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Journal articles on the topic 'Intuitionistic Fuzzy Set (IFS)'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Jeon, Joung Kon, Young Bae Jun, and Jin Han Park. "Intuitionistic fuzzy alpha-continuity and intuitionistic fuzzy precontinuity." International Journal of Mathematics and Mathematical Sciences 2005, no. 19 (2005): 3091–101. http://dx.doi.org/10.1155/ijmms.2005.3091.

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A characterization of intuitionistic fuzzyα-open set is given, and conditions for an IFS to be an intuitionistic fuzzyα-open set are provided. Characterizations of intuitionistic fuzzy precontinuous (resp.,α-continuous) mappings are given.

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Azzam, A. A., Radwan Abu-Gdairi, M. Aldawood, and Abdulaziz M. Alotaibi. "On Intuitionistic Fuzzy Soft Pretopology." International Journal of Analysis and Applications 22 (October 22, 2024): 193. http://dx.doi.org/10.28924/2291-8639-22-2024-193.

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This paper defines the following terms: intuitionistic fuzzy soft (IFS) pretopological space, IFS interior function, IFS pre-open set, IFS pre-closed set, trace of a IFS pretopology, IFS separation axioms, IFS subspace, IFS compactness, IFS connectedness, and some of their properties. In addition, the degree of soft non-vacuity, the soft α-cut, and the IFS preneighbourhood system at a soft point are defined. IFS preneighbourhoods produce IFS pretopologies.

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Robinson, John P., and Henry Amirtharaj E.C. "MAGDM Problems with Correlation Coefficient of Triangular Fuzzy IFS." International Journal of Fuzzy System Applications 4, no. 1 (2015): 1–32. http://dx.doi.org/10.4018/ijfsa.2015010101.

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Correlation coefficient of Intuitionistic Fuzzy Set (IFS), Interval valued IFS, Triangular IFS and Trapezoidal IFS are already present in the literature. This paper proposes the correlation coefficient for Triangular Fuzzy Intuitionistic Fuzzy set (TrFIFS). The method on uncertain Multiple Attribute Group Decision Making (MAGDM) problems based on aggregating intuitionistic fuzzy information is investigated for TrFIFSs. The Triangular Fuzzy Intuitionistic Fuzzy Ordered Weighted Averaging (TrFIFOWA) operator is proposed for TrFIFSs and the Triangular Fuzzy Intuitionistic Fuzzy Ordered Weighted G

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Saritha, Y. "A Study on IFM/IFG/1 Vacation Queueing System with Breakdown, Repair and Server Timeout in (Triangular, Trapezoidal & Pentagon) Intuitionistic Fuzzy Set using α-Cuts". International Journal for Research in Applied Science and Engineering Technology 9, № VIII (2021): 456–61. http://dx.doi.org/10.22214/ijraset.2021.37388.

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In this, we studied and investigated IFM/IFG/1 vacation queueing system/waiting line with server breakdowns, repair and server timeout, “by using (Triangular Trapezoidal and Pentagonal) IF (Intuitionistic Fuzzy) numbers with the application of IFS (Intuitionistic fuzzy set). Here we operate single server vacation queueing system in the following manner; when the system finds empty, the server waits for fixed time ’c’ known as server timeout. At the expiration of this time, if no one arrives into the system, then server takes the vacation. If anyone arrived in the system during the timeout peri

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Atanassov, Krassimir T. "Circular intuitionistic fuzzy sets." Journal of Intelligent & Fuzzy Systems 39, no. 5 (2020): 5981–86. http://dx.doi.org/10.3233/jifs-189072.

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Zishan Anwar, Muhammad, Shahida Bashir, and Muhammad Shabir. "An Efficient Model for the Approximation of Intuitionistic Fuzzy Sets in terms of Soft Relations with Applications in Decision Making." Mathematical Problems in Engineering 2021 (October 22, 2021): 1–19. http://dx.doi.org/10.1155/2021/6238481.

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The basic notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation. This paper proposes an intuitionistic fuzzy rough set (IFRS) model which is a combination of intuitionistic fuzzy set (IFS) and rough set. We approximate an IFS by using soft binary relations instead of fixed binary relations. By using this technique, we get two pairs of intuitionistic fuzzy (IF) soft sets, called the upper approximation and lower approximation with respect to foresets and aftersets. Properties of newly defined rough set model (IFRS) are studied. Similarity rel

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Oktaviani, Dinni Rahma, Muhammad Habiburrohman, and Ijtihadi Kamilia Amalina. "Application of intuitionistic fuzzy sets in determining the major in senior high school." Desimal: Jurnal Matematika 5, no. 3 (2022): 247–54. http://dx.doi.org/10.24042/djm.v5i3.13018.

