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Journal articles on the topic 'Fuzzy sets (FS)'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

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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Liu, Xiaoting, Huang Shan, and Kefeng Li. "Triangular Norm based Invex Fuzzy Sets." Advances in Engineering Technology Research 1, no. 1 (2022): 198. http://dx.doi.org/10.56028/aetr.1.1.198.

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Zadeh’s convex fuzzy set (CFS for short) have two important properties, (1) fuzzy set (FS for short) is convex iff its cuts are convex, (2) arbitrary intersection of CFSs is a CFS. Generalized CFS, named-invex FS is introduced. Meanwhile, two properties above are generalized into-invex FS.

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Abuhijleh, Eman A., Mourad Massa’deh, Amani Sheimat, and Abdulazeez Alkouri. "Complex Fuzzy Groups Based on Rosenfeld’s Approach." WSEAS TRANSACTIONS ON MATHEMATICS 20 (August 4, 2021): 368–77. http://dx.doi.org/10.37394/23206.2021.20.38.

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Complex fuzzy sets (CFS) generalize traditional fuzzy sets (FS) since the membership functions of CFS reduces to the membership functions of FS. FS values are always at [0, 1], unlike CFS which has values in the unit disk of C. This paper merges notion and concept in group theory and presents the notion of a complex fuzzy subgroup of a group. This proposed idea represents a more general and better optional mathematical tool as one of the approaches in the fuzzy group. However, this research defines the notion of complex fuzzy subgroupiod, complex fuzzy normal subgroup, and complex fuzzy left(r

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Chaudhary, Gopal, Amena .., and J. A. Lobo Marques. "Sentiment Analysis from Social Media Tweets Using Single-Valued Neutrosophic Sets and Fuzzy Sets." Journal of Neutrosophic and Fuzzy Systems 5, no. 2 (2023): 51–59. http://dx.doi.org/10.54216/jnfs.050205.

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In the last ten years, exciting work at the intersection of several academic disciplines has been done in the areas of view mining and sentiment analysis. The sheer amount of social media text that is now accessible for sentiment analysis has expanded by a factor of multiples with the development of social media networks, resulting in the creation of a formidable corpus. An examination of the sentiments included within tweets has been performed to measure the general public's perspective on breaking news, as well as a variety of laws, regulations, individuals, and political movements. In the a

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Liu, Sicong, and Rui Cai. "Uncertainty of Interval Type-2 Fuzzy Sets Based on Fuzzy Belief Entropy." Entropy 23, no. 10 (2021): 1265. http://dx.doi.org/10.3390/e23101265.

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Interval type-2 fuzzy sets (IT2 FS) play an important part in dealing with uncertain applications. However, how to measure the uncertainty of IT2 FS is still an open issue. The specific objective of this study is to present a new entropy named fuzzy belief entropy to solve the problem based on the relation among IT2 FS, belief structure, and Z-valuations. The interval of membership function can be transformed to interval BPA [Bel,Pl]. Then, Bel and Pl are put into the proposed entropy to calculate the uncertainty from the three aspects of fuzziness, discord, and nonspecificity, respectively, w

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Dai, Songsong. "Quaternionic Fuzzy Sets." Axioms 12, no. 5 (2023): 490. http://dx.doi.org/10.3390/axioms12050490.

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A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set of quaternions with modulus less than or equal to one, of which the real and quaternionic imaginary parts can be used for four different features. A discussion is made on the intuitive interpretation of quaternion-valued membership grades and the possible applications of QFSs. Several operations, including quaternionic fuzzy complement, union, int

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Ayub, Saba, Muhammad Shabir, Muhammad Riaz, Faruk Karaaslan, Dragan Marinkovic, and Djordje Vranjes. "Linear Diophantine Fuzzy Rough Sets on Paired Universes with Multi Stage Decision Analysis." Axioms 11, no. 12 (2022): 686. http://dx.doi.org/10.3390/axioms11120686.

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Rough set (RS) and fuzzy set (FS) theories were developed to account for ambiguity in the data processing. The most persuasive and modernist abstraction of an FS is the linear Diophantine FS (LD-FS). This paper introduces a resilient hybrid linear Diophantine fuzzy RS model (LDF-RS) on paired universes based on a linear Diophantine fuzzy relation (LDF-R). This is a typical method of fuzzy RS (F-RS) and bipolar FRS (BF-RS) on two universes that are more appropriate and customizable. By using an LDF-level cut relation, the notions of lower approximation (L-A) and upper approximation (U-A) are de

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Al-shami, Tareq M., Salem Saleh, Alaa M. Abd El-latif, and Abdelwaheb Mhemdi. "Novel categories of spaces in the frame of fuzzy soft topologies." AIMS Mathematics 9, no. 3 (2024): 6305–20. http://dx.doi.org/10.3934/math.2024307.

