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Journal articles on the topic 'Neutrosophic hesitant fuzzy set'

Author: Grafiati

Published: 2 June 2025

Last updated: 19 July 2025

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1

Ye, Jun. "Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment." Journal of Intelligent Systems 24, no. 1 (2015): 23–36. http://dx.doi.org/10.1515/jisys-2014-0001.

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AbstractOn the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted geometric

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2

Shao, Songtao, Xiaohong Zhang, Yu Li, and Chunxin Bo. "Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making." Symmetry 10, no. 9 (2018): 419. http://dx.doi.org/10.3390/sym10090419.

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The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced. By definition, we know that the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) is a special case of the probabilistic interval neutrosophic hesitant fuzzy set (PINHFS). PSVNHFSs can satisfy all the properties of PINHFSs. An example is given

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3

Rehman, Ateeq Ur, Muhammad Gulistan, Nasreen Kausar, Sajida Kousar, Mohammed M. Al-Shamiri, and Rashad Ismail. "Novel Development to the Theory of Dombi Exponential Aggregation Operators in Neutrosophic Cubic Hesitant Fuzzy Sets: Applications to Solid Waste Disposal Site Selection." Complexity 2022 (September 26, 2022): 1–16. http://dx.doi.org/10.1155/2022/3828370.

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The neutrosophic cubic hesitant fuzzy set can efficiently handle the complex information in a decision-making problem because it combines the advantages of the neutrosophic cubic set and the hesitant fuzzy set. The algebraic operations based on Dombi norms and co-norms are more flexible than the usual algebraic operations as they involve an operational parameter. First, this paper establishes Dombi algebraic operational laws, score functions, and similarity measures in neutrosophic cubic hesitant fuzzy sets. Then, we proposed Dombi exponential operational laws in which the exponents are neutro

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Akram, Muhammad, Sumera Naz, and Florentin Smarandache. "Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment." Symmetry 11, no. 8 (2019): 1058. http://dx.doi.org/10.3390/sym11081058.

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With the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SNHFS) is an efficient tool to process the vague information and contains the ideas of a single-valued neutrosophic hesitant fuzzy set (SVNHFS) and an interval neutrosophic hesitant fuzzy set (INHFS). In this paper, we propose a decision-making approach based on the maximizing deviation method and TOP

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Imran, Raiha, Kifayat Ullah, Zeeshan Ali, and Maria Akram. "An Approach to Multi-Attribute Decision-Making Based on Single-Valued Neutrosophic Hesitant Fuzzy Aczel-Alsina Aggregation Operator." Neutrosophic Systems with Applications 22 (October 1, 2024): 43–57. http://dx.doi.org/10.61356/j.nswa.2024.22387.

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A single-valued Neutrosophic hesitant fuzzy set (SVNHFS) is a combination of a single-valued neutrosophic set (SVNS) and hesitant fuzzy set (HFS) that has been developed to address insufficient, unreliable, and vague environments in which each element has several possible options determined by the truthiness, indeterminacy and falsity value. By considering this, in this paper, we have proposed the Aczel-Alsina aggregation operator (AAAO) for SVNHFS, which is more flexible t-norm and t-conorm than the other and due to the flexible nature of parameters to solve Multi-Attribute decision making (M

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Liu, Jia-Bao, Rashad Ismail, Muhammad Kamran, Esmail Hassan Abdullatif Al-Sabri, Shahzaib Ashraf, and Ismail Naci Cangul. "An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator." AIMS Mathematics 8, no. 9 (2023): 20612–53. http://dx.doi.org/10.3934/math.20231051.

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<abstract><p>The single valued neutrosophic probabilistic hesitant fuzzy rough Einstein aggregation operator (SV-NPHFRE-AO) is an extension of the neutrosophic probabilistic hesitant fuzzy rough set theory. It is a powerful decision-making tool that combines the concepts of neutrosophic logic, probability theory, hesitant fuzzy sets, rough sets, and Einstein aggregation operators. SV-NPHFRE-AO can be applied in many fields, including livestock decision making. Making judgments about a wide range of issues, including feed formulation, breeding program design, disease diagnostics, an

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Batool, Sania, Masooma Raza Hashmi, Muhammad Riaz, Florentin Smarandache, Dragan Pamucar, and Dejan Spasic. "An Optimization Approach with Single-Valued Neutrosophic Hesitant Fuzzy Dombi Aggregation Operators." Symmetry 14, no. 11 (2022): 2271. http://dx.doi.org/10.3390/sym14112271.