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Intuitionistic Fuzzy Set (IFS) is useful to construct a model with elaborate uncertainty and ambiguity involved in decision-making. In this paper, the concept relation and operation of intuitionistic fuzzy set and the application in major of senior high school determination using the normalized Euclidean distance method will be reviewed. Some theorem of relation and operation of intuitionistic fuzzy set are proved. In general, to prove the theorem the definition and some basic relation and operation laws of IFS are needed. The distance measure between IFS indicates the difference in grade betw

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Syahwildan, Junda, and Nova Nolza Bakar. "SUATU UKURAN KESAMAAN HIMPUNAN KABUR INTUITIONISTIC BERNILAI INTERVAL DAN APLIKASINYA UNTUK PENGENALAN POLA." Jurnal Matematika UNAND 7, no. 2 (2018): 76. http://dx.doi.org/10.25077/jmu.7.2.76-83.2018.

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Abstrak. Dalam kehidupan sehari-hari biasanya terjadi berbagai kasus yang rumit, di-mana kasus-kasus tersebut banyak sekali mengandung unsur ketidakpastian. Zadeh [6]memperkenalkan suatu teori baru yaitu himpunan kabur (fuzzy set). Kemudian semakinberkembang ilmu pengetahuan, banyak bentuk umum dari fuzzy set yang diusulkan, di-antaranya teori himpunan kabur intuitionistic bernilai interval (IvIFS) yang diusulkanoleh Atanassov, merupakan generalisasi dari teori himpunan kabur bernilai interval(IvFS) dan himpunan kabur intuitionistic (IFS). Salah satu topik penting dalam teorihimpunan kabur yai

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R. Irene Hepzibah and R.Vidhya. "Modified new operations for triangular intuitionistic fuzzy numbers." Malaya Journal of Matematik 2, no. 03 (2014): 301–7. http://dx.doi.org/10.26637/mjm203/017.

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Intuitionistic fuzzy sets (IFS) are a generalization of the concept of fuzzy set. In standard intuitionistic fuzzy arithmetic operations, we have some grievances in subtraction and division operations. In this paper, modified new operations for subtraction and division on triangular intuitionistic fuzzy numbers (TIFNS) are defined. Finally an illustrative example for solving Intuitionistic fuzzy multi-objective linear programming problem (IFMOLPP) using these modified operators is provided.

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Zhang, Zhen Hua, Jing Yu Yang, You Pei Ye, Yong Hu, and Qian Sheng Zhang. "A Novel Dynamic Real Time Controller Based on Score Function of Intuitionistic Fuzzy Sets with Time Parameter." Advanced Materials Research 490-495 (March 2012): 657–63. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.657.

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In this paper, we first present intuitionistic fuzzy sets with time parameter (IFSTP). Compared with intuitionistic fuzzy set (IFS), IFSTP can provide membership function with time parameter, non-membership function with time parameter, and hesitancy function with time parameter. Thus, IFSTP is more suitable for real-time controller than IFS. Then we propose a type of score function according to IFS and IFSTP. The results of pattern recognition show that the score function method is more effective than conventional distance measure method and similarity measure method. Finally, using the score

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Lupianez, Francisco Gallego. "On intuitionistic fuzzy topological spaces." Kybernetes 35, no. 5 (2006): 743–47. https://doi.org/10.1108/03684920610662494.

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In 2000, Wang and He published an important result on the theory of intuitionistic fuzzy sets (IFSs). Indeed, they showed that every IFS may be regarded as an L-fuzzy set for some appropriate lattice L. This paper aims to show that, nevertheless, the results obtained by various authors on intuitionistic fuzzy topological spaces (IFTSs), are not redundant with others for the ordinary fuzzy sense.

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Yusoff, B., A. Kilicman, D. Pratama, and R. Hasni. "Circular q-Rung Orthopair Fuzzy Set and Its Algebraic Properties." Malaysian Journal of Mathematical Sciences 17, no. 3 (2023): 363–78. http://dx.doi.org/10.47836/mjms.17.3.08.

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Circular intuitionistic fuzzy sets (CIFS) are a recent extension of intuitionistic fuzzy sets (IFS) that can handle imprecise membership values effectively. However, its representation is limited to the space under the intuitionistic fuzzy interpretation triangle (IFIT). To address this, a new generalization of CIFS called circular q-rung orthopair fuzzy sets (Cq-ROFS) is proposed, extending the IFIT to cover a larger space of imprecision. Several relations and operations, including algebraic operations for Cq-ROFS are proposed. In addition, modal operators and their properties are then invest

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Chaudhary, Priti, and Tanuj Kumar. "Intuitionistic fuzzy inventory model with quadratic demand rate, time-dependent holding cost and shortages." Journal of Physics: Conference Series 2223, no. 1 (2022): 012003. http://dx.doi.org/10.1088/1742-6596/2223/1/012003.