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<abstract><p>In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $ FS\delta $-separation and $ FS\delta $-regularity axioms by using fuzzy soft $ \delta $-open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the $ FS\delta $-separation and $ FS\delta $

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Zhang, Zhen Hua, Yong Hu, and Xiao Hua Ke. "A Dynamic Fuzzy Sets Method and its Application to Pattern Recognition." Applied Mechanics and Materials 263-266 (December 2012): 2602–5. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.2602.

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We present a novel dynamic fuzzy sets (DFS) method, which is the generalization of fuzzy sets (FS) and the dynamization of interval-valued intuitionistic fuzzy sets (IVIFS). First, by analyzing the degree of hesitancy, we propose a DFS model from IVIFS. Second, we introduce the distance measure of DFS. Finally, a pattern recognition example is given to demonstrate the application of DFS, and the experimental results show that the DFS method is more effective than some IVIFS methods.

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HEIDARZADE, ARMAGHAN, NEZAM MAHDAVI-AMIRI, and IRAJ MAHDAVI. "A NEW DISTANCE FOR INTERVAL TYPE-2 FUZZY SETS WITH AN APPLICATION TO CLUSTERING." International Journal of Computational Intelligence and Applications 13, no. 04 (2014): 1450020. http://dx.doi.org/10.1142/s1469026814500205.

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Type-2 fuzzy sets are generalizations of ordinary fuzzy sets, in which membership grades are characterized by fuzzy membership functions. Here, a problem of finding distance between two interval type-2 fuzzy sets (IT2-FSs) was considered. Based on a new definition of centroid for an IT2-FS, a formulation for calculation of the distance between two IT2-FSs was introduced, and an algorithm was explained to obtain it. The proposed distance formula was incorporated in Yang and Shih's clustering algorithm to reach a clustering method for interval type-2 fuzzy data sets. The applicability of the pro

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Zheng, Gao, and Shi Wei Yin. "An Entropy of Interval Type-2 Fuzzy Sets." Applied Mechanics and Materials 321-324 (June 2013): 1999–2003. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.1999.

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The entropy shows the fuzzy degree of a fuzzy set (FS) and can be used in various areas. Aiming at the characteristics of the fuzzy entropy and type-2 fuzzy sets (IT2 FSs), we introduce a new entropy of IT2 FSs in this paper. At first, we select an axiomatic definition for it. Then, considering a fact that the operations of IT2 FSs depend on the upper membership functions (UMFs) and lower membership functions (LMFs), we propose a calculation formula and verify it accords with the four axioms of the selected definition. Finally, we use an example to illuminate its reasonable performance.

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Guo, Wenping, Lvqing Bi, Bo Hu, and Songsong Dai. "Cosine Similarity Measure of Complex Fuzzy Sets and Robustness of Complex Fuzzy Connectives." Mathematical Problems in Engineering 2020 (July 22, 2020): 1–9. http://dx.doi.org/10.1155/2020/6716819.

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Complex fuzzy set (CFS), as a generalization of fuzzy set (FS), is characterized by complex-valued membership degrees. By considering the complex-valued membership degree as a vector in the complex unit disk, we introduce the cosine similarity measures between CFSs. Then, we investigate some invariance properties of the cosine similarity measure. Finally, the cosine similarity measure is applied to measure the robustness of complex fuzzy connectives and complex fuzzy inference.

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Parimala, Mani, and Saeid Jafari. "Spherical Linear Diophantine Fuzzy Graphs: Unleashing the Power of Fuzzy Logic for Uncertainty Modeling and Real-World Applications." Axioms 13, no. 3 (2024): 153. http://dx.doi.org/10.3390/axioms13030153.

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The theory of spherical linear Diophantine fuzzy sets (SLDFS) boasts several advantages over existing fuzzy set (FS) theories such as Picture fuzzy sets (PFS), spherical fuzzy sets (SFS), and T-spherical fuzzy sets (T-SFS). Notably, SLDFS offers a significantly larger portrayal space for acceptable triplets, enabling it to encompass a wider range of ambiguous and uncertain knowledge data sets. This paper delves into the regularity of spherical linear Diophantine fuzzy graphs (SLDFGs), establishing their fundamental concepts. We provide a geometrical interpretation of SLDFGs within a spherical

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Yasin Ali, Md, and Abedul Hadi. "Correlation Coefficients of Complex Fuzzy Sets and Their Application." GANIT: Journal of Bangladesh Mathematical Society 44, no. 2 (2024): 28–38. https://doi.org/10.3329/ganit.v44i2.78530.

