Quadruple Neutrosophic Theory And Applications Volume I Prof. Dr. Florentin Smarandache Prof. Dr. Memet Şahin Assistant Prof. Dr.Vakkas Uluçay Phd Abdullah Kargın T I F Quadruple Neutrosophic Theory And Applications Volume I Quadruple Neutrosophic Theory And Applications-Volume I Editors: Prof. Dr. Florentin Smarandache University of New Mexico, USA Prof. Dr. Memet Şahin Gaziantep University, Turkey Assistant Prof. Dr. Vakkas Uluçay Kilis 7 Aralık Universit, Turkey PhD Abdullah Kargın Gaziantep University, Turkey List of Reviewers Said Broumi, Hassan II University, Morocco Nasruddin Hassan, Universiti Kebangsaan Malaysia Adil Kılıç, Gaziantep University, Turkey Florentin Smarandache, University of New Mexico, USA İsmet Yıldız, Düzce University, Turkey Muhammad Akram, University of the Punjab, Pakistan İhsan Ünvar, Avrasya University, Turkey Muhammad Gulistan, Hazara University, Pakistan Mehmet Bektaş, Fırat University, Turkey Mohamed Abdel-Baset, Zagazig University, Egypt Ziya Yapar, Avrasya University, Turkey Xiaohong Zhang, Shaanxi University of Science &Technology,China Memet Şahin, Gaziantep University, Turkey Mustafa Dede, Kilis 7 Aralık University, Turkey Vakkas Uluçay, Kilis 7 Aralık University, Turkey Necati Olgun, Gaziantep University, Turkey Abdullah Kargın, Gaziantep University, Turkey Neutrosophic Science International Association President: Florentin Smarandache Pons asbl 5, Quai du Batelage, Brussells, Belgium, European Union President: Georgiana Antonescu DTP: George Lukacs ISBN:978-1-59973-647-1 Quadruple Neutrosophic Theory And Applications Volume I Pons Editions Brussels, Belgium, EU 2020 Aims and Scope Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more. Florentin Smarandache, Memet Şahin, Vakkas Uluçay and Abdullah Kargın Quadruple Neutrosophic Theory And Applications Volume I CONTENTS Aims and Scope Preface Acknowledgment SECTION ONE- NEUTROSOPHIC QUADRUPLE Chapter One Generalized Neutrosophic Quadruple Sets and Numbers ……………...…...11 Memet Şahin, Abdullah Kargın, Adil Kılıç Chapter Two Generalized Set Valued Neutrosophic Quadruple Sets and Numbers……….23 Memet Şahin, Abdullah Kargın, Adil Kılıç Chapter Three Neutrosophic Quadruple Goal Programming by using Excel Solver……..…41 N. Gayathri, M. Helen Chapter Four Neutrosophic Triplet Field and Neutrosophic Triplet Vector Space Based on Set Valued Neutrosophic Quadruple Number ………………………………52 Memet Şahin, Abdullah Kargın, İsmet Yıldız Chapter Five Neutrosophic Triplet Metric Space Based on Set Valued Neutrosophic Quadruple Number……………………………………………………...…...61 Memet Şahin, Abdullah Kargın 5 Editors: Florentin Smarandache, Memet Şahin, Vakkas Uluçay and Abdullah Kargın Chapter Six Transportation Problem using Neutrosophic Quadruple Numbers………...71 N. Gayathri, M. Helen SECTION TWO-DECISION MAKING Chapter Seven To Solve Assignment Problem by Centroid Method in Neutrosophic Environment ……..………………………………………………………….84 Tuhin Bera, Nirmal Kumar Mahapatra Chapter Eight Comparison of Cooking Methods in the Scope of Cuisine Dynamics: An Assessment From the Views of the Chefs in Neutrosophic Environment…..94 Ece Doğantan, Ezgi Demir, Bahri Baran Koçak, Çağlar Karamaşa Chapter Nine A Theoretic Approach to Decision Making Problems in Architecture with Neutrosophic Soft Set…………………………………………………...….113 Derya Bakbak, Vakkas Uluçay Chapter Ten Neutrosophic Sets in Multiple Objectives Decision Analysis ……….…….127 Willem K. M. Brauers SECTION THREE- NEUTROSOPHIC RELATED OTHER PAPERS Chapter Eleven Neutrosophic Triplet Bipolar Metric Spaces ………………………..……..150 Memet Şahin, Abdullah Kargın, Merve Sena Uz, Adil Kılıç 6 Quadruple Neutrosophic Theory And Applications Volume I Chapter Twelve Neutrosophic Measures of Central Tendency and Dispersion ………….....164 Muhammad Aslam, Rehan A. K. Sherwani, M.Waseem, Saeed A. Dobbah Chapter Thirteen Neutrosophic Triplet g - Metric Spaces …………………………………....181 Memet Şahin, Abdullah Kargın, Murat Yücel, Pelin Özkartepe Chapter Fourteen Soft Maximal Ideals on Soft Normed Rings ………………………..……..203 Memet Şahin, Vakkas Uluçay Chapter Fifteen Neutrosophic Triplet m - Metric Spaces ……………………..…………....213 Memet Şahin, Abdullah Kargın, Azize Dayan, Adil Kılıç Chapter Sixteen N-Neutrosophic Supra Topological Sets and Operators …………………..223 M. Arockia Dasan, G. Jayaparthasarathy, V. F. Little Flower Chapter Seventeen The Effect Of The Neutrosophic Logic On The Decision Tree…………...238 Necati Olgun, Ahmed Hatip Chapter Eighteen Combined Classic – Neutrosophic Sets and Numbers, Double Neutrosophic Sets and Numbers ………………………………………...……………......254 Memet Şahin, Abdullah Kargın, Florentin Smarandache Chapter Nineteen Bipolar Spherical Fuzzy Neutrosophic Cubic Graph and its Application ....266 Akalyadevi K, Antony Crispin Sweety C.,Sudamani Ramaswamy A. R. 7 Editors: Florentin Smarandache, Memet Şahin, Vakkas Uluçay and Abdullah Kargın Preface Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Smarandache introduce for the first time the neutrosophic quadruple numbers (of the form 𝑎 + 𝑏𝑇 + 𝑐𝐼 + 𝑑𝐹) and the refined neutrosophic quadruple numbers. Then Smarandache define an absorbance law, based on a prevalence order, both of them in order to multiply the neutrosophic components 𝑇,𝐼, 𝐹 or their sub-components 𝑇, 𝐼 , 𝐹 and thus to construct 𝑗 𝑘 𝑙 the multiplication of neutrosophic quadruple numbers. This first volume collects original research and applications from different perspectives covering different areas of neutrosophic studies, such as decision making, Quadruple, Metric, and some theoretical papers. This volume contains three sections: NEUTROSOPHIC QUADRUPLE, DECISION MAKING AND NEUTROSOPHIC RELATED OTHER PAPERS. 8 Quadruple Neutrosophic Theory And Applications Volume I Acknowledgment The editors and authors of this book thank all reviewers for their comments and the Pons Editions publisher for proving us the opportunity to write this collective book. Florentin Smarandache University of New Mexico, USA Memet Şahin Gaziantep University, Turkey Vakkas Uluçay Kilis 7 Aralık University, Turkey Abdullah Kargın Gaziantep University, Turkey 9