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Using the strength of a single-valued neutrosophic set (SVNS) with the flexibility of a hesitant fuzzy set (HFS) yields a robust model named the single-valued neutrosophic hesitant fuzzy set (SVNHFS). Due to the ability to utilize three independent indexes (truthness, indeterminacy, and falsity), an SVNHFS is an efficient model for optimization and computational intelligence (CI) as well as an intelligent decision support system (IDSS). Taking advantage of the flexibility of operational parameters in Dombi’s t-norm and t-conorm operations, new aggregation operators (AOs) are proposed, which ar

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8

Kamran, Muhammad, Shahzaib Ashraf, Shahid Khan, Aamir Khan, Hedia Zardi, and Saba Mehmood. "Integrated decision-making framework for hospital development: A single-valued neutrosophic probabilistic hesitant fuzzy approach with innovative aggregation operators." Yugoslav Journal of Operations Research, no. 00 (2023): 34. http://dx.doi.org/10.2298/yjor230915034k.

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This research article proposes an innovative algorithm for analyzing parallelism in the evolution of hospital building features, with the goal of advancing decisionmaking processes in both urban and rural hospitals. As an additional generalization of the concepts of fuzzy sets, intuitionistic fuzzy sets, single-valued neutrosophic sets, hesitant fuzzy sets, and probabilistic fuzzy sets this paper proposes a single-valued neutrosophic probabilistic hesitant fuzzy set (SV-NPHFS). It is derived from the combination of single-valued neutrosophic sets, probabilistic fuzzy sets, and hesitant fuzzy s

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Mandal, Debabrata. "A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings." International Journal of Fuzzy System Applications 10, no. 3 (2021): 1–17. http://dx.doi.org/10.4018/ijfsa.2021070101.

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The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and ca

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10

Liu, Donghai, Xiaohong Chen, and Dan Peng. "Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making." Symmetry 10, no. 11 (2018): 602. http://dx.doi.org/10.3390/sym10110602.

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This paper proposes a neutrosophic hesitant fuzzy linguistic term set (NHFLTS) based on hesitant fuzzy linguistic term set (HFLTS) and neutrosophic set (NS), which can express the inconsistent and uncertainty information flexibly in multiple criteria decision making problems. The basic operational laws of NHFLTS based on linguistic scale function are also discussed. Then we propose the generalized neutrosophic hesitant fuzzy linguistic distance measure and discuss its properties. Furthermore, a new similarity measure of NHFLTS combines the generalized neutrosophic hesitant fuzzy linguistic dis

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Kamran, Muhammad, Shahzaib Ashraf, Nadeem Salamat, Muhammad Naeem, and Thongchai Botmart. "Cyber security control selection based decision support algorithm under single valued neutrosophic hesitant fuzzy Einstein aggregation information." AIMS Mathematics 8, no. 3 (2022): 5551–73. http://dx.doi.org/10.3934/math.2023280.

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<abstract><p>The single-valued neutrosophic hesitant fuzzy set (SV-NHFS) is a hybrid structure of the single-valued neutrosophic set and the hesitant fuzzy set that is designed for some incomplete, uncertain, and inconsistent situations in which each element has a few different values designed by the truth membership hesitant function, indeterminacy membership hesitant function, and falsity membership hesitant function. A strategic decision-making technique can help the decision-maker accomplish and analyze the information in an efficient manner. However, in our real lives, uncerta

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Shao, Songtao, and Xiaohong Zhang. "Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes." Mathematics 7, no. 7 (2019): 649. http://dx.doi.org/10.3390/math7070649.