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Complex fuzzy set (CFS) is an extension of the fuzzy set (FS) which can deal with ambiguity by allowing a complex-valued membership degree of an element of a universal set. A host of researchers studied the complex fuzzy sets in theoretical and practical due to their amplitude term and phase term membership degrees. At present, various applications of fuzzy correlation and correlation coefficients have emerged by numerous researchers. But most of the works are related to real fuzzy data. In this article, we introduce the concept of the correlation coefficient of the complex fuzzy sets and some

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Mahmood, Tahir, Ubaid Ur Rehman, Zeeshan Ali, and Tariq Mahmood. "Hybrid vector similarity measures based on complex hesitant fuzzy sets and their applications to pattern recognition and medical diagnosis." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 625–46. http://dx.doi.org/10.3233/jifs-200418.

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Fuzzy set (FS) theory is one of the most important tool to deasl with complicated and difficult information in real-world. Now FS has many extensions and hesitant fuzzy set (HFS) is one of them. Further generalization of FS is complex fuzzy set (CFS), which contains only the membership grade, whose range is unit disc instead of [0, 1]. The aim of this paper is to present the idea of complex hesitant fuzzy set (CHFS) and to introduce its basic properties. Basically, CHFS is the combination of CFS and HFS to deal with two dimension information in a single set. Further, the vector similarity meas

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Al-Labadi, Manal, Shuker Khalil, Ahmed Naji Hassan, and Wasim Audeh. "New structure of bipolar fuzzy rho-ideals in rho-algebraic semigroups." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 4-A (2025): 1145–51. https://doi.org/10.47974/jdmsc-2120.

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In algebraic semigroups when we deal with classical sets every ρ-ideal does not have to be ρ–-ideal. As a result, it is demonstrated in this study with their expansion in some kinds of sets as fuzzy set (FS) & bipolar fuzzy set (BFS) is held. Also, a new construction of (BFS) is demonstrated in ρ-algebras. The study of novel notions such as ρ-semigroup (ρ-SG), ρ-subsemigroup (ρ-SSG), ρ–-ideal semigroup (ρ–-ISG), ρ-ideal semigroup (ρ-ISG), and other are given. Moreover, their extensions in fuzzy logic (FL) using Bipolar fuzzy are introduced. Additionally, a number of basic characteristics o

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Tehreem, Abdu Gumaei, and Amjad Hussain. "New Operators of Cubic Picture Fuzzy Information with Applications." Journal of Mathematics 2021 (May 19, 2021): 1–16. http://dx.doi.org/10.1155/2021/9938181.

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The researcher has been facing problems while handling imprecise and vague information, i.e., the problems of networking, decision-making, etc. For encountering such complicated data, the notion of fuzzy sets (FS) has been considered an influential tool. The notion was extended to its generalizations by a number of researchers in different ways which helps to understand and assess even more complex issues. This article characterizes imprecision with four kinds of values of membership. In this work, we aim to define and examine cubic picture fuzzy sets and give an application on averaging aggre

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Dai, Songsong, Lvqing Bi, and Bo Hu. "Distance Measures between the Interval-Valued Complex Fuzzy Sets." Mathematics 7, no. 6 (2019): 549. http://dx.doi.org/10.3390/math7060549.

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Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [ 0 , 1 ] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems i

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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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Abdullah, Walid. "A Study of Neutrosophic Sets and Deep Learning Models for Breast Cancer Classification." Multicriteria Algorithms with Applications 3 (April 28, 2024): 50–59. http://dx.doi.org/10.61356/j.mawa.2024.3237.

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Medical image classification and detection using artificial intelligence (AI) can help enhance medical care services. Unfortunately, most medical image modalities suffer from some noise and uncertainty, which decreases the performance of disease detection and classification. Neutrosophic sets (NS) can handle uncertainty data within medical images. NS can present images into three subsets: true (T), indeterminacy (I), and fuzzy sets (FS). In this study, we investigate the performance of deep learning (DL) models under the NS domain for breast cancer classification. The crisp image domain is con

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Ullah, Kifayat, T. Mahmood, N. Jan, S. Broumi, and Q. Khan. "On Bipolar-Valued Hesitant Fuzzy Sets and Their Applications in Multi-Attribute Decision Making." Nucleus 55, no. 2 (2018): 93–101. https://doi.org/10.71330/thenucleus.2018.417.

