Study of a classical critic of Avicenna's views on the existence and nature of God.

In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of \((\in, \in)\) and \((\in, \in\! \vee \, {q})\)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of \((\alpha,\beta)\)-fuzzy subalgebras and \((\alpha,\beta)\)-fuzzy ideals on equality algebras. (...) Also, by using the notion of \((\in, \in)\)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of \(X\), and we proved that the set of all classes of \(X\) by these order is a poset. (shrink)

The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filer are displayed.

The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filter are displayed.

When it comes to making decisions in vague problems, rough is one of the best tools to help analyzers. So based on rough and hoop concepts, two kinds of approximations (Lower and Upper) for filters in hoops are defined, and then some properties of them are investigated by us. We prove that these approximations- lower and upper- are interior and closure operators, respectively. Also after defining a hyper operation in hoops, we show that by using this hyper operation, set of (...) all rough filters is monoid. For more study, we define the implicative operation on the set of all rough filters and prove that this set with implication and intersection is made a hoop. (shrink)

The notions of soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.

The notions of soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.

The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations of positive implicative soju ideal are established. Finally, extension property for positive implicative soju ideal is constructed.

In this paper, considering \(L\)-algebras, which include a significant number of other algebraic structures, we present a definition of modules on \(L\)-algebras (\(L\)-modules). Then we provide some examples and obtain some results on \(L\)-modules. Also, we present definitions of prime ideals of \(L\)-algebras and \(L\)-submodules (prime \(L\)-submodules) of \(L\)-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime \(L\)-submodules.

In this paper, we apply the notion of \(n\)-fold filters to the \(EQ\)-algebras and introduce the concepts of \(n\)-fold pseudo implicative, \(n\)-fold implicative, \(n\)-fold obstinate, \(n\)-fold fantastic prefilters and filters on an \(EQ\)-algebra \(\mathcal{E}\). Then we investigate some properties and relations among them. We prove that the quotient algebra \(\mathcal{E}/F\) modulo an 1-fold pseudo implicative filter of an \(EQ\)-algebra \(\mathcal{E}\) is a good \(EQ\)-algebra and the quotient algebra \(\mathcal{E}/F\) modulo an 1-fold fantastic filter of a good \(EQ\)-algebra \(\mathcal{E}\) is an (...) \(IEQ\)-algebra. (shrink)

In this paper, by considering the notions of effect algebra and product effect algebra, we define the concept of effect module. Then we investigate some properties of effect modules, and we present some examples on them. Finally, we introduce some topologies on effect modules.

In this paper, we define the notion of PC-lattice, as a generalization of finite positive implicative BCK-algebras with condition and bounded commutative BCK-algebras. We investiate some results for Pc-lattices being a new class of BCK-lattices. Specially, we prove that any Boolean lattice is a PC-lattice and we show that if X is a PC-lattice with condition S, then X is an involutory BCK-algebra if and only if X is a commutative BCK-algebra. Finally, we prove that any PC-lattice with condition is (...) a distributive BCK-algebra. (shrink)

Study of a classical critic of Avicenna's views on the existence and nature of God.

More general form of -neutrosophic ideal is introduced, and their properties are investigated. Relations between -neutrosophic ideal and )-neutrosophic ideal are discussed. Characterizations of )-neutrosophic ideal are discussed, and conditions for a neutrosophic set to be an )-neutrosophic ideal are displayed.

Rough set theory is an excellent mathematical tool for the analysis of a vague description of actions in decision problems. Now, in this paper by considering the notion of an equality algebra, the notion of the lower and the upper approximations are introduced and some properties of them are given. Moreover, it is proved that the lower and the upper approximations define an interior operator and a closure operator, respectively. Also, using D-lower and D-upper approximation, conditions for a nonempty subset (...) to be definable are provided and investigated that under which condition D-lower and D-upper approximation can be filter. (shrink)

In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculated coproduct and pushout in a special case. Also, we constructed a free EQ-algebra on a singleton.