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Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming that will result in an inaccurate decision conclusion

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Zhang, Kecheng, Yawen Wang, and Zhicheng Chen. "A Multi-Attribute Decision-Making Approach for International Shipping Operator Selection Based on Single-Valued Neutrosophic Power Hamy Mean Operators." Symmetry 16, no. 6 (2024): 706. http://dx.doi.org/10.3390/sym16060706.

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Maritime shipping is a crucial method of transporting goods internationally and is vital in supporting global trade. However, due to its global scope, the international shipping market is susceptible to political and economic disturbances. The recent escalation in the Israeli–Palestinian conflict has severely impacted the international shipping market, particularly in the tense Red Sea region. Previous research has neglected the significance of evaluating international shipping companies, particularly their origins, within their evaluation frameworks. A fuzzy multi-attribute decision-making (M

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14

Samandarboy, Samandarboy. "A Probabilistic Neutrosophic Hesitant Fuzzy Set for Waste Water Treatment Plants." Journal of Sustainable Development and Green Technology 4, no. 2 (2024): 34–43. http://dx.doi.org/10.54216/jsdgt.040204.

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Decision-makers at wastewater treatment plants must increase process efficiency and circularity while preserving economic performance. They must comply with increasing requirements about lowering emissions, sustainability, and human health safety. To operate and choose technologies to fulfil these expectations leads to complicated multi-objective issues. As a consequence, the water industry has developed several decision support systems. Multi-criteria decision-making (MCDM) is used to deal with various criteria in the evaluation process. The MCDM methodology integrated with the probabilistic

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15

Kamran, Muhammad, Rashad Ismail, Esmail Hassan Abdullatif Al-Sabri, Nadeem Salamat, Muhammad Farman, and Shahzaib Ashraf. "An Optimization Strategy for MADM Framework with Confidence Level Aggregation Operators under Probabilistic Neutrosophic Hesitant Fuzzy Rough Environment." Symmetry 15, no. 3 (2023): 578. http://dx.doi.org/10.3390/sym15030578.

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In this research, we first offer unique notions of averaging and geometric aggregation operators with confidence level by employing a probabilistic neutrosophic hesitant fuzzy rough framework. Then, we look into other descriptions of the suggested operators, such as idempotency, boundedness, and monotonicity. Additionally, for the derived operators, we establish the score and accuracy functions. We also provide a novel approach to assessing the selection procedure for smart medical devices (SMDs). The selection criteria for SMDs are quite complex, which is the most noteworthy feature of this i

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Riaz, Muhammad, Yahya Almalki, Sania Batool, and Shaista Tanveer. "Topological Structure of Single-Valued Neutrosophic Hesitant Fuzzy Sets and Data Analysis for Uncertain Supply Chains." Symmetry 14, no. 7 (2022): 1382. http://dx.doi.org/10.3390/sym14071382.

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From production to retail, the food supply chain (FSC) encompasses all stages of food production. Food is now transmitted across continents over long ranges. People depend on supply chains for basic necessities such as food, water, drinks, etc. Any disruption in these shipment pipelines poses a serious threat to human life. Supplier selection (SS) has been identified as a crucial component of FSC, which has been contemplated as a multi-criteria decision-making (MCDM) problem in many studies. The failure of some specific MCDM problems is due to failure in contemplating the relationships between

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17

Ramaroson, Hans Eric, René Rakotomanana, and Hery Zo Andriamanohisoa. "Cosine Similarity Measure of Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Set and Their Applications to Multi-Attribute Decision-Making Process." European Journal of Mathematics and Statistics 2, no. 5 (2021): 9–16. http://dx.doi.org/10.24018/ejmath.2021.2.5.64.

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Cosine similarity measure plays a significant role in various fields. Literature consultation confirms that the theory of cosine similarity measure has received a great interest and attention from the researchers in the world. The concept of Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Sets (IVBNHFS) is recently presented and very interesting. Every element in IVBNHFS is characterized by six independent membership functions (three positive and three negative). There is no investigation on the Cosine Similarity Measure (CSM) of IVBNHFS. In this study, we firstly define a CSM and a weight

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Biswas, Pranab, Surapati Pramanik, and Bibhas C. Giri. "NH-MADM Strategy in Neutrosophic Hesitant Fuzzy Set Environment Based on Extended GRA." Informatica 30, no. 2 (2019): 213–42. http://dx.doi.org/10.15388/informatica.2019.204.