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In this manuscript, a novel structure of bipolar-valued hesitant fuzzy set (BPVHFS) is proposed as ageneralization of fuzzy set (FS). The basic set theoretic operations of BPVHFSs are defined and theirrelated results are studied. Based on the basic operations, some aggregation operators for BPVHFSsare developed and their fitness is verified using principle of mathematical induction. The multiattributedecision making (MADM) is established in the framework of BPVHFSs and a numericalexample is provided to illustrate the process. The article ended with some concluding remarks alongwith some future

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Bhatia, Mansi, H. D. Arora, and Anjali Naithani. "Some New Correlation Coefficient Measures Based on Fermatean Fuzzy Sets using Decision Making Approach in Pattern Analysis and Supplier Selection." International Journal of Mathematical, Engineering and Management Sciences 8, no. 2 (2023): 245–63. http://dx.doi.org/10.33889/ijmems.2023.8.2.015.

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Fermatean fuzzy set (FFS) is an effective tool to depict expert reasoning information in the decision‐making process than fuzzy sets (FS), intuitionistic fuzzy sets (IFS), and Pythagorean fuzzy sets (PFS). Keeping in mind the importance of correlation coefficient and application in medical diagnosis, decision making and pattern recognition, several studies on correlation coefficient measures have been proposed in the literature. As there does not exist any study concerning correlation coefficient measures for FFS, in this communication, we propose novel entropy-correlation measures for Fermate

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R., Srinivasan, and Rajesh K. "A NOTE ON PROPERTIES OF TEMPORAL INTUITIONISTIC FUZZY SETS OF SECOND TYPE." International Journal of Multidisciplinary Research and Modern Education 2, no. 2 (2016): 378–83. https://doi.org/10.5281/zenodo.174317.

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<em>Fuzzy Sets are generalized from the notion of classical (crisp) sets (Zadeh1965) [6]. A fuzzy subset A of E can be characterized with a membership function µ<sub>A</sub>: E → [0, 1]. Krassimir T. Atanassov further generalized fuzzy sets into Intuitionistic Fuzzy Sets (IFSs) in which non- membership function ν<sub>A </sub>: E → [0, 1] is also considered [1]. Further he extended IFSs into Temporal Intuitionistic Fuzzy Sets (TIFSs) in which time- moments are also taken into consideration. TIFSs are useful in time-based mathematical modeling. In this paper the present authors further introduce

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R., Srinivasan, and Rajesh K. "A NOTE ON PROPERTIES OF TEMPORAL INTUITIONISTIC FUZZY SETS OF SECOND TYPE." International Journal of Multidisciplinary Research and Modern Education 2, no. 2 (2016): 378–83. https://doi.org/10.5281/zenodo.204775.

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<em>Fuzzy Sets are generalized from the notion of classical (crisp) sets (Zadeh1965) [6]. A fuzzy subset A of X can be characterized with a membership function µ<sub>A</sub>: X → [0, 1]. Krassimir T. Atanassov further generalized fuzzy sets into Intuitionistic Fuzzy Sets (IFSs) in which non- membership function ν<sub>A</sub>: X → [0, 1] is also considered [1]. Further he extended IFSs into Temporal Intuitionistic Fuzzy Sets (TIFSs) in which time- moments are also taken into consideration. TIFSs are useful in time-based mathematical modeling. In this paper, the present authors further introduce

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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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Ibrahim, Hariwan Z., Tareq M. Al-shami, Murad Arar, and M. Hosny. "Complex nth power root fuzzy sets: Theory, and applications for multi-attribute decision making in uncertain environments." PLOS One 20, no. 5 (2025): e0319757. https://doi.org/10.1371/journal.pone.0319757.

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The newly introduced nth power root fuzzy set is a useful tool for expressing ambiguity and vagueness. It has an improved ability to manage uncertain situations compared to intuitionistic fuzzy set and Pythagorean fuzzy set theories, making nth power root fuzzy sets applicable in various everyday decision-making contexts. The notions of nth power root fuzzy sets and complex fuzzy sets are integrated in this study to offer complex nth power root fuzzy sets (CnPR-FSs), explaining its fundamental ideas and useful applications. The proposed CnPR-FS integrates the advantages of nth power root fuzzy

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Qiyas, Muhammad, Darjan Karabasevic, Neelam Khan, and Srdjan Maričić. "Einstein Exponential Operational Laws Based on Fractional Orthotriple Fuzzy Sets and Their Applications in Decision Making Problems." Mathematics 12, no. 20 (2024): 3216. http://dx.doi.org/10.3390/math12203216.

