ortho square root interval valued neutrosophic weighted geometric (q-rung SRIVNWG),

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M., M., Sadeq Damrah, Mutaz M. Abbas Ali, Abdallah Al Al-Husban, and M. Palanikumar. "Type-I extension Diophantine neutrosophic interval valued soft set in real life applications for a decision making." International Journal of Neutrosophic Science 24, no. 4 (2024): 151–64. http://dx.doi.org/10.54216/ijns.240411.

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We describe certain operations and present the theory of the Type-I extension Diophantine neutrosophic interval valued soft set. Additionally, we go over an algorithm that uses the Type-I soft set model to address the decision-making problem. We present a similarity measure between two Type-I extension Diophantine neutrosophic interval valued soft sets and talk about how it might be used in practical applications. A few exemplary cases are provided to demonstrate their practical application in solving uncertain problems.

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Khan, Majid, Muhammad Gulistan, and Mohammed M. Al-Shamiri. "The Approach of Induced Generalized Neutrosophic Cubic Shapley Choquet Integral Aggregation Operators via the CODAS Method to Solve Distance-Based Multicriteria Decision-Making Problems." Journal of Mathematics 2022 (June 1, 2022): 1–20. http://dx.doi.org/10.1155/2022/4898699.

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This study aims to define a conjecture that can handle complex frames of work more efficiently that occurs in daily life problems. In decision-making theory inter-relation of criteria, weights and choice decision-making method subject to the given circumstances which are an important component for appropriate decisions. For this, we define neutrosophic cubic Shapley–Choquet integral (NCSCI) measure; combinative distance-based assessment selection (CODAS) is accomplished over NCSCI and is implemented over a numerical example of a company foreign investment model as an application in decision-ma

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Yousef, Yousef, Yousef Al Al-Qudah, Abdulqader O. Hamadameen, et al. "Matrices and Correlation Coefficient for possibility interval-valued neutrosophic hypersoft sets and their applications in real-life." International Journal of Neutrosophic Science 26, no. 1 (2025): 254–65. https://doi.org/10.54216/ijns.260122.

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In this careful study , through the concept possibility interval valued neutrosophic hyper soft set (abbreviated as piv-NHSS) which is combined from the hypersoft set (HSS) and Interval-valued neutrosophic set under the posobolity degree and each iv-NHSS is assigned a possibility degree in the interval [0, 1]. Based on this concept, we present a more flexible, expanded method for a previous concept named possibility interval valued neutrosophic hyper soft matrix (piv-NHSM) as a new generalization of piv-NHSS. In this work, we also present nseveral algebraic operations and also all the mathemat

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Ebru, Ebru, Nasreen Kausar, Emre Ozbilge, and Ebru Ozbilge. "Extending the concepts of complex interval valued neutrosophic subbisemiring of bisemiring." International Journal of Neutrosophic Science 23, no. 4 (2024): 117–35. http://dx.doi.org/10.54216/ijns.230409.

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The objective of this paper is to investigate the innovative concept of complex neutrosophic subbisemiring. The novelty of the complex neutrosophic subbisemiring lies in its wide range of truth, indeterminacy, and false function values. It goes beyond the range of [0,1] in the complex plane in contrast to the traditional range [0,1]. Therefore, these three functions can be described mathematically using a complex number in the complex neutrosophic subbisemiring. We develop and analyze the concept of complex interval-valued neutrosophic subbisemiring (CIVNSBS). Moreover, we study homomorphic ch

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Manfe, Riyam K. "Further Algebraic Operations on Interval Critical Valued Neutrosophic Soft Sets with Their Application." International Journal of Neutrosophic Science 21, no. 4 (2023): 165–71. http://dx.doi.org/10.54216/ijns.210417.

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Deli developed the idea of interval-valued neutrosophic soft set (IVNSS) as an extension of soft set (SS) theory. The interval-valued neutrosophic soft set (IVNSS) plays a critical role in handling indeterminacy and inconsistent information during the decision-making process. Similar to other models, this newly proposed model has to fulfil some algebraic operations. The aim of this paper is to present further algebraic operations for the IVNSSs. Some algebraic operations on IVNSSs are introduced. Specifically, algebraic operations of addition, multiplication, scalar multiplication, and power f

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Arindam, Arindam, Said Broumi, Ranjan Kumar, and Jayanta Pratihar. "Fermatean Shortest Route Problem with Interval Fermatean Neutrosophic Fuzzy Arc Length: Formulation and a Modified Dijkstra’s Algorithm." International Journal of Neutrosophic Science 23, no. 3 (2024): 288–95. http://dx.doi.org/10.54216/ijns.230323.