Working memory is developed in one region of the brain called the dorsolateral prefrontal cortex. The dysfunction of this region leads to synaptic neuroplasticity impairment. It has been reported that several biochemical parameters and anthropometric measurements play a vital role in cognition and brain health. This study aimed to investigate the relationships between cognitive function, serum biochemical profile, and anthropometric measurements using DLPFC activation. A cross-sectional study was conducted among 35 older adults who experienced mild cognitive impairment. For this purpose, (...) we distributed a comprehensive interview-based questionnaire for collecting sociodemographic information from the participants and conducting cognitive tests. Anthropometric values were measured, and fasting blood specimens were collected. We investigated their brain activation using the task-based functional MRI, specifically in the DLPFC region. Positive relationships were observed between brain-derived neurotrophic factor and Mini-Mental State Examination ; however, negative relationships were observed between serum triglyceride and serum malondialdehyde with right DLPFC activation while the participants performed 1-back task after adjustments for age, gender, and years of education. In conclusion, higher serum triglycerides, higher oxidative stress, and lower neurotrophic factor were associated with lower right DLPFC activation among older adults with MCI. A further investigation needs to be carried out to understand the causal-effect mechanisms of the significant parameters and the DLPFC activation so that better intervention strategies can be developed for reducing the risk of irreversible neurodegenerative diseases among older adults with MCI. (shrink)

In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculated coproduct and pushout in a special case. Also, we constructed a free EQ-algebra on a singleton.

This text presents an analysis of a collection of Mathematics textbooks, carried out for the discipline “Analysis of Mathematics Books and Teaching Materials”, taught in the Graduate Program in Mathematics Education at the Universidade Estadual Paulista “Júlio de Mesquita Filho”. Inspired by the methodology of vertical and horizontal analysis of textbooks, this work aims to understand in what ways the law 10.639/2003 is effective in textbooks that satisfy the demands of the New High School and the BNCC – Base Nacional (...) Comum Curricular. Presenting the historical movements of black populations, mainly the Brazilian one, the text is inspired by the two decades of that law to conduct the analysis criteria and seek to understand in what ways the analyzed collection acts in the constitution of the mathematical identity of black students. At the end of the analysis, it is observed that the law is barely complied with, speaking through erasures and without delving into important points about racial discussions. It is concluded that changes are necessary for compliance with the law to produce positive effects on the constitution of mathematical identities of black subjects. (shrink)

Rajabʻalī Tabrīzī, -1669 or 1670 -- Philosophical thoughts -- Islamic philosophy - Iran.

The objective of this study is to conduct an analysis of the terminologies employed by Imam Ibn Rajab in his well-known work, "Fath al-Bari Sharh Sahih al-Bukhari," with the intention of enhancing our comprehension of his methodology in the field of Hadith studies. The study utilises a methodology that combines textual analysis and statistical techniques to examine the occurrence and usage of specific terms. The study also compares Ibn Rajab’s terminology with that of "Muqaddimah Ibn Salah" for a (...) thorough analysis. The study's main findings highlight the nuanced interpretations and variations in Ibn Rajab’s use of terminologies, specifically in synonymous terms like 'tafarrud' and 'garabah'. Furthermore, it emphasises his careful choice of the term "hasan" and the potential consequences it carries. The statistical analysis offers valuable insights into the frequency and patterns of these terminologies, which contributes to a quantitative understanding of their significance. After analysing the results, several suggestions are put forward. First, to gain a deeper understanding of Ibn Rajab's unique perspectives, it is recommended to thoroughly examine his methodologies throughout his entire body of work. Second, additional research is required to delve into the interpretations and implications of synonymous terms employed by Ibn Rajab. Third, conducting a thorough examination of his specific use of the term "hasan" would yield valuable insights into his criteria for evaluation. Fourth, it is important to conduct a thorough comparative analysis between the two texts, "Muqaddimah Ibn Salah" and the current text, to identify any similarities, differences, and potential influences. Fifth, it is recommended to broaden the statistical analysis to explore patterns, trends, and correlations within the dataset. Furthermore, gaining a broader understanding of Ibn Rajab’s contributions within the academic and scholarly landscape would greatly enhance comprehension. (shrink)

