A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation

The rough set (RS) and multi-granulation RS (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, the bipolar fuzzy sets (BFSs) are effective tools for handling bipolarity and fuzziness of the data. In this study, with the description of the background of risk decision-making problems in reality, we present $(\alpha, \beta)$-optimistic multi-granulation bipolar fuzzified preference rough sets ($(\alpha, \beta)^o$-MG-BFPRSs) and $(\alpha, \beta)$-pessimistic multi-granulation bipolar fuzzified preference rough sets ($(\alpha, \beta)^p$-MG-BFPRSs) using bipolar fuzzy preference relation (BFPR). Subsequently, the relevant properties and results of both $(\alpha, \beta)^o$-MG-BFPRSs and $(\alpha, \beta)^p$-MG-BFPRSs are investigated in detail. At the same time, a relationship among the $(\alpha, \beta)$-BFPRSs, $(\alpha, \beta)^o$-MG-BFPRSs and $(\alpha, \beta)^p$-MG-BFPRSs is given

New Challenges in Neutrosophic Theory and Applications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of indeterminacy/neutrality (I) as an independent component in the neutrosophic set. Thus, neutrosophic theory involves the degree of membership-truth (T), the degree of indeterminacy (I), and the degree of non-membership-falsehood (F). In recent years, the field of neutrosophic set, logic, measure, probability and statistics, precalculus and calculus, etc., and their applications in multiple fields have been extended and applied in various fields, such as communication, management, and information technology. We believe that this book serves as useful guidance for learning about the current progress in neutrosophic theories. In total, 22 studies have been presented and reflect the call of the thematic vision. The contents of each study included in the volume are briefly described as follows. The first contribution, authored by Wadei Al-Omeri and Saeid Jafari, addresses the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets in neutrosophic topological spaces. In the article “Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution”, the authors Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, and Abdur Razzaque Mughal discuss the use of probability distribution function of Birnbaum–Saunders distribution as a proportion of defective items and the acceptance probability in a fuzzy environment. Further, the authors Derya Bakbak, Vakkas Uluc¸ay, and Memet S¸ahin present the “Neutrosophic Soft Expert Multiset and Their Application to Multiple Criteria Decision Making” together with several operations defined for them and their important algebraic properties. In “Neutrosophic Multigroups and Applications”, Vakkas Uluc¸ay and Memet S¸ahin propose an algebraic structure on neutrosophic multisets called neutrosophic multigroups, deriving their basic properties and giving some applications to group theory. Changxing Fan, Jun Ye, Sheng Feng, En Fan, and Keli Hu introduce the “Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment” and test the effectiveness of their new methods. Another decision-making study upon an everyday life issue which empowered us to organize the key objective of the industry developing is given in “Neutrosophic Cubic Einstein Hybrid Geometric Aggregation Operators with Application in Prioritization Using Multiple Attribute Decision-Making Method” written by Khaleed Alhazaymeh, Muhammad Gulistan, Majid Khan, and Seifedine Kadry

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc

Threat assessment of aerial targets based on improved GRA-TOPSIS method and three-way decisions

Target threat assessment is a critical aspect of information warfare and can offer valuable auxiliary support to combat command decision-making. Aiming to address the shortcomings of three decision-making methods in air combat target assessment, such as the inability to effectively handle uncertain situation information and quantitatively rank the decision-making targets according to their importance, a dynamic intuitionistic fuzzy decision model based on the improved GRA-TOPSIS method and three-way decisions is proposed. First, the target attribute weight is obtained by cosine intuitionistic fuzzy entropy algorithm; then, a novel intuitionistic fuzzy distance measure is introduced, and grey incidence analysis and TOPSIS are used to build the conditional probability for three-way decisions that fully utilize the existing information and reflect the consistency of dynamic change trend; finally, the comprehensive loss function matrix is constructed and the threat classification results are obtained using the decision rules. The example analysis shows that the proposed method can not only effectively handle complex battlefield situations and dynamic uncertain information, but it can also classify targets, improving the effectiveness and rationality of decision-making and providing a reference basis for scientific command decision-making

Some New Operations of ( alpha, , ) Interval Cut Set of Interval Valued Neutrosophic Sets

