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Journal articles on the topic 'Measures of fuzziness'

Author: Grafiati

Published: 3 June 2025

Last updated: 1 August 2025

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1

Benvenuti, P., D. Vivona, and M. Divari. "Divergence and fuzziness measures." Soft Computing 4, no. 4 (2000): 210–13. http://dx.doi.org/10.1007/s005000000056.

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2

Sander, W. "On measures of fuzziness." Fuzzy Sets and Systems 29, no. 1 (1989): 49–55. http://dx.doi.org/10.1016/0165-0114(89)90135-8.

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3

Sgarro, Andrea. "Fuzziness measures for fuzzy rectangles." Fuzzy Sets and Systems 34, no. 1 (1990): 39–45. http://dx.doi.org/10.1016/0165-0114(90)90125-p.

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4

Ebanks, Bruce R. "Localizable composable measures of fuzziness." Publicationes Mathematicae Debrecen 52, no. 3-4 (1998): 343–55. http://dx.doi.org/10.5486/pmd.1998.1971.

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5

Dujet, Christiane. "Separation and measures of fuzziness." Fuzzy Sets and Systems 28, no. 3 (1988): 245–62. http://dx.doi.org/10.1016/0165-0114(88)90032-2.

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6

García, Fermin Suárez, and Pedro Gil Álvarez. "Measures of fuzziness of fuzzy events." Fuzzy Sets and Systems 21, no. 2 (1987): 147–57. http://dx.doi.org/10.1016/0165-0114(87)90160-6.

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7

Ban, A. I., and I. Fechete. "The application oft-measures of fuzziness." Korean Journal of Computational & Applied Mathematics 5, no. 1 (1998): 163–69. http://dx.doi.org/10.1007/bf03008945.

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8

Brillouët-Belluot, N., and B. Ebanks. "Localizable composable measures of fuzziness - II." Aequationes Mathematicae 60, no. 3 (2000): 233–42. http://dx.doi.org/10.1007/s000100050151.

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9

MIRANDA, P., E. TORRES, and P. GIL. "DIVERGENCE MEASURES AND AGGREGATION OPERATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 08, no. 06 (2000): 677–90. http://dx.doi.org/10.1142/s0218488500000496.

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In this paper we study the relations between divergence measures of two fuzzy sets and other well-known functions, namely aggregation operations and measures of fuzziness. We will show that these functions can be related. Therefore, we study some consequences of these properties as an application; indeed, we obtain some special cases of divergence measures whenever the aggregation operation fulfils some properties. Another application is the translation of some properties of divergence measures to measures of fuzziness.

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10

Arafat, S., and M. Skubic. "Modeling Fuzziness Measures for Best Wavelet Selection." IEEE Transactions on Fuzzy Systems 16, no. 5 (2008): 1259–70. http://dx.doi.org/10.1109/tfuzz.2008.924326.

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11

Roventa, E. "On a Class of Measures of Fuzziness." Journal of Mathematical Analysis and Applications 175, no. 2 (1993): 337–41. http://dx.doi.org/10.1006/jmaa.1993.1174.

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12

Huang, Liang-Kai, and Mao-Jiun J. Wang. "Image thresholding by minimizing the measures of fuzziness." Pattern Recognition 28, no. 1 (1995): 41–51. http://dx.doi.org/10.1016/0031-3203(94)e0043-k.

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13

Yager, R. "Measures of entropy and fuzziness related to aggregation operators." Information Sciences 82, no. 3-4 (1995): 147–66. http://dx.doi.org/10.1016/0020-0255(94)00030-f.

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14

Zeng, Wenyi, and Hongxing Li. "Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations." International Journal of Intelligent Systems 21, no. 6 (2006): 639–53. http://dx.doi.org/10.1002/int.20152.

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15

Pandey, Sakshi Dev, A. S. Ranadive, Sovan Samanta, and Biswajit Sarkar. "Bipolar-Valued Fuzzy Social Network and Centrality Measures." Discrete Dynamics in Nature and Society 2022 (June 29, 2022): 1–13. http://dx.doi.org/10.1155/2022/9713575.