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Dijkstra’s algorithm (DA) is a very popular approach for finding the shortest route (SR) in the shortest route problem (SRP). The SRP becomes a challenging and complex problem in real life scenarios. The Fermatean neutrosophic set is a mathematical model that combines Fermatean sets with neutrosophic sets. It can handle the unclear, ambiguous, inconsistent, confusing, and uncertain information that comes from real-world problems. Decision-makers face difficulty accurately determining the precise membership (MG) and non membership levels due to the lack of appropriate data available. The FNS ca

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R., R., KR Balasubramanian, and A. Vadivel. "Interval Valued Neutrosophic INK-Ideal Via INK-Algebra." International Journal of Neutrosophic Science 24, no. 1 (2024): 35–50. http://dx.doi.org/10.54216/ijns.240104.

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Based on Zadeh’s notion of interval-valued fuzzy set, we develop in this work the notion of interval-valued neutrosophic INK-ideals (briefly, IV N INK-ideals) in INK-algebra and evaluate some of its properties. We show that all N INK-ideals of INK-algebra A can be realized as IV level INK-ideals of INK-algebra A. We then deduce numerous related results, which are summarized in the abstract.

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Palanikumar, M., Aiyared Iampan, Said Broumi, and G. G.Balaji. "Generalization of neutrosophic interval-valued soft sets with different aggregating operators using multi-criteria group decision-making." International Journal of Neutrosophic Science 22, no. 1 (2023): 114–23. http://dx.doi.org/10.54216/ijns.220109.

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In this paper, we present the Pythagorean neutrosophic interval valued fuzzy soft set. This is a generalization of the Pythagorean interval valued fuzzy soft set as well as the neutrosophic interval valued fuzzy soft set. It is discussed in this paper how an aggregated operation is used to aggregate the decision matrix of PNIVS. There are a number of extensions to the normosophic fuzzy soft sets that involve the use of multi-criteria decisionmaking. The aim of this study is to develop a score function based on aggregating TOPSIS methods in order to find ideal solutions for PNIVS that have both

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Palanikumar, M., and Said Broumi. "Square root Diophantine neutrosophic normal interval-valued sets and their aggregated operators in application to multiple attribute decision making." International Journal of Neutrosophic Science 19, no. 3 (2022): 63–84. http://dx.doi.org/10.54216/ijns.190307.

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We discuss innovative square root Diophantine neutrosophic normal interval-valued set (SRDioNSNIVS)- based approaches to multiple attribute decision-making (MADM) problems. Square root neutrosophic sets, interval-valued Diophantine neutrosophic sets and neutrosophic normal interval-valued (NSNIV) sets are both extensions of square root Diophantine neutrosophic sets. In this section, we will look over several aggregating operations and how those interpretations have evolved over time. The article is focused on a novel idea known as square root NSNIV weighted averaging (SRDioNSNIVWA), square roo

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Palanikumar, M., K. Arulmozhi, Aiyared Iampan, and Said Broumi. "Medical diagnosis decision making using type-II generalized Pythagorean neutrosophic interval valued soft sets." International Journal of Neutrosophic Science 20, no. 1 (2023): 85–105. http://dx.doi.org/10.54216/ijns.200108.

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The theory of type-II generalized Pythagorean neutrosophic interval valued soft set (Type-II PyNSIVS) and its application to real problems are introduced in this study. Additionally, we define a few operations using the type-II PyNSIVS set. The Pythagorean neutrosophic interval valued soft (PyNSIVS) set and Pythagorean fuzzy soft set are both generalized to form the type-II PyNSIVS set. Complement, union, intersection, AND, and OR are some examples of operations that we define. In particular, we demonstrate the applicability of De Morgan’s laws, associative laws, and distributive laws in type-

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Sharifah, Sharifah, Nasreen Kausar, and Murugan Palanikumar. "New algebraic structures approach towards complex interval valued Q-neutrosophic subbisemiring of bisemiring." International Journal of Neutrosophic Science 24, no. 4 (2024): 451–63. http://dx.doi.org/10.54216/ijns.240434.

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The notion of complex interval-valued q-neutrosophic subbisemiring (CIVqNSBS) is developed and examined. Additionally, we examine the homomorphic features and significant attributes of CIVqNSBS. We suggest the CIVqNSBS level sets for bisemirings. Consider a complex neutrosophic subset of bisemiring Δ, denoted as ℵ if and only if every non-empty level set Z(∂,♭) is a subbisemiring, where ∂, ♭ ∈ D[0, 1], then Z) = Z,Z , Z) is a CIVqNSBS of Δ. Let ℵ be the strongest complex neutrosophic relation of bisemiring Δ, and let Ψ be a CIVqNSBS of bisemiring Δ, if and only if Ψ is a CIVqNSBS of Δ × Δ, the

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Al-Sharqi, Faisal Al, Ashraf Al Al-Quran, Noor Kareem Assi Halaf, Mona Aladil, and Maha M. Rasheed. "Algorithm for possibility interval-valued neutrosophic soft decision-making based on distance measures settings." International Journal of Neutrosophic Science 22, no. 3 (2023): 53–68. http://dx.doi.org/10.54216/ijns.220304.