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Abstract In the present work, we studied an inventory model under quadratic demand rate, linearly time-dependent holding cost, constant deterioration rate and allowed shortages. Intuitionistic fuzzy set (IFS) theory is an efficient tool to reduce the uncertainty that occurs due to hesitation, so we studied the considered model under intuitionistic fuzzy set theory. Further, the model is transformed into an intuitionistic fuzzy inventory model by taking the decision variables as triangular intuitionistic fuzzy numbers. To optimize the best inventory policy under the intuitionistic fuzzy environ

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Tian, Feng, Shousheng Liu, Zeshui Xu, and Qian Lei. "Diagram Illustrations of Aggregation Operations for the Intuitionistic Fuzzy Values." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 24, no. 05 (2016): 631–46. http://dx.doi.org/10.1142/s021848851650029x.

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Atanassov (Intuitionistic fuzzy set, Fuzzy Sets and Systems 20 (1986) 87–96) proposed the intuitionistic fuzzy set (A-IFS) that is a generalization of Zadeh's fuzzy set. The essential elements of an A-IFS are intuitionistic fuzzy values (IFVs), each of which is depicted by a membership degree and a non-membership degree. The existing literature only gives the explanation of the meaning and the aggregation operators of IFVs, which is very hard and non-visualized for us to comprehend. To overcome the above shortcomings, this paper puts forward the diagram method to analyze the structures of the

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Rajafillah, Chaymae, Karim El Moutaouakil, Alina-Mihaela Patriciu, Ali Yahyaouy, and Jamal Riffi. "INT-FUP: Intuitionistic Fuzzy Pooling." Mathematics 12, no. 11 (2024): 1740. http://dx.doi.org/10.3390/math12111740.

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Convolutional Neural Networks (CNNs) are a kind of artificial neural network designed to extract features and find out patterns for tasks such as segmentation, recognizing objects, and drawing up classification. Within a CNNs architecture, pooling operations are used until the number of parameters and the computational complexity are reduced. Numerous papers have focused on investigating the impact of pooling on the performance of Convolutional Neural Networks (CNNs), leading to the development of various pooling models. Recently, a fuzzy pooling operation based on type-1 fuzzy sets was introd

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Anwar, Muhammad Zishan, Shahida Bashir, Muhammad Aslam, and Muhammad Shabir. "Approximations of Intuitionistic Fuzzy Ideals over Dual Spaces by Soft Binary Relations." Journal of Function Spaces 2022 (June 2, 2022): 1–17. http://dx.doi.org/10.1155/2022/3996256.

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The major advantage of this proposed work is to investigate roughness of intuitionistic fuzzy subsemigroups (RIFSs) by using soft relations. In this way, two sets of intuitionistic fuzzy (IF) soft subsemigroups, named lower approximation and upper approximation regarding aftersets and foresets, have been introduced. In RIFSs, incomplete and insufficient information is handled in decision-making problems like symptom diagnosis in medical science. In addition, this new technique is more effective as compared to the previous literature because we use intuitionistic fuzzy set (IFS) instead of fuzz

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Hinduja, Akshay, and Manju Pandey. "A Distance-based Method for Computing Priorities of Intuitionistic Fuzzy Preference Relation and Its Application in AHP." Vision: The Journal of Business Perspective 23, no. 4 (2019): 329–40. http://dx.doi.org/10.1177/0972262919855848.

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The notion of multi-criteria decision-making is regarded as the process of finding the best possible alternative or course of action by decision-makers. Often, it entails handling vague, incomplete and inconsistent information. The intuitionistic fuzzy set (IFS) has been proven more effective than a fuzzy set in handling vagueness and uncertainty. The aim of the article is to incorporate the effectiveness of the IFS with the powerfulness of the analytic hierarchy process (AHP) and develop intuitionistic fuzzy AHP (IF-AHP) to cope with the decision problems involving imprecise and hesitant info

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Pu, Hong Bin, Xi Nan Zeng, and Wei Guang Li. "Configuration Evaluation of Printing Machine Based on Intuitionistic Fuzzy Entropy and TOPSIS." Advanced Materials Research 646 (January 2013): 113–19. http://dx.doi.org/10.4028/www.scientific.net/amr.646.113.