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The concept of bipolar-valued fuzzy relationships and their role in modeling bipolar-valued fuzzy social networks (BVFSN) are discussed. The goal of this study is to represent the bipolarity and fuzziness that are always present in the relationship between actors. Ranking the most central actors to achieve maximum spreading ability has been a difficult and critical topic thus far. Many centrality measures have been proposed to determine the significance of nodes in the central person detection process. In this article, we proposed two new centrality measures, BF-degree centrality and BF-closen

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16

Verma, Rohit Kumar, and M. Bhagya Laxmi. "Fuzzy Events of Theoretic Characteristics by Employing Pseudo Probabilistic Information Measure of Type Alpha." International Journal of Mathematics and Statistics Invention 13, no. 3 (2025): 24–35. https://doi.org/10.35629/4767-13032435.

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This study first examines a number of widely used fuzziness metrics for discrete fuzzy collections. We present a novel informative measure for discriminating between two fuzzy sets after examining a few of the current fuzzy set measures. We demonstrate that every class fulfills five well-known fuzziness measure axioms and show how a number of current measurements are related to these classes. The non-negative, monotony rising concave functions form the foundation of the multiplicative class. The only functions needed for the additive class are non-negative concave functions. There are also som

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17

Weiss, Brandi A., and William Dardick. "An Entropy-Based Measure for Assessing Fuzziness in Logistic Regression." Educational and Psychological Measurement 76, no. 6 (2016): 986–1004. http://dx.doi.org/10.1177/0013164415623820.

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This article introduces an entropy-based measure of data–model fit that can be used to assess the quality of logistic regression models. Entropy has previously been used in mixture-modeling to quantify how well individuals are classified into latent classes. The current study proposes the use of entropy for logistic regression models to quantify the quality of classification and separation of group membership. Entropy complements preexisting measures of data–model fit and provides unique information not contained in other measures. Hypothetical data scenarios, an applied example, and Monte Car

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18

Pal, Sankar K., and Albert B. Leigh. "Motion Frame Analysis and Scene Abstraction: Discrimination Ability of Fuzziness Measures." Journal of Intelligent and Fuzzy Systems 3, no. 3 (1995): 247–56. http://dx.doi.org/10.3233/ifs-1995-3306.

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19

Patwary, Muhammed J. A., Xi-Zhao Wang, and Dasen Yan. "Impact of Fuzziness Measures on the Performance of Semi-supervised Learning." International Journal of Fuzzy Systems 21, no. 5 (2019): 1430–42. http://dx.doi.org/10.1007/s40815-019-00666-2.

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20

Xu, Yingjun. "On Uncertainty Measures of the Interval-Valued Hesitant Fuzzy Set." Advances in Fuzzy Systems 2023 (June 17, 2023): 1–11. http://dx.doi.org/10.1155/2023/3228324.

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Interval-valued hesitant fuzzy sets (IVHFS), as a kind of decision information presenting tool which is more complicated and more scientific and more elastic, have an important practical value in multiattribute decision-making. There is little research on the uncertainty of IVHFS. The existing uncertainty measure cannot distinguish different IVHFS in some contexts. In my opinion, for an IVHFS, there should exist two types of uncertainty: one is the fuzziness of an IVHFS and the other is the nonspecificity of the IVHFS. To the best of our knowledge, the existing index to measure the uncertainty

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21

Ghosh, Ashish. "Use of fuzziness measures in layered networks for object extraction: a generalization." Fuzzy Sets and Systems 72, no. 3 (1995): 331–48. http://dx.doi.org/10.1016/0165-0114(94)00291-e.

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22

Maung, Ian. "A note on measures of fuzziness applied to nonmonotonic fuzzy propositional logic." Fuzzy Sets and Systems 67, no. 2 (1994): 199–209. http://dx.doi.org/10.1016/0165-0114(94)90088-4.

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23

Yager, Ronald R. "Measures of Information in Generalized Constraints." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 06, no. 06 (1998): 519–32. http://dx.doi.org/10.1142/s0218488598000409.

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The concept of a generalized constraint is introduced and as means of representing different kinds of information. The measurement of the amount of information contained in these constraints is then considered. First we consider possibilistic constraints, those in which the associated variable can take on only one value and show that the measure of specificity provides the appropriate measure. We then provide a measure of information in a fuzzy graph. We next turn to veristic constraints, those in which the associated variable can assume multiple values, and show that the associated measure of

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24

Czogała, E., and J. Łȩski. "Application of entropy and energy measures of fuzziness to processing of ECG signal." Fuzzy Sets and Systems 97, no. 1 (1998): 9–18. http://dx.doi.org/10.1016/s0165-0114(96)00359-4.