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Soft set(SS) is one of the soft computing techniques that plays an important role in addressing the hiddenness and uncertainty associated with uncertain data. In other hand the idea of interval-valued neutrosophic soft sets (IVNSSs) is a new generalization of the neutrosophic soft sets to the neutrosophic sets when the authors combine the critical features of IVNS and soft sets (SSs) in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this h

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Hernandez, S. Alvarez, P. P. Jairo Mauricio, and L. Vázquez Maikel. "Neutrosophic TOPSIS for prioritization Social Responsibility Projects." International Journal of Neutrosophic Science 19, no. 1 (2022): 350–62. http://dx.doi.org/10.54216/ijns.190132.

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Social responsibility is the most important thing to consider while working on a project. When deciding on a project or taking part in a bid, it is crucial to understand the nature and potential consequences of the risks involved. Attempting to implement projects with cutting-edge technologies appears to be necessary, necessitating up-to-date and continuous planning to implement the relevant matters in light of the ever-increasing growth of urban communities, the need to carry out tasks, and the rising standard of living. Due to the strong demand, these strategies try to improve quality while

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Prabha, S. Krishna, M. Clement Joe Anand, V. Vidhya, et al. "Sorting Out Interval Valued Neutrosophic Fuzzy Shortest Cycle Route Problem by Reduced Matrix Method." International Journal of Neutrosophic Science 23, no. 2 (2024): 91–103. http://dx.doi.org/10.54216/ijns.230208.

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The assertiveness theory next addresses the difficulties of the travelling salesman after discussing the problem with transportation and assignment. The Shortest Cycling Route Problem (SCRP) finds the shortest route that stops in each city exactly once using a preset set of cities and their bilateral distances. The arc lengths in TSO are typically seen as representing travel time or travel expenses rather than actual distance. The precise arc length cannot be predicted because cargo, climate, road conditions, and other factors also can affect the journey time or cost. For handling the unpredic

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Luis, Luis, Patricia M. Andrade Aulestia, César R. Delgado .., Rafael A. Garzón Jarr� Jarrín, and Xavier C. Quishpe Mendoza. "Neutrosophic Approach to Increasing Production in Small Guinea Pig Breeding Systems: Exploring Tree Set Soft." International Journal of Neutrosophic Science 25, no. 1 (2025): 358–69. http://dx.doi.org/10.54216/ijns.250132.

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The article examines the neutrosophic approach as an innovative tool to optimize production in small guinea pig farming systems. Through the exploration of bipolar sets and interval values, the application of this methodology in improving breeding processes is investigated, thus identifying areas of improvement and opportunities for economic and sustainable growth in the sector. The research highlights the importance of considering the uncertainty and imprecision inherent in these systems, proposing a flexible and adaptive framework that allows informed and strategic decision making to increas

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Palanikumar, M., Aiyared Iampan, and Said Broumi. "MCGDM based on VIKOR and TOPSIS proposes neutrsophic Fermatean fuzzy soft with aggregation operators." International Journal of Neutrosophic Science 19, no. 3 (2022): 85–94. http://dx.doi.org/10.54216/ijns.190308.

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In this study, we presented a new generalization of the Fermatean interval valued fuzzy soft set (FIVFSS) and the neutrosophic interval valued soft set called the neutrsophic Fermatean interval valued soft set (NSFIVSS). The NSFIVSS decision matrix aggregated operations are the topic of our current discussion. Strong points of view for the generalization of the interval valued fuzzy soft set (IVFSS) known as multi-criteria group decision making (MCGDM) are the TOPSIS and VIKOR techniques. We discuss a score function that combines TOPSIS, VIKOR, and NSFIVSS-positive ideal solution (PIS) and NSF

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Hashim, Hazwani, Noor Azzah Awang, and Lazim Abdullah. "A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making." International Journal of Neutrosophic Science 22, no. 1 (2023): 86–103. http://dx.doi.org/10.54216/ijns.220107.

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Decision-making problems involve uncertain and incomplete information, which can be well represented by the Neutrosophic set (NS). Various extensions of NS are available in the literature for solving such problems. However, the published extensions of NS have some restrictions such as single based membership degree. Neutrosophic vague set (NVS) is a newly developed theory to address the shortcomings of previous set theory. NVS is structured based on interval membership in the context of dependent membership functions. Beside uncertainty information, aggregation operators (AOs) are critical com

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Maksim, Maksim, Irina Kosorukova, Veronika Denisovich, Elena Klochko, and Alexey Dengaev. "Effective Data Classification using Interval Neutrosophic Covering Rough Sets based on Neighborhoods for FinTech Applications." International Journal of Neutrosophic Science 25, no. 3 (2025): 206–18. http://dx.doi.org/10.54216/ijns.250319.

