Enhanced Manhattan-based Clustering using Fuzzy C-Means Algorithm for High Dimensional Datasets

The problem of mining a high dimensional data includes a high computational cost, a high dimensional dataset composed of thousands of attribute and or instances. The efficiency of an algorithm, specifically, its speed is oftentimes sacrificed when this kind of dataset is supplied to the algorithm. Fuzzy C-Means algorithm is one which suffers from this problem. This clustering algorithm requires high computational resources as it processes whether low or high dimensional data. Netflix data rating, small round blue cell tumors (SRBCTs) and Colon Cancer (52,308, and 2,000 of attributes and 1500, 83 and 62 of instances respectively) dataset were identified as a high dimensional dataset. As such, the Manhattan distance measure employing the trigonometric function was used to enhance the fuzzy c-means algorithm. Results show an increase on the efficiency of processing large amount of data using the Netflix ,Colon cancer and SRCBT an (39,296, 38,952 and 85,774 milliseconds to complete the different clusters, respectively) average of 54,674 milliseconds while Manhattan distance measure took an average of (36,858, 36,501 and 82,86 milliseconds, respectively)  52,703 milliseconds for the entire dataset to cluster. On the other hand, the enhanced Manhattan distance measure took (33,216, 32,368 and 81,125 milliseconds, respectively) 48,903 seconds on clustering the datasets. Given the said result, the enhanced Manhattan distance measure is 11% more efficient compared to Euclidean distance measure and 7% more efficient than the Manhattan distance measure respectively

Görüntü bulanık kümelerde altkümelik ve çok kriterli karar vermeye uygulanması

Picture fuzzy set is a direct generalization of intuitionistic fuzzy set and is therefore more capable of dealing with uncertainty while working on real life problems. The concept of inclusion is a subject that is frequently studied in family of fuzzy sets and has many applications in real life problems. Therefore, in this work, the measuring degree of inclusion between picture fuzzy sets is introduced. For this purpose, firstly axioms for subsethood measure are given and then a subsethood measure based on a distance measure for picture fuzzy sets is proposed. Then, a numerical example is provided to illustrate the applicability and usefulness of the presented measure. Finally, results are compared with the existing methods and aggregation operator to show validity of subsethood measure for PFS.Görüntü bulanık küme, sezgisel bulanık kümenin doğrudan bir genellemesidir ve bu nedenle gerçek hayat problemleri üzerinde çalışırken belirsizlikle başa çıkma konusunda daha yeteneklidir. Kapsama kavramı, bulanık kümeler ailesinde sıklıkla çalışılan ve gerçek hayat problemlerinde birçok uygulaması olan bir konudur. Bu nedenle, bu çalışmada, görüntü bulanık kümeleri arasındaki kapsama derecesinin ölçülmesi tanıtılmıştır. Bu amaçla, önce altkümelik ölçüsü için aksiyomlar verilmiş, ardından görüntü bulanık kümeleri için uzaklık ölçüsüne dayalı bir altküme ölçüsü önerilmiştir. Sonra, verilen ölçünün uygulanabilirliğini ve kullanışlılığını göstermek için sayısal bir örnek verilmiştir. Son olarak, sonuçlar PFS için altkümelik ölçüsünün geçerliliğini göstermek için mevcut yöntemler ve ortalama operatörleri ile karşılaştırılmıştır

NEW DISSIMILARITY MEASURES ON PICTURE FUZZY SETS AND APPLICATIONS

The dissimilarity measures between fuzzy sets/intuitionistic fuzzy sets/picture fuzzy sets are studied and applied in various matters. In this paper, we propose some new dissimilarity measures on picture fuzzy sets. This new dissimilarity measures overcome the restrictions of all existing dissimilarity measures on picture fuzzy sets. After that, we apply these new measures to the pattern recognition problems. Finally, we introduce a multi-criteria decision making (MCDM) method that used the new dissimilarity measures and apply them in the supplier selection problems

COPRAS method for multiple attribute group decision making under picture fuzzy environment and their application to green supplier selection

The green supplier selection (GSS) is a significant part in green supply chain management (GSCM). Choosing optimal green supplier can not only realize the sustainable development of enterprises, but also maximize the utilization rate of resources and diminish the negative effect of environmental issues, which conforms to the theme of green development. As a multiple attribute group decision-making (MAGDM) issue, selecting optimal green supplier is of vital important to enterprises. However, how to select the optimal supplier for enterprises is a great challenge. To handle this issue, a novel picture fuzzy COPRAS (COmplex PRoportional Assessment) method is devised. First, some necessary theories related to picture fuzzy sets (PFSs) are briefly reviewed. In addition, a method called CRITIC (Criteria Importance Though Intercrieria Correlation) is utilized to calculate criteria’s weights. Afterwards, the conventional COPRAS method is extended to the PFSs to calculate each alternative’s utility degree. At last, the designed method is exacted to an application which is related to GSS and there also conduct some comparative analysis to demonstrate the designed method’s superiority. The final results show that the proposed model can be utilized to decide the optimum green supplier