In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties

Kaba küme tabanlı çok kriterli karar verme yöntemi ve uygulaması

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Çok kriterli karar verme problemi, çağımız yöneticilerinin sıklıkla başvurmuş olduğu yöntemlerden birisidir. Verilerin belirsiz ya da eksik olması durumunda, mevcut olan çok kriterli karar verme yöntemleri yetersiz kalırken, önermiş olduğumuz kaba küme tabanlı çok kriterli karar verme algoritması, bu eksikliği gidermede en büyük yardımcı olarak karşımıza çıkmaktadır. Bununla birlikte, hızla artan veri trafiğinde, mevcut verilerin verimli bir şekilde kullanılması da beraberinde önemli bir durumu ortaya çıkartmaktadır. 1982 yılında ilk olarak Pawlak[1] tarafından önerilen kaba küme kavramı, büyük veri tabanlarını kullanarak gerekli olan bilginin keşfini sağlayan önemli bir araç olarak kullanılmaktadır. Kaba küme kavramı, çok kriterli karar verme problemlerinde kullanılmak üzere, kesin olmayan yapıların analizi için bulanık mantık yaklaşımından türetilmiştir. Kaba küme teorisi, kural indirgeme ve sınıflandırma yaklaşım özellikleri ile büyük verilerin analiz işleminin yanı sıra çok kriterli karar verme problemlerinde de kullanılabilmektedir. Kaba küme teorisi bulanık küme teorisinin bir alt kolu olarak geliştirilmiştir. Eksik, belirsiz verilerin değerlendirilmesi sürecinde, alt ve üst yaklaşımlar kullanılarak, veriler analiz edilmektedir. Bulanık kümeler gibi kesin sınırlamaları içermeyen bir yapıya sahiptir. Eksik bilgi analizi, bilgi tabanı indirgemesi yöntemleri kullanılarak, verilerdeki belirsizlik en aza indirgenmeye çalışılmaktadır. Tutarsız, eksik bilgi içeren veri yapılarından kural çıkarımı ve sınıflandırma konusunda kaba küme teorisi ilerleyen zamanlarda daha fazla tercih edilecek bir yöntem olarak çıkabilecektir. Bu çalışmada kaba kümeleme teorisine ait temel kavramlar kaba küme tabanlı bilgi keşfi ve kaba küme kavramı dikkate alınarak geliştirilen algoritma ile birlikte, çok kriterli karar verme probleminin çözümüne yönelik algoritma geliştirilmiştir ve diğer ÇKKV algoritmaları ile karşılaştırılmıştır. Anahtar kelimeler:Kaba Küme Teorisi, Çok Kriterli Karar Verme EntropiThe multi-criteria decision-making problem is one of the methods that preffered and applied by the managers. Multi criteria decision making data set may include the uncertain or incomplete data, in this situation, decision is getting difficult and impossible, the suggested rough set based multi criteria decision making algorithm can able to solve this manner problem. However, in the rapidly increasing data traffic, the efficient use of existing data also brings about an important situation. The rough set concept firstly proposed by Pawlak in 1982[1] that is used as an important tool for the discovery of the necessary information by using large databases. In the case of multi-criteria decision-making problems, the concept of rough set theory is derived from the fuzzy logic approach to perform the analysis of uncertain structures. The rough set theory also has the property of being able to be used in multi-criteria decision-making problems with the rules of rule reduction and classification during the analysis of large data. Rough set theory has a structure that does not contain definite limitations, such as fuzzy sets. Therefore, the rough set approach can able to analysis of the incomplete, inadequate and ambiguous information suitable for data analysis, uses incomplete information analysis, knowledge base reduction methods during this process. Rough set theory can be used as a natural method that deals with inconsistent and incomplete information, which is the basic problem of rule extraction and classification. In this study, the basic concepts of rough set theory is given. The algorithm for solving multi-criteria decision making has been developed by considering the rough set based knowledge discovery and rough set concept. Keywords: Rough Set Theory, Multi Criteria Decision Making Entrop

Some New Operations of (α,β,γ) Interval Cut Set of Interval Valued Neutrosophic Sets

In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties. The notions of the (α,β,γ) interval cut set of interval valued neutrosophic sets and the (α,β,γ) strong interval cut set of interval valued neutrosophic sets are put forward. Some related properties have been established with proof, examples and counter examples

Positive region: An enhancement of partitioning attribute based rough set for categorical data

Datasets containing multi-value attributes are often involved in several domains, like pattern recognition, machine learning and data mining. Data partition is required in such cases. Partitioning attributes is the clustering process for the whole data set which is specified for further processing. Recently, there are already existing prominent rough set-based approaches available for group objects and for handling uncertainty data that use indiscernibility attribute and mean roughness measure to perform attribute partitioning. Nevertheless, most of the partitioning attribute methods for selecting partitioning attribute algorithm for categorical data in clustering datasets are incapable of optimal partitioning. This indiscernibility and mean roughness measures, however, require the calculation of the lower approximation, which has less accuracy and it is an expensive task to compute. This reduces the growth of the set of attributes and neglects the data found within the boundary region. This paper presents a new concept called the "Positive Region Based Mean Dependency (PRD)”, that calculates the attribute dependency. In order to determine the mean dependency of the attributes, that is acceptable for categorical datasets, using a positive region-based mean dependency measure, PRD defines the method. By avoiding the lower approximation, PRD is an optimal substitute for the conventional dependency measure in partitioning attribute selection. Contrary to traditional RST partitioning methods, the proposed method can be employed as a measure of data output uncertainty and as a tailback for larger and multiple data clustering. The performance of the method presented is evaluated and compared with the algorithmes of Information-Theoretical Dependence Roughness (ITDR) and Maximum Indiscernible Attribute (MIA)