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25

Alcalde, C., A. Burusco, and R. Fuentes-González. "Ambiguity and fuzziness measures defined on the set of closed intervals in [0,1]." Information Sciences 177, no. 7 (2007): 1687–98. http://dx.doi.org/10.1016/j.ins.2006.09.006.

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26

Ghosh, A., N. R. Pal, and S. K. Pal. "Self-organization for object extraction using a multilayer neural network and fuzziness measures." IEEE Transactions on Fuzzy Systems 1, no. 1 (1993): 54. http://dx.doi.org/10.1109/tfuzz.1993.390285.

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27

Di Nola, Antonio, Witold Pedrycz, and Salvatore Sessa. "On measures of fuzziness of solutions of fuzzy relation equations with generalized connectives." Journal of Mathematical Analysis and Applications 106, no. 2 (1985): 443–53. http://dx.doi.org/10.1016/0022-247x(85)90121-0.

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28

Klir, George J. "Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like?" Fuzzy Sets and Systems 24, no. 2 (1987): 141–60. http://dx.doi.org/10.1016/0165-0114(87)90087-x.

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29

Yang, Guang, and Meng Yang. "Multistage Warning Indicators of Concrete Dam under Influences of Random Factors." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/6581204.

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Warning indicators are required for the real-time monitoring of the service conditions of dams to ensure safe and normal operations. Warnings are traditionally targeted at some “single point deformation” by deformation measuring points of concrete dam, and scientific warning theory on “overall deformation” measured is nonexistent. Furthermore, the influences of random factors are not considered. In this paper, the overall deformation of the dam was seen as a deformation system of single interactional observation points with different contribution degrees. The spatial deformation entropy, which

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30

Filintas, Agathos, Nikolaos Gougoulias, Nektarios Kourgialas, and Eleni Hatzichristou. "Management Zones Delineation, Correct and Incorrect Application Analysis in a Coriander Field Using Precision Agriculture, Soil Chemical, Granular and Hydraulic Analyses, Fuzzy k-Means Zoning, Factor Analysis and Geostatistics." Water 15, no. 18 (2023): 3278. http://dx.doi.org/10.3390/w15183278.

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The objective of our investigation was to study the various effects of correct and incorrect application of fuzziness exponent, initial parameterization and fuzzy classification algorithms modeling on homogeneous management zones (MZs) delineation of a Coriandrum sativum L. field by using precision agriculture, soil chemical, granular and hydraulic analyses, fuzzy k-means zoning algorithms with statistical measures like the introduced Percentage of Management Zones Spatial Agreement (PoMZSA) (%), factor and principal components analysis (PCA) and geostatistical nutrients GIS mapping. Results o

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31

Le, Bui Hai. "Actuator saturation control of a benchmark structure using hedge-algebras-based fuzzy controller." Vietnam Journal of Mechanics 37, no. 2 (2015): 91–104. http://dx.doi.org/10.15625/0866-7136/37/2/5144.

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In this paper, the problem of actuator saturation control of a benchmark structure using hedge-algebras-based fuzzy controller (HAC) is presented. In HAC, linguistic values of linguistic terms are obtained through semantically quantifying mappings (SQMs) based on few fuzziness parameters of each linguistic variable without using any fuzzy set and inherent order relationships between linguistic values of each linguistic variable are always ensured. Hence, the design of a HAC leads to determining parameters of SQMs, which are fuzziness measures of primary terms and linguistic hedges occurring in

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32

Djebara, Sabiha, Farida Achemine, and Moussa Larbani. "Solving constrained matrix games with fuzzy random linear constraints." Yugoslav Journal of Operations Research, no. 00 (2024): 13. http://dx.doi.org/10.2298/yjor231122013d.

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In real-world games, players may face an uncertain environment where fuzziness and randomness coexist. The main difficulty in dealing with games involving fuzziness and randomness arises when comparing the payoffs. The purpose of this paper is to introduce a new approach to deal with constrained matrix games where the entries of the constraint matrices are LR-fuzzy random variables. Our methodology is based on constructing a new matrix game using the chance constraint method adapted to the probability-possibility measures. First, a specific type of saddle point is defined as an equilibrium sol

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33

Zhang, Yaqiong, Nan He, Yijing Li, Yiyang Chen, Lei Wang, and Yunlong Ran. "Risk Assessment of Water Environment Treatment PPP Projects Based on a Cloud Model." Discrete Dynamics in Nature and Society 2021 (November 11, 2021): 1–15. http://dx.doi.org/10.1155/2021/7027990.