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Servo system plays a critical role in printing and die-cutting machinery of corrugated board (PDCMCB) with electronic line-shafting, and the configuration of servo can contribute to the performance of PDCMCB with electronic line-shafting. The paper presented the evaluation approach of servo configuration with intuitionistic fuzzy set (IFS), intuitionistic fuzzy entropy (IFE ) and technique for order preference by similarity to ideal solution (TOPSIS) to improve the effectiveness and objectivity of servo configuration evaluation of PDCMCB. IFS and IFE were used to obtain criteria weights integr

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Mareay, R., Ibrahim Noaman, Radwan Abu-Gdairi, and M. Badr. "On Covering-Based Rough Intuitionistic Fuzzy Sets." Mathematics 10, no. 21 (2022): 4079. http://dx.doi.org/10.3390/math10214079.

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Intuitionistic Fuzzy Sets (IFSs) and rough sets depending on covering are important theories for dealing with uncertainty and inexact problems. We think the neighborhood of an element is more realistic than any cluster in the processes of classification and approximation. So, we introduce intuitionistic fuzzy sets on the space of rough sets based on covering by using the concept of the neighborhood. Three models of intuitionistic fuzzy set approximation space based on covering are defined by using the concept of neighborhood. In the first and second model, we approximate IFS by rough set based

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Aruna Kumar, S. V., and B. S. Harish. "A Modified Intuitionistic Fuzzy Clustering Algorithm for Medical Image Segmentation." Journal of Intelligent Systems 27, no. 4 (2018): 593–607. http://dx.doi.org/10.1515/jisys-2016-0241.

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Abstract This paper presents a modified intuitionistic fuzzy clustering (IFCM) algorithm for medical image segmentation. IFCM is a variant of the conventional fuzzy C-means (FCM) based on intuitionistic fuzzy set (IFS) theory. Unlike FCM, IFCM considers both membership and nonmembership values. The existing IFCM method uses Sugeno’s and Yager’s IFS generators to compute nonmembership value. But for certain parameters, IFS constructed using above complement generators does not satisfy the elementary condition of intuitionism. To overcome this problem, this paper adopts a new IFS generator. Furt

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Nik Badrul Alam, Nik Muhammad Farhan Hakim, and Nazirah Ramli. "Time Series Forecasting Model Based on Intuitionistic Fuzzy Set via Equal Distribution of Hesitancy De-I-Fuzzification." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 29, no. 06 (2021): 1015–29. http://dx.doi.org/10.1142/s0218488521500458.

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The fuzzy time series forecasting model is a powerful tool in forecasting the time series data. The nature of the fuzzy set exhibits its role in handling the uncertainty of the data. The intuitionistic fuzzy set (IFS) is a generalization of a fuzzy set that makes the forecasting process more precise and accurate. This paper proposes a new fuzzy forecasting model based on IFS via the de-i-fuzzification approach, namely equal distribution of hesitancy. The proposed model consists of four main parts; the fuzzification of historical data; the establishment of the IFS; the de-i-fuzzification; and t

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Rukhsar, Maleha, Kifayat Ullah, Zeeshan Ali, and Abrar Hussain. "Analysis of power aggregation operators through circular intuitionistic fuzzy information and their applications in machine learning analysis." Engineering review 44, no. 4 (2024): 141–59. https://doi.org/10.30765/er.2571.

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Machine learning language is very valuable for depicting different problems, especially computer language, data mining, data sciences, and machine language. The circular intuitionistic fuzzy set (C-IFS) is a flexible approach to fuzzy sets and intuitionistic fuzzy sets. Keep in mind the flexibility of C-IFS, decision-maker used C-IFS to cope with incomplete and redundant human opinions accurately. Furthermore, power operators are used for depicting or aggregating the collection of data into a singleton set. In this manuscript, we explore the power operators for circular intuitionistic fuzzy (C

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WEI, G. W. "SOME GEOMETRIC AGGREGATION FUNCTIONS AND THEIR APPLICATION TO DYNAMIC MULTIPLE ATTRIBUTE DECISION MAKING IN THE INTUITIONISTIC FUZZY SETTING." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 02 (2009): 179–96. http://dx.doi.org/10.1142/s0218488509005802.

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The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy sets", Information and Control8 (1965) 338–356] to deal with fuzziness and uncertainty. In this paper, the dynamic multiple attribute decision making (DMADM) problems with intuitionistic fuzzy information are investigated. The notions of intuitionistic fuzzy variable and uncertain intuitionistic fuzzy variable are defined, and two

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Bharati, S. K., and S. R. Singh. "Interval-Valued Intuitionistic Fuzzy Linear Programming Problem." New Mathematics and Natural Computation 16, no. 01 (2020): 53–71. http://dx.doi.org/10.1142/s1793005720500040.