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The fractional orthotriple fuzzy set (FOFS) model is a recently created extension of fuzzy sets (FS) for coping with ambiguity in DM. The purpose of this study is to define new exponential and Einstein exponential operational (EO) laws for fractional orthotriple fuzzy sets and the aggregation procedures that accompany them. We present the operational laws for exponential and Einstein exponential FOFSs which have crisp numbers as base values and fractional orthotriple fuzzy numbers as exponents (weights). The proposed operations’ qualities and characteristics are then explored. Based on the def

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Arora, H. D., and Anjali Naithani. "Multi-Criteria Decision Making to Logarithmic Pythagorean Fuzzy Entropy Measure Under TOPSIS Approach." International Journal of Fuzzy System Applications 11, no. 4 (2022): 1–23. http://dx.doi.org/10.4018/ijfsa.312237.

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One of the most essential ideas for tracing the best objects among a set of possible ones is decision-making theory. We make decisions to gain a wide range of advantages from them based on our previous experiences. The concept of Pythagorean fuzzy sets (PFS) was first established by Yager to provides a new technique to describe ambiguity with great precision when compared to intuitionistic fuzzy sets (IFS) and fuzzy sets (FS). The study of PFS is recently gaining importance due to its wide application in situations involving ambiguity. It can easily be merged with MADM techniques to solve real

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Rahmad Putra, Al Rifqi. "KOEFISIEN KORELASI BEBERAPA HIMPUNAN KABUR." Jurnal Matematika UNAND 7, no. 3 (2019): 1. http://dx.doi.org/10.25077/jmu.7.3.1-8.2018.

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Teori himpunan kabur (fuzzy set) telah diperkenalkan oleh Zadeh pada tahun 1965, dimana teori ini dapat menjadi alternatif yang lebih baik dalam mencari solusi permasalahan yang mengandung ketidakpastian. Kemudian semakin berkembang ilmu pengetahuan, maka semakin banyak bentuk umum dari himpunan kabur (fuzzy set/FS) yang diusulkan dan dikembangkan, diantaranya ada himpunan kabur intuisionistik (Intuitionistic Fuzzy Sets/IFS), himpunan kabur hesitant (Hesitant Fuzzy Sets (HFS)), dan himpunan kabur dual hesitant (Dual Hesitant Fuzzy Sets (DHFS)). Pada penelitian ini akan dikaji tentang koefisien

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Kreinovich, Vladik, and Vyacheslav Kalashnikov. "Selected Papers from ISMEf2010." Journal of Advanced Computational Intelligence and Intelligent Informatics 15, no. 4 (2011): 399. http://dx.doi.org/10.20965/jaciii.2011.p0399.

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The International Society of Management Engineers (ISME), founded in April 2003 to support ME innovation and research, covers methods and techniques related to industrial production and management, in contrast to conventional industrial engineering. Recent examples include innovative research on such topics as ? logistics, ? service, ? supply chain management, ? knowledge management. These topics, among others, are part of ME. Other important ME areas are mobile business and e-commerce. The ISME organized its first symposium in 2004, with such symposiums becoming a regular event. This special

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Sinan, Karadeniz, and Ulu Cenk. "Linguistic Hedge Based Constrained Representation of Interval Type-2 Fuzzy Sets." International Journal of Applied Engineering and Technology 4, no. 3 (2022): 11–19. https://doi.org/10.5281/zenodo.7602028.

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In general representation, a type-2 fuzzy set is defined as being composed of all its embedded type-1 fuzzy sets (ET1-FSs) which can be non-convex, sub-normal, and/or discontinuous. However, interval type-2 fuzzy sets (IT2-FSs) are constructed by blurring a baseline type-1 membership function form in many applications, and thus, uncertainties are actually modeled by using only ET1-FSs which preserve the similar meaningful functional form. Therefore, the derived results can be too generic in such cases when all ET1-FSs are included in type-2 fuzzy computations. In this study, a new constrained

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Rosyida, Isnaini, and Suryono Suryono. "Coloring picture fuzzy graphs through their cuts and its computation." International Journal of Advances in Intelligent Informatics 7, no. 1 (2021): 63. http://dx.doi.org/10.26555/ijain.v7i1.612.

