The k-means algorithm is generally the most known and used clustering method. There are various extensions of to be proposed in literature. Although it an unsupervised learning pattern recognition machine learning, its always influenced by initializations with a necessary number clusters priori. That is, not exactly In this paper, we construct schema for so that free without parameter selection can also simultaneously find optimal clusters. propose novel (U-k-means) automatically finding...

The theory of complex spherical fuzzy sets (CSFSs) is a mixture two theories, i.e., (CFSs) and (SFSs), to cope with uncertain unreliable information in realistic decision-making situations. CSFSs contain three grades the form polar coordinates, e.g., truth, abstinence, falsity, belonging unit disc plane, condition that sum squares real part falsity not exceeded by interval. In this paper, we first consider some properties their operational laws CSFSs. Additionally, based on CSFSs, Bonferroni...

Aczel-Alsina t-norm (TN) and t-conorm (TCN) were proposed by Aczel Alsina in 1982 are more flexible than the other TN TCN. Since TCN have a great impact due to variableness of involved parameters, they good applications multi-attribute decision making (MADM) under fuzzy sets (FSs) construction. Recently, Senapati <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2022) developed aggregation operators (AOs) intuitionistic FSs (IFSs)...

Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding not generally symmetric on grounds that it does provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due their parameter variableness, they been well applied in MADM under construction. Recently, AOs intuitionistic sets (IFSs), interval-valued IFSs and T-spherical proposed literature. In this article, we develop new types of...

In this article we exploit the concept of probability for defining fuzzy entropy intuitionistic sets (IFSs). We then propose two families measures IFSs and also construct axiom definition properties. Two definitions proposed by Burillo Bustince in 1996 Szmidt Kacprzyk 2001 are used. The first one allows us to measure degree intuitionism an IFS, whereas second is a nonprobabilistic-type with geometric interpretation used comparison our numerical comparisons. results show that seem be more...

This paper presents an alternating optimization clustering procedure called a similarity-based method (SCM). It is effective and robust approach to on the basis of total similarity objective function related approximate density shape estimation. We show that data points in SCM can self-organize local optimal cluster number volumes without using validity functions or variance-covariance matrix. The proposed also noise outliers based influence gross error sensitivity analysis. Therefore,...

Fuzzy clustering algorithms generally treat data points with feature components under equal importance. However, there are various datasets irrelevant features involved in process that may cause bad performance for fuzzy algorithms. That is, different should take In this paper, we present a novel method improving can automatically compute individual weight, and simultaneously reduce these components. clustering, the c-means (FCM) algorithm is best known. We first consider FCM objective...

In this paper, the novel approach of complex T-spherical fuzzy sets (CTSFSs) and their operational laws are explored also verified with help examples. CTSFS composes grade truth, abstinence, falsity a condition that sum q-power real part (also for imaginary part) grades cannot be exceeded from unit interval. Additionally, to examine interrelationships among numbers (CTSFNs), we propose two aggregation operators, called weighted averaging (CTSFWA) geometric (CTSFWG) operators. A...

The k-means clustering algorithm is the oldest and most known method in cluster analysis. It has been widely studied with various extensions applied a variety of substantive areas. Since internet, social network, big data grow rapidly, multi-view become more important. For analyzing data, algorithms have studied. However, literature cannot give feature reduction during procedures. In general, there often exist irrelevant components sets that may cause bad performance for these algorithms....

Pythagorean fuzzy sets (PFSs) were proposed by Yager in 2013 to treat imprecise and vague information daily life more rigorously efficiently with higher precision than intuitionistic sets. In this paper, we construct new distance similarity measures of PFSs based on the Hausdorff metric. We first develop a method calculate between Hasudorff metric, along proving several properties theorems. then consider generalization other measures, such as Hamming distance, Euclidean their normalized...

A similarity measure is a useful tool for determining the between two objects. Although there are many different measures among intuitionistic fuzzy sets (IFSs) proposed in literature, Jaccard index has yet to be considered as way define them. The statistic used comparing and diversity of sample sets. In this study, we propose new IFSs induced by index. According our results, based on present better properties. Several examples compare approach with several existing methods. Numerical...