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19

Močkoř, Jiří. "Semiring-Valued Fuzzy Sets and F-Transform." Mathematics 9, no. 23 (2021): 3107. http://dx.doi.org/10.3390/math9233107.

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The notion of a semiring-valued fuzzy set is introduced for special commutative partially pre-ordered semirings, including basic operations with these fuzzy structures. It is showed that many standard MV-algebra-valued fuzzy type structures with standard operations, such as hesitant, intuitionistic, neutrosophic or fuzzy soft sets are, for appropriate semirings, isomorphic to semiring-valued fuzzy sets with operations defined. F-transform and inverse F-transform are introduced for semiring-valued fuzzy sets and properties of these transformations are investigated. Using the transformation of M

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Močkoř, Jiří, Petr Hurtik, and David Hýnar. "Rough Semiring-Valued Fuzzy Sets with Application." Mathematics 10, no. 13 (2022): 2274. http://dx.doi.org/10.3390/math10132274.

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Many of the new fuzzy structures with complete MV-algebras as value sets, such as hesitant, intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into one type of fuzzy set with values in special complete algebras, called AMV-algebras. The category of complete AMV-algebras is isomorphic to the category of special pairs (R,R*) of complete commutative semirings and the corresponding fuzzy sets are called (R,R*)-fuzzy sets. We use this theory to define (R,R*)-fuzzy relations, lower and upper approximations of (R,R*)-fuzzy sets by (R,R*)-relations, and rough (R,R*)-fuzzy sets, and w

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Kamran, Muhammad, Shahzaib Ashraf, and Muhammad Naeem. "A promising approach for decision modeling with single-valued neutrosophic probabilistic hesitant fuzzy Dombi operators." Yugoslav Journal of Operations Research, no. 00 (2023): 7. http://dx.doi.org/10.2298/yjor230115007s.

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A combination of the single-valued neutrosophic set (SV-NS) and the probabilistic hesitant fuzzy set is the single-valued neutrosophic probabilistic hesitant fuzzy (SV-NPHF) environment (PHFS). It is intended for some unsatisfactory, ambiguous, and contradictory circumstances in which each element has a number of various values that are brought about by the situation?s actuality. The decision-maker can quickly gather and analyze the facts by employing a strategic decision-making technique. On the other hand, uncertainty will be a big part of our daily lives when we are learning. We present a d

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Garg, Harish, Zeeshan Ali, Ibrahim M. Hezam, and Jeonghwan Gwak. "Decision-Making Approach Based on Generalized Aggregation Operators with Complex Single-Valued Neutrosophic Hesitant Fuzzy Set Information." Mathematical Problems in Engineering 2022 (January 10, 2022): 1–20. http://dx.doi.org/10.1155/2022/9164735.

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A strategic decision-making technique can help the decision maker to accomplish and analyze the information in an efficient manner. However, in our real life, an uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm under the single-valued neutrosophic (SVN) environment. The SVN is a powerful way to deal the information in terms of three degrees, namely, “truth,” “falsity,” and “indeterminacy,” which all are considered independent. The main objective of this study is divided into three fol

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Liu, Chun-fang, and Yue-Sheng Luo. "New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making." Pattern Analysis and Applications 22, no. 2 (2017): 417–27. http://dx.doi.org/10.1007/s10044-017-0635-6.

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Mishra, Akansha, and Amit Kumar. "Commentary on “New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making”." Pattern Analysis and Applications 22, no. 3 (2018): 1207–9. http://dx.doi.org/10.1007/s10044-018-0718-z.

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Iampan, Aiyared, S. Yamunadevi, P. Maragatha Meenakshi, and N. Rajesh. "Neutrosophic hesitant fuzzy UP (BCC)-filters." International Journal of Neutrosophic Science 20, no. 1 (2023): 121–33. http://dx.doi.org/10.54216/ijns.210111.