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In a fuzzy set (FS), there is a concept of alpha-cuts of the FS for alpha in [0,1]. Further, this concept was extended into (alpha,delta)-cuts in an intuitionistic fuzzy set (IFS) for delta in [0,1]. One of the expansions of FS and IFS is the picture fuzzy set (PFS). Hence, the concept of (alpha,delta)-cuts was developed into (alpha,delta,beta)-cuts in a PFS where beta is an element of [0,1]. Since a picture fuzzy graph (PFG) consists of picture fuzzy vertex or edge sets or both of them, we have an idea to construct the notion of the (alpha,delta,beta)-cuts in a PFG. The steps used in this pap

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Zhang, Baosheng, Tahir Mahmood, Jabbar Ahmmad, Qaisar Khan, Zeeshan Ali, and Shouzhen Zeng. "Cubic q-Rung Orthopair Fuzzy Heronian Mean Operators and Their Applications to Multi-Attribute Group Decision Making." Mathematics 8, no. 7 (2020): 1125. http://dx.doi.org/10.3390/math8071125.

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The cubic q-rung orthopair fuzzy set (Cq-ROFS) contains much more information to determine the interval valued q-rung orthopair fuzzy sets (IVq-ROFSs) and q-rung orthopair fuzzy sets (q-ROFSs) simultaneously for coping with the vagueness in information. It provides more space for decision makers (DMs) to describe their opinion in the environment of fuzzy set (FS) theory. In this paper, firstly, we introduce the conception of Cq-ROFS and their characteristics. Further, the Heronian mean (HM) operator based on Cq-ROFS, called the weighted HM operator, are explored. To overcome the deficiency of

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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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Shen, Xiaomin, Sidra Sakhi, Kifayat Ullah, Muhammad Nabeel Abid, and Yun Jin. "Information Measures Based on T-Spherical Fuzzy Sets and Their Applications in Decision Making and Pattern Recognition." Axioms 11, no. 7 (2022): 302. http://dx.doi.org/10.3390/axioms11070302.

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The T-spherical fuzzy set (TSFS) is a modification of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), q-rung orthopair fuzzy set (q-ROFS), and picture fuzzy set (PFS), with three characteristic functions: the membership degree (MD) denoted by , the nonmembership degree (NMD) denoted by , and the abstinence degree (AD) denoted by . It can be used to solve problems of uncertain information with no restrictions. The distance measure (DM) is a tool that sums up the difference between points, while the similarity measure (SM) is a method applied to calculate the si

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Wang, Li, Zhang, and Han. "New Distance Measures for Dual Hesitant Fuzzy Sets and Their Application to Multiple Attribute Decision Making." Symmetry 12, no. 2 (2020): 191. http://dx.doi.org/10.3390/sym12020191.

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Multiple attribute decision making (MADM) is full of uncertainty and vagueness due to intrinsic complexity, limited experience and individual cognition. Representative decision theories include fuzzy set (FS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) and so on. Compared with IFS and HFS, DHFS has more advantages in dealing with uncertainties in real MADM problems and possesses good symmetry. The membership degrees and non-membership degrees in DHFS are simultaneously permitted to represent decision makers’ preferences by a given set having divers

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Naeem, Muhammad, Muhammad Qiyas, Mohammed M. Al-Shomrani, and Saleem Abdullah. "Similarity Measures for Fractional Orthotriple Fuzzy Sets Using Cosine and Cotangent Functions and Their Application in Accident Emergency Response." Mathematics 8, no. 10 (2020): 1653. http://dx.doi.org/10.3390/math8101653.

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The fractional orthotriple fuzzy set (FOFS) is more generalized than the spherical fuzzy set (SFS) and picture fuzzy set (PFS) to cope with awkward and complex information in fuzzy set (FS) theory. The FOFS is a more powerful technique with respect to the existing drawbacks because of its conditions, i.e., the sum of the f powers of positive, neutral, and negative grades is bounded to [0,1]. With the advantages of the FOFS, in this paper, we study the basic definitions and some existing similarity measures (SMs) of intuitionistic fuzzy sets (IFSs), PFSs, Pythagorean fuzzy sets (PyFSs) and SFSs

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Ali, Riaz, Saleem Abdullah, Shakoor Muhammad, Muhammad Naeem, and Ronnason Chinram. "Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection." Journal of Intelligent & Fuzzy Systems 41, no. 1 (2021): 517–38. http://dx.doi.org/10.3233/jifs-202254.

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Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also dev

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Mutlag, Ammar Hussein, Hussein Shareef, Azah Mohamed, Jamal Abd Ali, and Maytham S. Ahmed. "Performance Evaluation of Various Adaptive Neuro Fuzzy Inference System Based Maximum Power Point Tracking for Photovoltaic System." Applied Mechanics and Materials 785 (August 2015): 215–19. http://dx.doi.org/10.4028/www.scientific.net/amm.785.215.