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Neutrosophic set (NS) is particularly appropriate in applications where data is incomplete, unclear, or inconsistent, which offers an effectual means for analyzing and exhibiting complex mechanisms. An NS is a mathematical technique to manage uncertainty, indeterminacy, and imprecision. It enlarges classical sets, IF sets, and fuzzy sets by presenting three degrees such as indeterminacy (I), false (F), and truth (T). Financial technology (Fintech) plays an essential part in advancing modern society, technology, economies, and various fields. Financial crisis prediction (FCP) plays a crucial ro

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Andrade-Aulestia, Patricia M. "Enhancing Guinea Pig Farming: A Neutrosophic Approach with Interval-Valued and Bipolar Sets in Decision-Making Methods." International Journal of Neutrosophic Science 24, no. 4 (2024): 93–104. http://dx.doi.org/10.54216/ijns.240407.

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The study emphasizes the need of implementing several ways to promote guinea pig farming in small family units. It highlights the relevance of enhanced nutrition, effective health management, genetic enhancement, and acceptable habitat conditions as essential factors for enhancing productivity and profitability. Suggestions encompass the adoption of advanced breeding methods, offering training and technical support, and expanding the range of goods and markets to ensure the long-term economic viability of guinea pig farming. The utilization of neutrosophic sets provided a strong framework for

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A., A., P. Sugapriya, D. .., S. Santhosh .., K. .., and F. Nirmala Irudayam. "Enhanced Brain Tumor Diagnosis Through Differential and Canonical Quadri –Partitioned Neutrosophic Set Classification Methods:A Comparative Study." International Journal of Neutrosophic Science 24, no. 4 (2024): 277–92. http://dx.doi.org/10.54216/ijns.240420.

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An early cancer diagnosis is carried out for adequate management of diseases. Magnetic resonance imaging (MRI) is most commonly preferred method for cancer diagnosis. Due to the uncontrolled and rapid growth of cells, brain tumor is occurred. If not treated at a preliminary phase, it may lead to death. Thus, a noteworthy prerequisite for a successful treatment outcome is an early and precise diagnosis.Many conventional methods are discussed for performing efficient tumor detection. But, conventional classification methods not distinguish MRI as primary and metastases tumors in an accurate mann

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Arias, Edmundo Jalón, Luis Freire Lescano, Giovanny Pineda Silva, and Maha Ibrahim. "Choice Optimal Fuel Alternative in Thermal Power Station Using Neutrosophic Set and MCDM Methodology." International Journal of Neutrosophic Science 23, no. 1 (2024): 216–29. http://dx.doi.org/10.54216/ijns.230119.

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In a power plant, the fuel choice directly impacts the efficiency, cost, and ecological impact of generating electricity. For power plants to produce electricity effectively and affordably to fulfill the needs of consumers in homes, companies, and communities, they need a fuel supply that is constant, dependable, and inexpensive. In this study, we used the concept of multi-criteria decision-making (MCDM) to deal with the various criteria of fuel alternatives. We used the EDAS method as an MCDM methodology to rank the fuel alternatives and select the best one. The EDAS method is employed with t

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Haibin, Wang, Madiraju Praveen, Zhang Yanqing, and Sunderraman Rajshekhar. "Interval Neutrosophic Sets." September 7, 2014. https://doi.org/10.5281/zenodo.32260.

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Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the set-theoretic operators on an instance of neutrosophic set, we call it interval neutrosophic set (INS).We prove various properties of INS, which are connected to the operations and relations over INS. Fi

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Ye, Jun. "Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods." September 4, 2016. https://doi.org/10.5281/zenodo.235671.

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An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems.

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Said, Broumi, and Smarandache Florentin. "Correlation Coefficient of Interval Neutrosophic Set." November 19, 2014. https://doi.org/10.5281/zenodo.30149.

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Said, Broumi, and Smarandache Florentin. "Correlation Coefficient of Interval Neutrosophic Set." October 31, 2013. https://doi.org/10.5281/zenodo.48908.

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In this paper we introduce for the first time the concept of correlation coefficients of  interval valued neutrosophic set (INS for short).  Respective numerical examples are presented. 

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Said, Broumi, and Smarandache Florentin. "Correlation Coefficient of Interval Neutrosophic Set." July 6, 2013. https://doi.org/10.5281/zenodo.49131.

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 In this paper we introduce for the first time the concept of correlation coefficients of  interval valued neutrosophic set (INS for short).  Respective numerical examples are presented. 

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