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In many existing methods of linear programming problem (LPP), precise values of parameters have been used but parameters of LPP are imprecise and ambiguous due to incomplete information. Several approaches and theories have been developed for dealing LPP based on fuzzy set (FS), intuitionistic fuzzy set (IFS) which are characterized by membership degree, membership and non-membership degrees, respectively. It’s interesting to note that single membership and non-membership degrees do not deal properly the state of uncertainty and hesitation. Further, we face a kind of uncertainty occurs a kind

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Verma, Rajkumar. "On intuitionistic fuzzy order-α divergence and entropy measures with MABAC method for multiple attribute group decision-making". Journal of Intelligent & Fuzzy Systems 40, № 1 (2021): 1191–217. http://dx.doi.org/10.3233/jifs-201540.

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The development of information measures associated with fuzzy and intuitionistic fuzzy sets is an important research area from the past few decades. Divergence and entropy are two significant information measures in the intuitionistic fuzzy set (IFS) theory, which have gained wider attention from researchers due to their extensive applications in different areas. In the literature, the existing information measures for IFSs have some drawbacks, which make them irrelevant to use in application areas. In order to obtain more robust and flexible information measures for IFSs, the present work dev

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Garg, Harish, Monica Rani, and S. P. Sharma. "Reliability Analysis of the Engineering Systems Using Intuitionistic Fuzzy Set Theory." Journal of Quality and Reliability Engineering 2013 (September 11, 2013): 1–10. http://dx.doi.org/10.1155/2013/943972.

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The present paper investigates the reliability analysis of industrial systems by using vague lambda-tau methodology in which information related to system components is uncertain and imprecise in nature. The uncertainties in the data are handled with the help of intuitionistic fuzzy set (IFS) theory rather than fuzzy set theory. Various reliability parameters are addressed for strengthening the analysis in terms of degree of acceptance and rejection of IFS. Performance as well as sensitivity analysis of the system parameter has been investigated for accessing the impact of taking wrong combina

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Pratama, Dian, Binyamin Yusoff, Lazim Abdullah, and Adem Kilicman. "The generalized circular intuitionistic fuzzy set and its operations." AIMS Mathematics 8, no. 11 (2023): 26758–81. http://dx.doi.org/10.3934/math.20231370.

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<abstract><p>The circular intuitionistic fuzzy set (<italic>CIFS</italic>) is an extension of the intuitionistic fuzzy set (<italic>IFS</italic>), where each element is represented as a circle in the <italic>IFS</italic> interpretation triangle (<italic>IFIT</italic>) instead of a point. The center of the circle corresponds to the coordinate formed by membership ($ \mathcal{M} $) and non-membership ($ \mathcal{N} $) degrees, while the radius, $ r $, represents the imprecise area around the coordinate. However, despite enhancing the re

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Saleem, Kholoud W., Abir K. Salib, and Abrahim A. A.Tentush. "SEMIGROUPS IN TERMS OF INTUITIONISTIC FUZZY BI-IDEALS." EPH - International Journal of Applied Science 7, no. 1 (2021): 23–30. http://dx.doi.org/10.53555/eijas.v7i1.73.

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Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory. The concept of 'intuitionistic fuzzy set' (IFS) was introduced by Atanassov as a generalization of the concept fuzzy set by gives both a degree of membership and the degree of non-membership. As for fuzzy sets, the degree of membership is a real number between 0 and 1. This is also the case for the degree of non-membership, and further the sum of these two degrees is not greater than 1. Since fuzzy bi-ideal play a

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Lupianez, Francisco Gallego. "On neutrosophic topology." Kybernetes 37, no. 6 (2008): 797–800. https://doi.org/10.1108/03684920810876990.

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Recently, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs). Also, this author defined the notion of neutrosophic topology on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and the neutrosophic topology. This paper aims to show that this is false. 

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XU, Z. S. "MODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, no. 03 (2007): 285–97. http://dx.doi.org/10.1142/s0218488507004686.

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The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by Atanassov [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy Sets", Information and Control 8 (1965) 338–353] to deal with fuzziness and uncertainty. In this paper, we investigate the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs). We f

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Song, Yafei, Xiaodan Wang, Lei Lei, and Aijun Xue. "A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/384241.

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As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity meas

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Lupianez, Francisco Gallego. "On various neutrosophic topologies." Kybernetes 38, no. 6 (2009): 1009–13. https://doi.org/10.1108/03684920910973207.

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Recently, F. Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs) and also defined various notions of neutrosophic topologies on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and neutrosophic topologies on the non-standard interval. The purpose of this paper is to show that this is false.