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The maximum output power of a photovoltaic (PV) system with a DC-DC converter depends mainly on the solar irradiance (G) and the temperature (T). Therefore, a maximum power point tracking (MPPT) mechanism is required to improve the overall system. The conventional MPPT approaches such as the perturbation and observation (P&O) technique have difficulty in finding true maximum power point. Thus various intelligent MPPT systems such as fuzzy logic controllers (FLC) are recently introduced. In FLC based MPPT, selecting the type of the membership function (MF) and the number of the fuzzy sets (

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Hussain, Abrar, Chaudhary Amir Raza, and Kifayat Ulllah. "Advanced Decision-Making With Complex q-Rung Orthopair Fuzzy Muirhead Mean Models." Spectrum of Decision Making and Applications 3, no. 1 (2025): 316–38. https://doi.org/10.31181/sdmap31202644.

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Reliable and adaptable approaches are essential in MADM to address the complexities of medical diagnosis. To enhance decision-making (DM) processes, we propose a novel method combining the Muirhead mean (MM) with q-rung orthopair fuzzy sets (q-ROFS). The q-ROFS framework offers an advanced solution for handling ambiguity and vagueness in medical diagnoses by enabling a three-dimensional representation of expert opinions through membership degrees (MDs). The proposed method leverages MM's strength in capturing interrelationships among features, ensuring a more accurate and balanced integration

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Gora, Pawan. "Intuitionistic Fuzzy Modulus Similarity Measure." International Journal of Decision Support System Technology 15, no. 1 (2023): 1–22. http://dx.doi.org/10.4018/ijdsst.315757.

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The concept of intuitionistic fuzzy sets (IFSs) is an expected explanation for finding the appropriate information. It originated from concept of fuzzy set (FS) theory, which extends the classical conception of a fuzzy set. This paper examines a number of widely employed similarity measures then proposes an IFSs modulus similarity measure and a weight similarity measure. Initially, the authors have discussed numerous existing similarity measures, some of which are unable to justify the axioms of being a similarity measure. Furthermore, some numerical examples are presented to compare the exist

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Hussain, Zahid, Sahar Abbas, and Miin-Shen Yang. "Distances and Similarity Measures of Q-Rung Orthopair Fuzzy Sets Based on the Hausdorff Metric with the Construction of Orthopair Fuzzy TODIM." Symmetry 14, no. 11 (2022): 2467. http://dx.doi.org/10.3390/sym14112467.

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In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater accuracy than intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The characterization of a measure of similarity between q-ROFSs is important, as they have applications in different areas, including pattern recognition, clustering, image segmentation and decision making. Therefore, this article is dedicated to the construction of a

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Zhou, Chao, Dongyu Liu, Pengfei Zhou, Jie Luo, Serhat Yuksel, and Hasan Dincer. "Hybrid Predictive Decision-Making Approach to Emission Reduction Policies for Sustainable Energy Industry." Energies 13, no. 9 (2020): 2220. http://dx.doi.org/10.3390/en13092220.

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Carbon emissions are a prominent issue for sustainable energy production and management. Energy policies under the growing competitive environment could change the priorities of emission reduction and investment decisions. This paper aims to forecast carbon emissions from China and to rank the importance of carbon emissions with interval type 2 (IT2) fuzzy sets (FS) for sustainable energy investments. For this purpose, the quadratic model is applied to measuring emission trends and the Qualitative Flexible Multiple Criteria Method (QUALIFLEX) is used for measuring sustainable energy investment

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M, Premkumar, A. Rifayathali M, Prasanna A, Juliet Jeyapackiam J, Kumar Shukla Dhirendra, and Parameswari R. "On the Construction of the Properties of t - Norms in the Q-Fuzzy T-Sub algebra and Ideals in the BP-Algebra." Indian Journal of Science and Technology 17, SP1 (2024): 52–57. https://doi.org/10.17485/IJST/v17sp1.144.

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Abstract In the present piece, we propound t- norms of the QFTSA ὦȴȵŦὦȴὦȵ in BP-Algebra and also t- norms of the QFTI  ὦὦȴὦȴɉŦŦὦȴȵɉὦȵὦȵ , ȴȵɉĜ of the BP-Algebra and we assay some of their features. Likewise, we define Cartesian products of QFTSAs and QFTI of BP algebras. These, as well as other algebraic features, are bandied in depth. <strong>Objective:</strong> This article generally aimed at investigating t- norms concepts. It can also be applied to the algebraic properties of Q-Fuzzy T-Ideals, Q-Fuzzy T-Sub algebra and also defined for Cartesian products of QFTSAs and QFTI o

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Sukri, Windi Adrian, and Yanita Yanita. "UKURAN ENTROPI BARU UNTUK HIMPUNAN KABUR INTUISIONISTIK." Jurnal Matematika UNAND 8, no. 1 (2019): 318. http://dx.doi.org/10.25077/jmu.8.1.318-322.2019.