Some New De Morgan Picture Operator Triples in Picture Fuzzy Logic

A new concept of picture fuzzy sets (PFS) were introduced in 2013, which are directextensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS withsome properties are considered in [ 9,10 ]. Some basic operators of fuzzy logic as negation, tnorms, t-conorms for picture fuzzy sets firstly are defined and studied in [13,14]. This paper isdevoted to some classes of representable picture fuzzy t-norms and representable picture fuzzyt-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic – De Morgan triples ofpicture operators

Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory. In 1965, L.A. Zadeh had published “Fuzzy Sets” [335]. After only one year, the first effects of this seminal paper began to emerge, with the pioneering paper on clustering by Bellman, Kalaba, Zadeh [33], in which they proposed a prototypal of clustering algorithm based on the fuzzy sets theory

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

Collected Papers (on Neutrosophic Theory and Applications), Volume VI

This sixth volume of Collected Papers includes 74 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2015-2021 by the author alone or in collaboration with the following 121 co-authors from 19 countries: Mohamed Abdel-Basset, Abdel Nasser H. Zaied, Abduallah Gamal, Amir Abdullah, Firoz Ahmad, Nadeem Ahmad, Ahmad Yusuf Adhami, Ahmed Aboelfetouh, Ahmed Mostafa Khalil, Shariful Alam, W. Alharbi, Ali Hassan, Mumtaz Ali, Amira S. Ashour, Asmaa Atef, Assia Bakali, Ayoub Bahnasse, A. A. Azzam, Willem K.M. Brauers, Bui Cong Cuong, Fausto Cavallaro, Ahmet Çevik, Robby I. Chandra, Kalaivani Chandran, Victor Chang, Chang Su Kim, Jyotir Moy Chatterjee, Victor Christianto, Chunxin Bo, Mihaela Colhon, Shyamal Dalapati, Arindam Dey, Dunqian Cao, Fahad Alsharari, Faruk Karaaslan, Aleksandra Fedajev, Daniela Gîfu, Hina Gulzar, Haitham A. El-Ghareeb, Masooma Raza Hashmi, Hewayda El-Ghawalby, Hoang Viet Long, Le Hoang Son, F. Nirmala Irudayam, Branislav Ivanov, S. Jafari, Jeong Gon Lee, Milena Jevtić, Sudan Jha, Junhui Kim, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Songül Karabatak, Abdullah Kargın, M. Karthika, Ieva Meidute-Kavaliauskiene, Madad Khan, Majid Khan, Manju Khari, Kifayat Ullah, K. Kishore, Kul Hur, Santanu Kumar Patro, Prem Kumar Singh, Raghvendra Kumar, Tapan Kumar Roy, Malayalan Lathamaheswari, Luu Quoc Dat, T. Madhumathi, Tahir Mahmood, Mladjan Maksimovic, Gunasekaran Manogaran, Nivetha Martin, M. Kasi Mayan, Mai Mohamed, Mohamed Talea, Muhammad Akram, Muhammad Gulistan, Raja Muhammad Hashim, Muhammad Riaz, Muhammad Saeed, Rana Muhammad Zulqarnain, Nada A. Nabeeh, Deivanayagampillai Nagarajan, Xenia Negrea, Nguyen Xuan Thao, Jagan M. Obbineni, Angelo de Oliveira, M. Parimala, Gabrijela Popovic, Ishaani Priyadarshini, Yaser Saber, Mehmet Șahin, Said Broumi, A. A. Salama, M. Saleh, Ganeshsree Selvachandran, Dönüș Șengür, Shio Gai Quek, Songtao Shao, Dragiša Stanujkić, Surapati Pramanik, Swathi Sundari Sundaramoorthy, Mirela Teodorescu, Selçuk Topal, Muhammed Turhan, Alptekin Ulutaș, Luige Vlădăreanu, Victor Vlădăreanu, Ştefan Vlăduţescu, Dan Valeriu Voinea, Volkan Duran, Navneet Yadav, Yanhui Guo, Naveed Yaqoob, Yongquan Zhou, Young Bae Jun, Xiaohong Zhang, Xiao Long Xin, Edmundas Kazimieras Zavadskas