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Ren, Wenjuan, Zhanpeng Yang, and Xipeng Li. "Distance Measures Based on Metric Information Matrix for Atanassov’s Intuitionistic Fuzzy Sets." Axioms 12, no. 4 (2023): 376. http://dx.doi.org/10.3390/axioms12040376.

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The metric matrix theory is an important research object of metric measure geometry and it can be used to characterize the geometric structure of a set. For intuitionistic fuzzy sets (IFS), we defined metric information matrices (MIM) of IFS by using the metric matrix theory. We introduced the Gromov–Hausdorff metric to measure the distance between any two MIMs. We then constructed a kind of metric information matrix distance knowledge measure for IFS. The proposed distance measures have the ability to measure the distance between two incomplete intuitionistic fuzzy sets. In order to reduce th

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Dymova, Ludmila, Krzysztof Kaczmarek, Pavel Sevastjanov, Łukasz Sułkowski, and Krzysztof Przybyszewski. "An Approach to Generalization of the Intuitionistic Fuzzy Topsis Method in the Framework of Evidence Theory." Journal of Artificial Intelligence and Soft Computing Research 11, no. 2 (2021): 157–75. http://dx.doi.org/10.2478/jaiscr-2021-0010.

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Abstract A generalization of technique for establishing order preference by similarity to the ideal solution (TOPSIS) in the intuitionistic fuzzy setting based on the redefinition of intuitionistic fuzzy sets theory (A IFS) in the framework of Dempster-Shafer theory (DST) of evidence is proposed. The use of DST mathematical tools makes it possible to avoid a set of limitations and drawbacks revealed recently in the conventional Atanassov’s operational laws defined on intuitionistic fuzzy values, which may produce unacceptable results in the solution of multiple criteria decision-making problem

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Dutta, Palash. "Decision Making in Medical Diagnosis via Distance Measures on Interval Valued Fuzzy Sets." International Journal of System Dynamics Applications 6, no. 4 (2017): 63–83. http://dx.doi.org/10.4018/ijsda.2017100104.

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The uncertain and sometimes vague, imprecise nature of medical documentation and information make the field of medical diagnosis is the most important and interesting area for applications of fuzzy set theory (FST), intuitionistic fuzzy set (IFS) and interval valued fuzzy set (IVFS). In this present study, first resemblance between IFS and IVFS has been established along with reviewed some existing distance measures for IFSs. Later, an attempt has been made to derive distance measures for IVFSs from IFSs and establish some properties on distance measures of IVFSs. Finally, medical diagnosis ha

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Ramadhani, Hafizah, and Yanita . "UKURAN ENTROPI DAN UKURAN KESAMAAN HIMPUNAN KABUR INTUISIONISTIK BERNILAI INTERVAL." Jurnal Matematika UNAND 7, no. 2 (2018): 61. http://dx.doi.org/10.25077/jmu.7.2.61-69.2018.

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Abstrak. Dalam kehidupan tidak semua masalah dapat dinilai salah atau benarnya,karena ada berbagai jenis masalah yang mengandung unsur ketidakpastian. L.A. Zadehmemperkenalkan teori himpunan kabur (fuzzy set) yang dapat menjadi alternatif yanglebih baik dalam mencari solusi permasalahan yang mengandung ketidakpastian. Ke-mudian banyak bentuk umum dari himpunan kabur (fuzzy set/FS) yang diusulkandan dikembangkan, diantaranya ada himpunan kabur intuisionistik (Intuitionistic FuzzySets/IFS), himpunan kabur bernilai interval (Interval Valued Fuzzy Sets/IVFS), danhimpunan kabur intuisionistik berni

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Lupianez, Francisco Gallego. "On neutrosophic sets and topology." Procedía Computer Science 120 (June 5, 2017): 975–82. https://doi.org/10.1016/j.procs.2018.01.090.

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Recently, F.Smarandache generalized the Atanassov’s intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets. Also, This author defined the notion of neutrosophic topology on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology on an IFS and the neutrosophic topology. We show in this work that this is false.

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Farhadinia, Bahram, and Francisco Chiclana. "Extended Fuzzy Sets and Their Applications." Mathematics 9, no. 7 (2021): 770. http://dx.doi.org/10.3390/math9070770.

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This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is def

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Thakur, Parul, Bartłomiej Kizielewicz, Neeraj Gandotra, et al. "A New Entropy Measurement for the Analysis of Uncertain Data in MCDA Problems Using Intuitionistic Fuzzy Sets and COPRAS Method." Axioms 10, no. 4 (2021): 335. http://dx.doi.org/10.3390/axioms10040335.