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In this paper, we introduce the concept of neutrosophic hesitant fuzzy UP (BCC)-filters of UP (BCC)-algebras. The characteristic neutrosophic hesitant fuzzy UP (BCC)-filters have also been studied. The relationship between neutrosophic hesitant fuzzy UP (BCC)-filters and their level subsets is provided. The Cartesian product of neutrosophic hesitant fuzzy UP (BCC)-filters is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic hesitant fuzzy UP (BCC)-filters.

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Fahmi, Aliya, Muhammad Aslam, and Saleem Abdullah. "Analysis of migraine in mutlicellular organism based on trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method." International Journal of Biomathematics 12, no. 08 (2019): 1950084. http://dx.doi.org/10.1142/s1793524519500840.

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In this paper, we define a new idea of trapezoidal neutrosophic cubic hesitant fuzzy number based on migraine diseases. We define and the migraine diseases on trapezoidal neutrosophic cubic hesitant fuzzy number and operational laws of trapezoidal neutrosophic cubic hesitant fuzzy number and hamming distance of TrNCHFNs. The new concept of trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method is introduced. Furthermore, we extend MCDM method based on the trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method. Finally, an illustrative example is given to verify and demonstrate the pr

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Iampan, Aiyared, S. Yamunadevi, P. Maragatha Meenakshi, and N. Rajesh. "A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets." International Journal of Neutrosophic Science 20, no. 4 (2023): 78–92. http://dx.doi.org/10.54216/ijns.200406.

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In this paper, we introduce the concepts of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals of UP (BCC)-algebras. The characteristic neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals have also been studied. The relationshipbetween neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals and their level subsets is provided. The Cartesian product of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals is also supplied. Finally, we

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Amin, Fazli, and Aliya Fahmi. "Human Immunodeficiency Virus (HIV) infection model based on triangular neutrosophic cubic hesitant fuzzy number." International Journal of Biomathematics 12, no. 05 (2019): 1950055. http://dx.doi.org/10.1142/s1793524519500554.

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In this paper, we define the basic concept of triangular neutrosophic cubic hesitant fuzzy number and their properties. We develop a triangular neutrosophic cubic hesitant fuzzy ordered weighted arithmetic averaging (TNCHFOWAA) operator and a triangular neutrosophic cubic hesitant fuzzy ordered weighted geometric averaging (TNCHFOWGA) operator to aggregate triangular neutrosophic cubic hesitant fuzzy number (TNCHFN) information and investigate their properties. Furthermore, a multiple attribute decision-making method based on the TNCHFOWAA operator and triangular neutrosophic cubic hesitant fu

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Wang, Li, and Yan-Ling Bao. "Multiple-Attribute Decision-Making Method Based on Normalized Geometric Aggregation Operators of Single-Valued Neutrosophic Hesitant Fuzzy Information." Complexity 2021 (May 5, 2021): 1–15. http://dx.doi.org/10.1155/2021/5580761.

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As a generalization of both single-valued neutrosophic element and hesitant fuzzy element, single-valued neutrosophic hesitant fuzzy element (SVNHFE) is an efficient tool for describing uncertain and imprecise information. Thus, it is of great significance to deal with single-valued neutrosophic hesitant fuzzy information for many practical problems. In this paper, we study the aggregation of SVNHFEs based on some normalized operations from geometric viewpoint. Firstly, two normalized operations are defined for processing SVNHFEs. Then, a series of normalized aggregation operators which fulfil

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Pantachang, Kittikun, Roengchai Tansuchat, and Woraphon Yamaka. "Improving the Accuracy of Forecasting Models Using the Modified Model of Single-Valued Neutrosophic Hesitant Fuzzy Time Series." Axioms 11, no. 10 (2022): 527. http://dx.doi.org/10.3390/axioms11100527.