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Risk assessment of public-private partnership projects has been recently acknowledged as a crucial issue in infrastructure projects. Objective assessment of risk status is conducive to the establishment of scientific and reasonable management measures. The particularity of evaluating water environment treatment PPP projects means that random errors in the evaluation index and the threshold fuzziness of evaluation degrees are issues that require attention. This paper uses the Pythagorean fuzzy cloud model to process the randomness and fuzziness of the indicators. This study assessed the risks o

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34

Suman, Shilpa, Dheeraj Kumar, and Anil Kumar. "Fuzzy Based Convolutional Noise Clustering Classifier to Handle the Noise and Heterogeneity in Image Classification." Mathematics 10, no. 21 (2022): 4056. http://dx.doi.org/10.3390/math10214056.

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Conventional Noise Clustering (NC) algorithms do not consider any spatial information in the image. In this study, three algorithms have been presented, Noise Local Information c-means (NLICM) and Adaptive Noise Local Information c-Means (ADNLICM), which use NC as the base classifier, and Noise Clustering with constraints (NC_S), which incorporates spatial information into the objective function of the NC classifier. These algorithms enhance the performance of classification by minimizing the effect of noise and outliers. The algorithms were tested on two study areas, Haridwar (Uttarakhand) an

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35

Maheshwari, Maheshwari, Sapna Thakur, and M. A. Siddiqui. "Generalized Parametric Fuzzy Information Measure." Indian Journal Of Science And Technology 17, no. 37 (2024): 3922–28. http://dx.doi.org/10.17485/ijst/v17i37.2527.

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Objective: To generalize an existing fuzzy information measure and verify its important properties. Methods: Both objective and descriptive methods have been adopted; problem-solving and problem-posing methods have been used. A collection of properties presented by De Luca and Termini is used as a standard for establishing new fuzzy information measures. Findings: This study has analysed the different features of the parametric measure of fuzzy information that we have presented. The suggested fuzzy entropy measure is a legitimate measure of fuzzy information since it meets all necessary requi

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36

Gandhi, C. P. "Continuous & Piecewise Convex Behavior Of Maximum Values Of Some Generalized Measures Of Fuzzy Cross Entropy." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 8, no. 2 (2013): 820–26. http://dx.doi.org/10.24297/ijct.v8i2.3392.

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Consider two fuzzy sets A and B with same supporting points and the corresponding fuzzy vectors and respectively, where each can vary subject to the total fuzziness and each is known to us .In this paper, a comprehensive and straightforward procedure is made available to find the maximum values of some existing measures of generalized fuzzy cross entropy. Further, the continuous and piecewise convex behavior of the values so obtained is also discussed mathematically as well as graphically. Finally, a numerical example is used to illustrate the proposed method.

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37

Mao, Junjun, Yuan Zhao, and Chuang Ma. "A New Type of Compositive Information Entropy for IvIFS and Its Applications." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/7652540.

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We first show the interval-valued intuitionistic fuzzy entropy which reflects intuitionism and fuzziness of interval-valued intuitionistic fuzzy set (IvIFS) based on interval-valued intuitionistic fuzzy cross-entropy. As for intuitionism and fuzziness of IvIFS, we propose interval-valued intuitionistic entropy and interval-valued fuzzy entropy, respectively. Furthermore, we establish the interval-valued span entropy describing the uncertainty of membership degree and nonmembership degree and show some concrete measure formulas. Combining intuitionistic factor, fuzzy factor, and span factor, we

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38

Saqlain, Muhammad, Raiha Imran, and Sabahat Hassan. "TOPSIS Technique of MCDM under Cubic Intuitionistic Fuzzy Soft Set Environment." Scientific Inquiry and Review 7, no. 1 (2023): 33–52. http://dx.doi.org/10.32350/sir.71.03.

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A powerful tool for dealing with ambiguity, attributive values, fuzziness, and inconsistency is the cubic intuitionistic fuzzy soft set. In this paper, multi-criteria group decision-making (MCGDM) technique called extended TOPSIS based on distance and similarity measures is presented. Furthermore, a real-world problem is resolved by applying CIFS-set to support the theoretical visualization. Arguably, the proposed technique works well and has practical uses.

