Intuitionistic fuzzy two-factor variance analysis of movie ticket sales

2021 ◽  
pp. 1-11
Author(s):  
Velichka Traneva ◽  
Stoyan Tranev

Analysis of variance (ANOVA) is an important method in data analysis, which was developed by Fisher. There are situations when there is impreciseness in data In order to analyze such data, the aim of this paper is to introduce for the first time an intuitionistic fuzzy two-factor ANOVA (2-D IFANOVA) without replication as an extension of the classical ANOVA and the one-way IFANOVA for a case where the data are intuitionistic fuzzy rather than real numbers. The proposed approach employs the apparatus of intuitionistic fuzzy sets (IFSs) and index matrices (IMs). The paper also analyzes a unique set of data on daily ticket sales for a year in a multiplex of Cinema City Bulgaria, part of Cineworld PLC Group, applying the two-factor ANOVA and the proposed 2-D IFANOVA to study the influence of “ season ” and “ ticket price ” factors. A comparative analysis of the results, obtained after the application of ANOVA and 2-D IFANOVA over the real data set, is also presented.

2020 ◽  
Vol 10 (4) ◽  
pp. 728-738
Author(s):  
E. E. Nechvaloda ◽  

Introduction: the article is devoted to the analysis of the early sources on the Udmurt ancient woman headwear. The chronological framework of the study is limited, on the one hand, by the very first confirmation of the ayshon (XVI century), and on the other hand, by the era of the first expeditions in Russia (XVIII century), which laid the foundation for future ethnographic research. Objective: to determine the degree of reliability and informativity of descriptions and images of the Udmurt headwear of the XVI–XVIII centuries. Research materials: works of travelers of the XVI–XVIII centuries, containing data about ayshon. Results and novelty of the research: the article provides a comparative analysis of materials about ayshon in the sources of the XVI–XVIII centuries. Texts, engravings with texts, and early sources with ethnographic materials of the end of the XIX – beginning XX centuries are compared. For the first time, all original graphic images and descriptions of this headwear related to the specified time period are published together. The characteristics of the ayshon in the descriptions generally correspond to each other, as well as its known images and later ethnographic data. The materials of the article can be used in ethnographic and source studies.


Author(s):  
Dmytro Savon

Relevance and scientific novelty of the selected subject for the research. In the Ukrainian musicology, the motets written by Johann Bach were mainly studied from the compositional means standpoint, considering the system of polyphony, the role of chorale and fugue in dramaturgy as well as the composition of works. Scientists have not previously researched the motets performance specificity. Meanwhile, motets, particularly the one reviewed in the article “Jesu, meine Freude”, are among the most frequently performed works of the choral repertoire. For the first time in the Ukrainian musicology, three edited versions of the motet “Jesu, meine Freude” are analyzed from the standpoint of historically oriented performance. Based on the study of editors’ comments and source literature (mostly German), the question of compliance of the musical text with the task of performing reconstruction of the baroque vocal and choral style was studied. The aim of the article lies in the need to find out specificity of the editors’ interpretation of motet “Jesu, meine Freude” written by Johann Bach and suitability extent of different edited versions for the historical reconstruction of the vocal-choral style of the German Baroque. During the development of particular article, such methods were utilized: historical — the history of edited versions of “Jesu, meine Freude” motet was traced, comparative — the comparative analysis of three edited versions of motet “Jesu, meine Freude” written by Johann Bach (Franz Wulner, Konrad Ameln and Mykhailo Berdennykov) was completed. Main results and conclusions. According to the completed comparative analysis, the first two of the three considered edited versions are textual, while the third one is adopted for performing. Textual versions are characterized by the preservation of the composer’s text in the smallest details, including comments to clearly identify the extent of changes made by the editor in the text. The peculiarities of the version adopted for performing contain the large amount of remarks added by the editor, covering dynamic shades, strokes, tempo notation, etc. It is noted that the choice of version type is determined by performance goals: to perform the works of Johann Bach in an authentic manner, the conductor should focus on facsimile versions, and if they are absent (as in the case of the “Jesu, meine Freude” motet), the one should use textual type of edited versions. The version developed for performing cannot correspond to the authentic performing, as the first does not reflect specific tendencies of the time when it was created. It is specified that the conductor should be familiar with the peculiarities of fixing the means of performance in the musical text of the Baroque era.


2021 ◽  
Vol 27 (1) ◽  
pp. 53-59
Author(s):  
Mladen V. Vassilev-Missana

The inequality \mu^{\frac{1}{\nu}} + \nu^{\frac{1}{\mu}} \leq 1 is introduced and proved, where \mu and \nu are real numbers, for which \mu, \nu \in [0, 1] and \mu + \nu \leq 1. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E. Also, a generalization of the above inequality for arbitrary n \geq 2 is proposed and proved.


2019 ◽  
Vol 16 (4) ◽  
pp. 0937
Author(s):  
Saad Et al.

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.


Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1121
Author(s):  
Krassimir Atanassov ◽  
Evgeniy Marinov

In the paper, for the first time, four distances for Circular Intuitionistic Fuzzy Sets (C-IFSs) are defined. These sets are extensions of the standard IFS that are extensions of Zadeh’s fuzzy sets. As it is shown, the distances for the C-IFS are different than those for the standard IFSs. At the moment, they do not have analogues in fuzzy sets theory. Examples, comparing the proposed distances, are given and some ideas for further research are formulated.