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Proposed in this study is a modified model for a single-valued neutrosophic hesitant fuzzy time series forecasting of the time series data. The research aims at improving the previously presented single-valued neutrosophic hesitant fuzzy time series (SVNHFTS) model by including several degrees of hesitancy to increase forecasting accuracy. The Gaussian fuzzy number (GFN) and the bell-shaped fuzzy number (BSFN) were used to incorporate the degree of hesitancy. The cosine measure and the single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator were applied to analyze the p

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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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Prabha, S. Krishna. "An Innovative Method to Unravel Neutroshopic Transportation Problem Using Harmonic Mean." International Journal of Fuzzy System Applications 10, no. 3 (2021): 55–66. http://dx.doi.org/10.4018/ijfsa.2021070104.

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As a simplification of fuzzy sets and intuitionistic fuzzy sets to symbolize hesitant, conflicting, and curtailed information about factual world tribulations, neutrosophic sets have been established. There are many existing techniques accessible to solve transportation problems in neutrosophic environment. Among those existing routines, the harmonic mean scheme is applied to obtain the optimal resolution to neutrosophic transportation problem. A numerical example is publicized that the proposed technique gives an improved estimate when compared with the existing techniques.

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Alshayea, Maryam Abdullah, and Kholood Alsager. "M-polar Q-hesitant Anti-fuzzy Set in BCK/BCI-algebras." European Journal of Pure and Applied Mathematics 17, no. 1 (2024): 338–55. http://dx.doi.org/10.29020/nybg.ejpam.v17i1.4952.

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The main objective of this paper is to effectively define a new concept of the fabulous fuzzy set theory that is called m-polar Q-hesitant anti-fuzzy set and apply it to the BCK/BCI-algebras. The m-polar Q-hesitant anti-fuzzy set is an astonishing development of the combination between the m-polar fuzzy set and the Q-hesitant fuzzy set. However, we introduce knowledge of the m-polar Q-hesitant anti-fuzzy subalgebra, m-polar Q-hesitant anti-fuzzy ideal, closed m-polar Q-hesitant anti-fuzzy ideal, m-polar Q hesitant anti-fuzzy commutative ideal, m-polar Q-hesitant anti-fuzzy implicative ideal, a

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Oriza, Sri Delvia, and Nova Noliza Bakar. "HIMPUNAN LEMBUT KABUR HESITANT DAN APLIKASINYA DALAM PENGAMBILAN KEPUTUSAN." Jurnal Matematika UNAND 6, no. 3 (2017): 23. http://dx.doi.org/10.25077/jmu.6.3.23-31.2017.

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Abstract. Molodstov's soft set theory is a newly emerging mathematical tool to handleuncertainty. The soft set theory can be combined with other mathematical theory like asfuzzy set theory. This paper aims to extend hesitant fuzzy set to hesitant fuzzy soft sets.Then, the complement, "AND", "OR", union, intersection operations and De Morgan'slaw are dened on hesitant fuzzy soft sets. Finally, with the help of level soft set, thehesitant fuzzy soft sets are applied to a decision making problem.Kata Kunci: Soft set, Fuzzy set, Hesitant fuzzy set, Hesitant fuzzy soft set, Level softset

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Muhiuddin, G., and Shuaa Aldhafeeri. "Subalgebras and Ideals in BCK/BCI-algebras Based on Uni-hesitant Fuzzy Set Theory." European Journal of Pure and Applied Mathematics 11, no. 2 (2018): 417–30. http://dx.doi.org/10.29020/nybg.ejpam.v11i2.3246.

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In the present paper, the notions of uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals in BCK-algebras and BCI-algebras are introduced, and several related properties are investigated. Characterizations of uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals are considered, and a new uni-hesitant fuzzy algebra (resp. uni-hesitant fuzzy (closed) ideal) from old one is established. Relations between uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals are discussed, and conditions for a uni-hesitant fuzzy ideal to be hesitant closed are provided.

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36

Abbasi, Mohammad Y., Aakif F. Talee, Sabahat A. Khan та Kostaq Hila. "A Hesitant Fuzzy Set Approach to Ideal Theory in Γ-Semigroups". Advances in Fuzzy Systems 2018 (2 вересня 2018): 1–6. http://dx.doi.org/10.1155/2018/5738024.