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39

Wei, Cuiping, and Yuzhong Zhang. "Entropy Measures for Interval-Valued Intuitionistic Fuzzy Sets and Their Application in Group Decision-Making." Mathematical Problems in Engineering 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/563745.

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Entropy measure is an important topic in the fuzzy set theory and has been investigated by many researchers from different points of view. In this paper, two new entropy measures based on the cosine function are proposed for intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets. According to the features of the cosine function, the general forms of these two kinds of entropy measures are presented. Compared with the existing ones, the proposed entropy measures can overcome some shortcomings and be used to measure both fuzziness and intuitionism of these two fuzzy sets; as a r

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40

Magdalena, Luis, Carmen Torres-Blanc, Susana Cubillo, and Jesus Martinez-Mateo. "Different Types of Entropy Measures for Type-2 Fuzzy Sets." Axioms 13, no. 8 (2024): 556. http://dx.doi.org/10.3390/axioms13080556.

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In this work, we consider De Luca and Termini’s notion of non-probabilistic entropy, and we extend some entropy-like measures of the degree of fuzziness to type-2 fuzzy sets. With this aim, we first study different entropy measures proposed in the frameworks of fuzzy, intuitionistic, and interval-valued fuzzy sets. Then, we propose three possible novel axiomatizations for entropy in type-2 fuzzy sets. The proposed types of entropy measures evaluate how much a type-2 fuzzy set is non-crisp, non-fuzzy, and non-interval-valued fuzzy. This can also be interpreted as how far a type-2 fuzzy set is f

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41

Manzoor, Saima, Safina Peerzada, and Mirza A. K. Baig. "Application of Generalized Measure of ‘Useful’ R-norm Inaccuracy and Total Ambiguity." International Journal of Intelligent Systems and Applications 13, no. 1 (2021): 17–33. http://dx.doi.org/10.5815/ijisa.2021.01.02.

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In the present paper, we introduce generalized measure of 'useful' R-norm inaccuracy having two parameters and its analogue 'useful' R-norm total ambiguity measure by merging together the concepts of probability, fuzziness, R-norm, 'useful' information and inaccuracy. Along with the basic properties, some other important properties of these two proposed measures are stated. These measures are generalizations of some well-known inaccuracy measures. Further, the monotonic behaviour of the proposed 'useful' R-norm inaccuracy measures is studied and the graphical overview is given. The measure of

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42

Yang, Jie, Taihua Xu, and Fan Zhao. "Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance." Mathematical Problems in Engineering 2018 (August 6, 2018): 1–11. http://dx.doi.org/10.1155/2018/4160905.

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As an extension of Pawlak’s rough sets, rough fuzzy sets are proposed to deal with fuzzy target concept. As we know, the uncertainty of Pawlak’s rough sets is rooted in the objects contained in the boundary region, while the uncertainty of rough fuzzy sets comes from three regions (positive region, boundary region, and negative region). In addition, in the view of traditional uncertainty measures, the two rough approximation spaces with the same uncertainty are not necessarily equivalent, and they cannot be distinguished. In this paper, firstly, a fuzziness-based uncertainty measure is propose

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43

Hirota, Kaoru, Hajime Yoshino, Ming Qiang Xu, Yan Zhu, Xiao Yi Li, and Daigo Horie. "An Application of Fuzzy Theory to the Case-Based Reasoning of the CISG." Journal of Advanced Computational Intelligence and Intelligent Informatics 1, no. 2 (1997): 86–93. http://dx.doi.org/10.20965/jaciii.1997.p0086.

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In legal case-based reasoning (CBR), there exist problems concerning fuzziness, e.g., representation of precedents, their retrieval, and similarity measures. In our proposed fuzzy legal CBR system, the issues and features of precedent are characterized on the basis of the facts of precedent and statute rule. The case rule that is used for interpreting the court judgment, which cannot be obtained from the statute rule directly, is made by experts. Fuzziness is represented by membership functions. Features and case rules, written in terms of Compound Predicate Formula (CPF) and frame, are stored

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44

El Santty, Mohamed Ibrahim, Hegazy Mohamed Zaher, and Naglaa Ragaa Saeid. "Organization Performance Composite Index Under Fuzziness: Application on Manufacturing Organization." Production Engineering Archives 29, no. 1 (2023): 14–22. http://dx.doi.org/10.30657/pea.2023.29.3.