Der Islam ◽  
2019 ◽  
Vol 96 (1) ◽  
pp. 42-86
Author(s):  
Matthew Melvin-Koushki

Abstract This study presents and intellectual- and literary-historically contextualizes a remarkable but as yet unpublished treatise by Ibn Turka (d. 1432), foremost occult philosopher of Timurid Iran: the Munāẓara-yi bazm u razm. As its title indicates, this ornate Persian work, written in 1426 in Herat for the Timurid prince-calligrapher Bāysunghur (d. 1433), takes the form of a literary debate, a venerable Arabo-Persian genre that exploded in popularity in the post-Mongol period. Yet it triply transgresses the bounds of its genre, and doubly marries Arabic-Mamluk literary and imperial culture to Persian-Timurid. For here Ibn Turka recasts the munāẓara as philosophical romance and the philosophical romance as mirror for princes, imperializing the razm u bazm and sword vs. pen tropes within an expressly lettrist framework, making explicit the logic of the coincidentia oppositorum (majmaʿ al-aḍdād) long implicit in the genre in order to ideologically weaponize it. For the first time in the centuries-old Arabo-Persian munāẓara tradition, that is, wherein such debates were often rhetorically but never theoretically resolved, Ibn Turka marries multiple opposites in a manner clearly meant to be instructive to his Timurid royal patron: he is to perform the role of Emperor Love (sulṭān ʿishq), transcendent of all political-legal dualities, avatar of the divine names the Manifest (al-ẓāhir) and the Occult (al-bāṭin). This lettrist mirror for Timurid princes is thus not simply unprecedented in Persian or indeed Arabic literature, a typical expression of the ornate literary panache and genre-hybridizing proclivities of Mamluk-Timurid-Ottoman scientists of letters, and index of the burgeoning of Ibn ʿArabian-Būnian lettrism in late Mamluk Cairo; it also serves as key to Timurid universalist imperial ideology itself in its formative phase – and consciously epitomizes the principle of contradiction driving Islamicate civilization as a whole. To show the striking extent to which this munāẓara departs from precedent, I provide a brief overview of the sword vs. pen subset of that genre; I then examine our text’s specific political-philosophical and sociocultural contexts, with attention to Naṣīr al-Dīn Ṭūsī’s (d. 1274) Akhlāq-i Nāṣirī and Jalāl al-Dīn Davānī’s (d. 1502) Akhlāq-i Jalālī on the one hand – which seminal Persian mirrors for princes assert, crucially, the ontological-political primacy of love over justice – and the Ẓafarnāma of Sharaf al-Dīn Yazdī (d. 1454), Ibn Turka’s student and friend, on the other. In the latter, much-imitated history Amir Temür (r. 1370‒1405) was definitively transformed, on the basis of astrological and lettrist proofs, into the supreme Lord of Conjunction (ṣāḥib-qirān); most notably, there Yazdī theorizes the Muslim world conqueror as historical manifestation of the coincidentia oppositorum – precisely the project of Ibn Turka in his Debate of Feast and Fight. But these two ideologues of Timurid universal imperialism and leading members of the New Brethren of Purity network only became such in Mamluk Cairo, where lettrism (ʿilm al-ḥurūf) was first sanctified, de-esotericized and adabized; I accordingly invoke the overtly occultist-neopythagoreanizing ethos specific to the Mamluk capital by the late 14th century, especially that propagated at the court of Barqūq (r. 1382‒1399). For it is this Cairene ethos, I argue, that is epitomized by our persophone lettrist’s munāẓara, which it effectively timuridizes. To demonstrate the robustness of this Mamluk-Timurid ideological-literary continuity, I situate the Munāẓara-yi bazm u razm within Ibn Turka’s own oeuvre and imperial ideological program, successively developed for the Timurid rulers Iskandar Sulṭān (r. 1409‒1414), Shāhrukh (r. 1409‒1447) and Ulugh Beg (r. 1409‒1449); marshal three contemporary instances of the sword vs. pen munāẓara, one Timurid and two Mamluk, by the theologian Sayyid Sharīf Jurjānī (d. 1413), the secretary-encyclopedist Aḥmad al-Qalqashandī (d. 1418) and the historian Ibn Khaldūn (d. 1406), respectively; and provide an abridged translation of Ibn Turka’s offering as basis for comparative analysis.


Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 447
Author(s):  
Jiří Močkoř ◽  
David Hýnar

The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is proven that ad hoc defined basic concepts in individual theories, such as concepts of power set structures in these theories, relations or approximation operators defined by these relations are only special examples of applications of the monad theory in categories. This makes it possible, on the one hand, to unify basic constructions in all these theories and, on the other hand, to verify the legitimacy of ad hoc definitions of these constructions in individual theories. This common background also makes it possible to transform these basic concepts from one theory to another.


2019 ◽  
Author(s):  
Amer Dardagan

This paper in a simple and transparent way critically examines the rejected belief in science that Bosnian Church and its followers doctrinally and organisationally belonged to the dualist sect of Bogomilism. The research was carried out by a comparative analysis of the basic dualistic postulates of Gnosticism, Manichaeism and Bogomilism on the one hand and the available domestic sources of the Bosnian Church on the other. The importance of the work is reflected in the concise and detailed scientific argumentation that undermines "Bogomil Bosnian Church" myth, while offering a new scientific thesis on the religious and doctrinological affiliation of the "Bosnian faith" and the Bosnian "krs'tjani". In the first part, the paper deals with the problem of extreme and moderate dualism, with a special emphasis on the Neognostic, Neomanichaean and Bogomil communities in medieval Balkans. In the second part, the basic premises of Christian mysticism are given, including the possibility of its philosophical and theological compatibility with the teachings of the Bosnian Church, where for the first time the phenomenon of the name "kr'stjani" is explained in relation to the mystical union ("unio mystica").


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