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In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance. The Complex Proportional Assessment (COPRAS) method identifies the preferences and ranking of decisional variants. It also allows for a more comprehensive analysis of complex decision-making problems, where many opposite criteria are observed. This

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Ouhibi, Abir, and Hela Moalla Frikha. "An intuitionistic fuzzy extension of the CODAS-SORT method." Multiple Criteria Decision Making 16 (2021): 110–21. http://dx.doi.org/10.22367/mcdm.2021.16.06.

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Currently, an important issue in multi-criteria decision-making (MCDM) problems are vagueness and lack of precision of decision- -making information because of insufficient data and incapability of the decision maker to process the information. Intuitionistic fuzzy sets (IFS) are a solution to eliminate the vagueness and the uncertainty. While fuzzy sets (FS) deal with ambiguity and vagueness problem, IFSs have more advantages. Moreover, the CODAS-SORT method cannot handle the uncertainty and ambiguity of information provided by human judgments. The aim of this study is to develop an IF extens

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Joshi, Rajesh, and Satish Kumar. "Jensen-Tsalli’s Intuitionistic Fuzzy Divergence Measure and Its Applications in Medical Analysis and Pattern Recognition." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 27, no. 01 (2019): 145–69. http://dx.doi.org/10.1142/s0218488519500077.

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Vagueness in scientific studies poses a challenge. Intuitionistic Fuzzy Set (IFS) theory has emerged as a powerful and flexible tool to counter such challenge. So, there is a need to develop such measures which can not only measure the vagueness but also quantify the differences in underlying IFSs. The aim of this communication is to introduce one such divergence measure called Intuitionistic Fuzzy Jensen-Tsalli Divergence measure in the settings of IFS theory. The presence of parameters makes the proposed divergence measure flexible and competent for applications. Besides discussing some of i

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Haribabu, Maruturi, and Velmathi Guruviah. "An Improved Multimodal Medical Image Fusion Approach Using Intuitionistic Fuzzy Set and Intuitionistic Fuzzy Cross-Correlation." Diagnostics 13, no. 14 (2023): 2330. http://dx.doi.org/10.3390/diagnostics13142330.

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Multimodal medical image fusion (MMIF) is the process of merging different modalities of medical images into a single output image (fused image) with a significant quantity of information to improve clinical applicability. It enables a better diagnosis and makes the diagnostic process easier. In medical image fusion (MIF), an intuitionistic fuzzy set (IFS) plays a role in enhancing the quality of the image, which is useful for medical diagnosis. In this article, a new approach to intuitionistic fuzzy set-based MMIF has been proposed. Initially, the input medical images are fuzzified and then c

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Robinson, P. John, and P. Wilson Arul Prakash. "Application of Improved Class of Weighted Averaging Operators in Intuitionistic Fuzzy Ann Guided MAGDM E-Commerce Problems." Indian Journal Of Science And Technology 17, no. 29 (2024): 3026–36. http://dx.doi.org/10.17485/ijst/v17i29.1872.

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Objectives: To propose a novel and improvised Artificial Neural Network (ANN) technique to solve Multiple Attribute Group Decision Making (MAGDM) problems and an improved class of Aggregation operators for combining Intuitionistic Fuzzy Set (IFS) matrices for the ANN algorithm. Methods: A novel class of improved aggregation operators namely the Improved Intuitionistic Fuzzy Weighted Arithmetic Averaging (IM-IFWAA) operator and the Improved Intuitionistic Fuzzy Ordered Weighted Averaging (IM-IFOWA) operator are proposed in this work. The proposed improved class of aggregation operators will agg

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D.Nagarajan, D., A. A.Rajkumar, D. D.Nagarajan, and Broumi Said. "Shortest Path Problem on Neutrosophic Environment using Modified Circle Breaking Algorithm." International Journal of Neutrosophic Science 18, no. 4 (2022): 385–94. http://dx.doi.org/10.54216/ijns.180432.

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Neutrosophic set (NS) is generalization of Intuitionistic Fuzzy Set(IFS) and Fuzzy Set (FS) where Neutrosophic Set(NS) is the collection of Membership, Non-Membership, Indeterminacy Membership of the constituent element. This paper includes the modified circle breaking techinque which is used to evaluate the Shortest Path Problem in which edge weight are protrayed in Single Valued Linear Heptagonal Neutrosophic Number (SVLHNN) and an numerical illustration is given for the efficiency of the given algorithm.