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We apply the hesitant fuzzy sets theory to Γ-semigroups and provide some characterizations of hesitant fuzzy left (right and bi-) ideals. We introduce the hesitant fuzzy left (resp., right and two-sided) ideal, hesitant fuzzy bi-ideal, and hesitant fuzzy interior ideal in Γ-semigroup and study some properties of them. Finally, a characterization of a simple Γ-semigroup by means of a hesitant fuzzy simple Γ-semigroup is obtained.

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37

Jun, Young Bae, Sun Shin Ahn, and G. Muhiuddin. "Hesitant Fuzzy Soft Subalgebras and Ideals inBCK/BCI-Algebras." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/763929.

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As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories inBCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (closed) hesitant fuzzy soft ideals are introduced, and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra and a (closed) hesitant fuzzy soft ideal are discussed. Condit

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38

Rıdvan, Şahin, and Liu Peide. "Correlation coefficients of single valued neutrosophic hesitant fuzzy sets and their applications in decision making." December 5, 2014. https://doi.org/10.5281/zenodo.34793.

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As a combination of the hesitant fuzzy set (HFS) and the single valued neutrosophic set (SVNS), the single valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real-life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompass the fuzzy set (FS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) and singlevalued neutrosophi

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39

Rıdvan, Sahin, and Piede Liu. "Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making." June 7, 2016. https://doi.org/10.5281/zenodo.235413.

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As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truthhesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS.

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40

Ateeq, Ur Rehman, Gulistan Muhammad, Khan Zahid, and S. Al-Duais Fuad. "A Study of Neutrosophic Cubic Hesitant Fuzzy Hybrid Geometric Aggregation Operators and its Application to Multi Expert Decision Making System." June 29, 2022. https://doi.org/10.5281/zenodo.6774643.

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Hesitancy is an imperative part of belief system. In order to counter the hesitancy in neutrosophic cubic set (NCS), the notion of neutrosophic cubic hesitant fuzzy set (NCHFS) is presented. NCHFS couple NCS with hesitant fuzzy set (HFS). Operational laws in NCHFS are developed with examples. To meet the challenges of decision making problems, neutrosophic cubic hesitant fuzzy geometric (NCHFG) aggregation operators, neutrosophic cubic hesitant fuzzy Einstein geometric (NCHFEG) aggregation operators, neutrosophic cubic hesitant fuzzy hybrid geometric (NCHFHEG) aggregation operators are develop

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41

Rıdvan, Sahin, and Liu Peide. "Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making." January 10, 2016. https://doi.org/10.5281/zenodo.1412550.

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As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truthhesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS.

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42

Peide, Liu, and Shi Lanlan. "The Generalized Hybrid Weighted Average Operator Based on Interval Neutrosophic Hesitant Set and Its Application to Multiple Attribute Decision Making." March 15, 2015. https://doi.org/10.5281/zenodo.32282.

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The Neutrosophic set and Hesitant set are the important tools to describe the fuzzy information, in this paper, we combine the interval neutrosophic sets (INSs) and interval valued hesitant fuzzy sets (IVHFSs), and propose the concept of the interval neutrosophic hesitant fuzzy set (INHFS) in order to use the advantages of them. Then we present the operations and comparison method of INHFS, and develop some new aggregation operators for the interval neutrosophic hesitant fuzzy information, including interval neutrosophic hesitant fuzzy generalized weighted (INHFGWA) operato

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43

Jun, Ye. "Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment." June 12, 2014. https://doi.org/10.5281/zenodo.23139.

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On the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted ge

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44

Peide, Liu, and Shia Lanlan. "The Generalized Hybrid Weighted Average Operator Based on Interval Neutrosophic Hesitant Set and Its Application to Multiple Attribute Decision Making." October 6, 2015. https://doi.org/10.5281/zenodo.34908.

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The Neutrosophic set and Hesitant set are the important and effective tools to describe the uncertain information, in this paper, we combine the interval neutrosophic sets (INSs) and interval valued hesitant fuzzy sets (IVHFSs), and propose the concept of the interval neutrosophic hesitant fuzzy set (INHFS) in order to use the advantages of them.