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Himpunan kabur (fuzzy set/FS) hadir atau diperkenalkan untuk mengatasi permasalahan dalam kehidupan sehari-hari yang banyak mengandung unsur ketidakjelasan. Himpunan kabur ini diperkenalkan oleh L.A. Zadeh (1965). Kemudian beberapa bentuk umum dari himpunan kabur telah diusulkan dan dipelajari untuk mengatasi ketidakjelasan. Salah satunya ada himpunan kabur intuisionistik (Intuitionistic Fuzzy Sets/IFS). Dalam teori himpunan kabur ada salah satu topik penting yang telah diteliti serta diusulkan oleh banyak peneliti, yaitu ukuran entropi himpunan kabur intuisionistik. Pada tulisan ini akan dius

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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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Szilveszter Kov?cs. "Special Issue on Fuzzy Rule Interpolation." Journal of Advanced Computational Intelligence and Intelligent Informatics 15, no. 3 (2011): 253. http://dx.doi.org/10.20965/jaciii.2011.p0253.

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Fuzzy Rule Interpolation (FRI) methods are well known tools for reasoning in case of insufficient knowledge expressed as sparse fuzzy rule-bases. It also provides a simple way to define fuzzy functions. Despite these advantages, FRI techniques are relatively rarely applied in practice. Enabling sparse fuzzy rule-bases, FRI dramatically simplifies rule-base creation. Regardless of whether the rule-base is generated by a human expert, or automatically from input-output data, the ability to provide reasonable interpolated conclusions even if no rule fires for a given observation, help to concentr

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Sakai, Hiroshi, Hiroaki Ishii, and Junzo Watada. "Special Issue on Forum for Interdisciplinary Mathematics 2013." Journal of Advanced Computational Intelligence and Intelligent Informatics 18, no. 6 (2014): 927–28. http://dx.doi.org/10.20965/jaciii.2014.p0927.

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This special issue focuses on recent research in interdisciplinary mathematics and mathematical sciences. For the last four decades, the Forum for Interdisciplinary Mathematics (FIM), a society for researchers in mathematical sciences, has focused on mathematics, combinatorics, statistics, operations research, computer science, fuzzy sets, rough sets, bioinformatics, etc. The 22nd International Conference of FIM on Interdisciplinary Mathematics, Statistics and Computational Techniques (IMSCT 2013-FIM XXII) was held in Kitakyushu, Japan, on November 10-12, 2013. This conference was organized by

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Fatima, Adan, Shahzaib Ashraf, and Chiranjibe Jana. "Approach to Multi-Attribute Decision Making Based on Spherical Fuzzy Einstein Z-Number Aggregation Information." Journal of Operations Intelligence 2, no. 1 (2024): 179–201. http://dx.doi.org/10.31181/jopi21202411.

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Spherical fuzzy sets are an enhanced framework of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), and picture fuzzy set (PFS) with the restriction that the total square sum of the membership, indeterminacy, and non-membership degrees must be in 0 and 1. In contrast, the Z-number, a revolutionary idea that captures both the restriction and the reliability of evaluation, is more significant than fuzzy numbers in the fields of decision-making (DM), risk assessment, etc. However, there are still few and insufficient discussions of how to effectively deal with the

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50

Premkumar, M., M. A. Rifayathali, A. Prasanna, J. Juliet Jeyapackiam, Dhirendra Kumar Shukla, and R. Parameswari. "On the Construction of the Properties of t - Norms in the Q-Fuzzy T-Sub algebra and Ideals in the BP-Algebra." Indian Journal Of Science And Technology 17, SPI1 (2024): 52–57. http://dx.doi.org/10.17485/ijst/v17sp1.144.

Full text

Abstract:

In the present piece, we propound t- norms of the QFTSA ὦȴȵŦὦȴὦȵ in BP-Algebra and also t- norms of the QFTI ὦὦȴὦȴɉŦŦὦȴȵɉὦȵὦȵ , ȴȵɉĜ of the BP-Algebra and we assay some of their features. Likewise, we define Cartesian products of QFTSAs and QFTI of BP algebras. These, as well as other algebraic features, are bandied in depth. Objective: This article generally aimed at investigating t- norms concepts. It can also be applied to the algebraic properties of Q-Fuzzy T-Ideals, Q-Fuzzy T-Sub algebra and also defined for Cartesian products of QFTSAs and QFTI of BP algebras.Methods: t -norms concepts c

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