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Parimala, Mani, Arwa Almunajam, Muthusamy Karthika, and Ibtesam Alshammari. "Pythagorean Fuzzy Digraphs and Its Application in Healthcare Center." Journal of Mathematics 2021 (September 6, 2021): 1–6. http://dx.doi.org/10.1155/2021/5459654.

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The notion of fuzzy set is introduced to deal with uncertainty, whereas the conventional sets are used for certainty. The extensions of fuzzy set theory such as intuitionistic fuzzy set (IFS) and Pythagorean fuzzy sets (PyFS) were introduced to overcome drawbacks in fuzzy theory. Fuzzy graph structure is used to deal with the uncertainty in a network and describe its relation on the nonempty vertex set. One of the extensions of intuitionistic fuzzy digraph (IFDG) is Pythagorean fuzzy digraph (PyFDG). IFDG cannot handle if the sum of degree of acceptance and degree of rejection for an arc weigh

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Bakhshizadeh, Alireza, Abdolreza Yazdani-Chamzini, Masoumeh Latifi Benmaran, Jonas Šaparauskas, and Zenonas Turskis. "EXTRACTING AND PRIORITIZING THE ATTRACTIVENESS PARAMETERS OF SHOPPING CENTERS UNDER INTUITIONISTIC FUZZY NUMBERS." International Journal of Strategic Property Management 28, no. 2 (2024): 130–42. http://dx.doi.org/10.3846/ijspm.2024.21376.

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Shopping center plays an important role in distribution system and marketing. These canters provide an appropriate atmosphere for customers; so that, the customers achieve the best service within a short time. However, there is an intense competition among shopping centers to attract more customers for increasing the profit. Therefore, a powerful model assists authorities in identifying the critical competitive aspects and directing their efforts toward performance improvement. However, a number of strategies have been developed to identify the most relevant components. The Delphi technique un

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Yan, Zhijia, Wenting Yang, Xiaoling Huang, Xiangrong Shi, and Wenyu Zhang. "A Reputation-Enhanced Hybrid Approach for Supplier Selection with Intuitionistic Fuzzy Evaluation Information." Mathematics 7, no. 3 (2019): 298. http://dx.doi.org/10.3390/math7030298.

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Selecting optimal suppliers in fuzzy environments has become a major challenge for enterprises. Reputation plays an important role in the process of supplier selection because of its fuzziness, dynamicity, and transitivity. In this study, we first present a novel intuitionistic fuzzy sets (IFS)-hyperlink-induced topic search (HITS) method that combines the intuitionistic fuzzy set with the hyperlink-induced topic search (HITS) algorithm to extend the ability of processing fuzzy information in order to obtain post-propagated reputation values of suppliers. Then, we employ the dynamic intuitioni

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Gandotra, Neeraj, Bartłomiej Kizielewicz, Abhimanyu Anand, et al. "New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis." Entropy 23, no. 12 (2021): 1600. http://dx.doi.org/10.3390/e23121600.

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The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The

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Ye, Jun, Shigui Du, and Rui Yong. "Similarity Measures between Intuitionistic Fuzzy Credibility Sets and Their Multicriteria Decision-Making Method for the Performance Evaluation of Industrial Robots." Mathematical Problems in Engineering 2021 (January 19, 2021): 1–10. http://dx.doi.org/10.1155/2021/6630898.

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To enhance the credibility level/measure of an intuitionistic fuzzy set (IFS), this study proposes the notion of an intuitionistic fuzzy credibility set (IFCS) to express the hybrid information of a pair of a membership degree and a credibility degree and a pair of a nonmembership degree and a credibility degree. Next, we propose generalized distance and similarity measures between IFCSs and then further generalize the weighted generalized distance measure of IFCSs to the trigonometric function-based similarity measures of IFCSs, including the cosine, sine, tangent, and cotangent similarity me

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P, John Robinson, and Wilson Arul Prakash P. "Application of Improved Class of Weighted Averaging Operators in Intuitionistic Fuzzy Ann Guided MAGDM E-Commerce Problems." Indian Journal of Science and Technology 17, no. 29 (2024): 3026–36. https://doi.org/10.17485/IJST/v17i29.1872.

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Abstract <strong>Objectives:</strong> To propose a novel and improvised Artificial Neural Network (ANN) technique to solve Multiple Attribute Group Decision Making (MAGDM) problems and an improved class of Aggregation operators for combining Intuitionistic Fuzzy Set (IFS) matrices for the ANN algorithm. <strong>Methods:</strong> A novel class of improved aggregation operators namely the Improved Intuitionistic Fuzzy Weighted Arithmetic Averaging (IM-IFWAA) operator and the Improved Intuitionistic Fuzzy Ordered Weighted Averaging (IM-IFOWA) operator are proposed in this work. The

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