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45

Pankaj, Kakati, Borkotokey Surajit, Mesiar Radko, and Rahman Saifur. "Interval neutrosophic hesitant fuzzy choquet integral in multicriteria decision making." May 20, 2019. https://doi.org/10.5281/zenodo.3053211.

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We define the Interval Neutrosophic Hesitant Fuzzy Choquet Integral (INHFCI) operator as a useful tool for multicriteria decision making (MCDM). The INHFCI operator generalizes both the interval neutrosophic hesitant fuzzy ordered weighted averaging operator and the interval neutrosophic hesitant fuzzy weighted averaging operator. A modified version of the score function to make comparison among Interval Neutrosophic Hesitant Fuzzy elements is proposed. We develop an approach for multicriteria decision making based on the interval neutrosophic hesitant fuzzy choquet integral operator that appl

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46

Songtao, Shao, Zhang Xiaohong, Bo Chunxin, and SMARANDACHE FLORENTIN. "Neutrosophic Hesitant Fuzzy Subalgebras and Filters in Pseudo-BCI Algebras." September 6, 2018. https://doi.org/10.5281/zenodo.1410343.

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The notions of the neutrosophic hesitant fuzzy subalgebra and neutrosophic hesitant fuzzy filter in pseudo-BCI algebras are introduced, and some properties and equivalent conditions are investigated. The relationships between neutrosophic hesitant fuzzy subalgebras (filters) and hesitant fuzzy subalgebras (filters) is discussed. Five kinds of special sets are constructed by a neutrosophic hesitant fuzzy set, and the conditions for the two kinds of sets to be filters are given. Moreover, the conditions for two kinds of special neutrosophic hesitant fuzzy sets to be neutrosophic hesitant fu

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47

Yongfeng, Pang, and Yang Wei. "Hesitant Neutrosophic Linguistic Sets and Their Application in Multiple Attribute Decision Making." September 11, 2018. https://doi.org/10.5281/zenodo.1413067.

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In this paper, the hesitant neutrosophic linguistic set is first defined by extending a hesitant fuzzy set to accommodate linguistic terms and neutrosophic fuzzy values. Some operational laws are defined for hesitant neutrosophic linguistic fuzzy information.

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48

Ye, Yun, Mahmood Tahir, and Qaisar Khan. "Vector Similarity Measures For Simplied Neutrosophic hesitant fuzzy Set And Their Applications." January 8, 2014. https://doi.org/10.5281/zenodo.233834.

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In this article we present three similarity measures between simplied neutrosophic hesitant fuzzy sets, which contain the concept of single valued neutrosophic hesitant fuzzy sets and interval valued neutrosophic hesitant fuzzy sets, based on the extension of Jaccard similarity measure,

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49

Peide, Liu, and Zhang Lili. "The Extended VIKOR Method for Multiple Criteria Decision Making Problem Based on Neutrosophic Hesitant Fuzzy Set." December 6, 2014. https://doi.org/10.5281/zenodo.34907.

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Neutrosophic hesitant fuzzy set is the generalization of neutrosophic set and the hesitant fuzzy set, and the VIKOR method is an effective decision making method which select the optimal alternative by the maximum ‘‘group utility’’ and minimum of an ‘‘individual regret’’. In this paper, we firstly introduced some operational laws, comparison rules and the Hamming distance measure of neutrosophic hesitant fuzzy set, and detailedly described the decision making steps of VIKOR method.

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50

TAHIR, MAHMOOD, YE JUN, and KHAN QAISAR. "VECTOR SIMILARITY MEASURES FOR SIMPLIFIED NEUTROSOPHIC HESITANT FUZZY SET AND THEIR APPLICATIONS." November 3, 2017. https://doi.org/10.5281/zenodo.1041721.

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In this article we present three similarity measures between simplified neutrosophic hesitant fuzzy sets, which contain the concept of single valued neutrosophic hesitant fuzzy sets and interval valued neutrosophic hesitant fuzzy sets, based on the extension of Jaccard similarity measure, Dice similarity measure and Cosine similarity in the vector space.

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