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Abstract Measuring the organization’s performance is essential for continuous improvement and operational excellence. Appropriate organizational measures include multiple dimensions. The relative importance of the multiple dimensions varies depending on the organization’s context and the management team’s visions. The vagueness and ambiguity in the management team’s perspective toward the dimensions and associated sub-indicators show fuzzy property. This paper aims to synthesize the overall organization performance in one aggregated index, engage the management team through index formulation,

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45

Cui, Wen-Hua, and Jun Ye. "Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets." Entropy 20, no. 11 (2018): 844. http://dx.doi.org/10.3390/e20110844.

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In order to quantify the fuzziness in the simplified neutrosophic setting, this paper proposes a generalized distance-based entropy measure and a dimension root entropy measure of simplified neutrosophic sets (NSs) (containing interval-valued and single-valued NSs) and verifies their properties. Then, comparison with the existing relative interval-valued NS entropy measures through a numerical example is carried out to demonstrate the feasibility and rationality of the presented generalized distance-based entropy and dimension root entropy measures of simplified NSs. Lastly, a decision-making

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46

Heikkila, Eric J., Ti-Yan Shen, and Kai-Zhong Yang. "Fuzzy Urban Sets: Theory and Application to Desakota Regions in China." Environment and Planning B: Planning and Design 30, no. 2 (2003): 239–54. http://dx.doi.org/10.1068/b12820.

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This paper outlines a method for using the mathematics of fuzzy sets that is well suited to measure and characterize periurbanizing ( desakota) systems typical of China, Southeast Asia, and other areas experiencing rapid urbanization. Drawing on Kosko's ‘fuzzy hypercube’, we derive three distinct but interdependent measures: (1) extent of urbanization, (2) level of fuzziness, and (3) degree of entropy. The feasibility of the proposed method is demonstrated by using remote sensing data for Ningbo, China.

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47

Tiwari, Pratiksha. "Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making." International Journal of Fuzzy System Applications 10, no. 1 (2021): 64–93. http://dx.doi.org/10.4018/ijfsa.2021010104.

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Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets

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48

Maheshwari, Thakur Sapna, and A. Siddiqui M. "Generalized Parametric Fuzzy Information Measure." Indian Journal of Science and Technology 17, no. 37 (2024): 3922–28. https://doi.org/10.17485/IJST/v17i37.2527.

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Abstract <strong>Objective</strong>: To generalize an existing fuzzy information measure and verify its important properties. <strong>Methods:</strong> Both objective and descriptive methods have been adopted; problem-solving and problem-posing methods have been used. A collection of properties presented by De Luca and Termini is used as a standard for establishing new fuzzy information measures.<strong> Findings:</strong> This study has analysed the different features of the parametric measure of fuzzy information that we have presented. The suggested fuzzy entropy measure

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49

Dombi, József, Jenő Fáró, and Tamás Jónás. "A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers." Mathematics 13, no. 3 (2025): 526. https://doi.org/10.3390/math13030526.

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In group decision making, the knowledge, skills, and experience of the decision-makers may not be at the same level. Hence, the need arises to take into account not only the opinion, but also the relative importance of the opinion of each decision-maker. These relative importance values can be treated as weights. In a group decision making situation, it is not only the weighted aggregate output that matters, but also the weighted measure of the group consensus. Noting that weighted group consensus measures have not yet been intensely studied, in this study, based on well-known requirements for

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Wang, Hongpeng, Caikuan Tuo, Zhiqin Wang, Guoye Feng, and Chenglong Li. "Enhancing Similarity and Distance Measurements in Fermatean Fuzzy Sets: Tanimoto-Inspired Measures and Decision-Making Applications." Symmetry 16, no. 3 (2024): 277. http://dx.doi.org/10.3390/sym16030277.

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Abstract:

Fermatean fuzzy sets (FFSs) serve as a nascent yet potent approach for coping with fuzziness, with their efficacy recently being demonstrated across a spectrum of practical contexts. Nevertheless, the scholarly literature remains limited in exploring the similarity and distance measures tailored for FFSs. The limited existing measures on FFSs sometimes yield counter-intuitive outcomes, which can obfuscate the accurate quantification of similarity and difference among FFSs. This paper introduces a suite of similarity and distance measures tailored for FFSs, drawing inspiration from the Tanimoto

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