Edition and study of P.Vindob. A.Ch. 36616, a literary paper fragment from 3rd/9th-century Egypt. The fragment contains a tradition that depicts ʿAlī b. Abī Ṭālib (d. 40/661) performing a four-rakʿa prayer and reciting a special supplication on the 15th of the month of Rajab. The tradition is only known from noncanonical Shīʿī ḥadīth collections. Situating it in a broader historical context, the paper provides a glimpse on the Shīʿī presence in Egypt as well as the sanctity of the month (...) of Rajab in Sunnī and Shīʿī literatures. This tradition, in conclusion, presents an early evidence for the observances of the month of Rajab in general and the middle of the month in particular in the local Shīʿī community in pre-Fatimid Egypt. (shrink)

The exceptional intellectual richness of seventeenth-century Safavid Iran is epitomised by the philosophical school of Isfahan, and in particular by its ostensible founder, Mir Damad (d. 1631), and his great student Mulla Sadra (aka Sadr al-Din Shirazi, d. 1636). Equally important to the school is the apophatic wisdom of Rajab 'Ali Tabrizi that followed later (d. 1669/70). However, despite these philosophers' renown, the identification of the 'philosophical school of Isfahan' was only proposed in 1956, by the celebrated French Iranologist (...) Henry Corbin, who noted the unifying Islamic Neoplatonist character of some 20 thinkers and spiritual figures; this grouping has subsequently remained unchallenged for some fifty years. In this highly original work, Janis Esots investigates the legitimacy of the term 'school', delving into the complex philosophies of these three major Shi'i figures and drawing comparisons between them. The author makes the case that Mulla Sadra's thought is independent and actually incompatible with the thoughts of Mir Damad and Rajab Ali Tabrizi. This not only presents a new way of thinking about how we understand the 'school of Isfahan', it also identifies Mir Damad and Rajab Ali Tabrizi as pioneers in their own right. (shrink)

: A rich array of twelfth to fifteenth century Arabic texts captures the advent of a supererogatory prayer known as ṣalāt al-raghā’ib, on the eve of the first Friday of the month of Rajab in late eleventh-century Jerusalem, and its wide dissemination. This corpus offers an unusually vivid picture of the formation and the transformation of a medieval bid’a, or, of an ‘invention of tradition’. Combining our expertise in Islamic law and in Ayyūbid and Mamluk era history, we use (...) this corpus for an in-depth study of popular piety, power politics, scholarly polemics and legal discourse. Twenty eight translated excerpts of various texts are presented in this paper, preceded by a detailed introduction. Exploring legal reasoning in its concrete political and social context provides a nuanced understanding of the development, mass proliferation and ensuing debate over a highly controversial and extraordinary potent religious practice. (shrink)

The Abrahamic tradition that the Arabs value most was ḥajj. The ḥajj, which means to visit Kaʿba was the greatest means of getting closer to Allāh. The Kaʿba was the house of Allāh. And the visitors of the Kaʿba were Allāh’s guests. For this reason, the Arabs used to great respect to the visitors and they never used to attack a man in the ḥarem (the area around the Kaʿba). The same respect included visitors’ travels to the Kaʿba. There were (...) two Abrahamic traditions that ensured the safety of visitors and sacrifices: Ḥaram months and qalāid. Ḥaram months were Dhū l-Qaʿdah, Dhū l-Ḥijjah, Muḥarram and Rajab. And the Arabs did not used to attack anyone in those months. For visits outside the ḥaram months, the visitors used to use the qalāid as a primitive visa. Qalāid is the plural of the word qilāda, meaning necklace. The Arab, who saw the qilādas, used to understand that the person who wore the qilāda wanted to go to the Kaʿba or had returned home from the Kaʿba. Qilādas used to be knitted from wool ropes and they used to be hung on animals’ neck or humps. Sometimes horseshoes used to hang on these qilādas. On the way back from Kaʿba, the barks of the ḥarem trees used to hang on the qilādas instead of the horseshoes. The Qurʾān orders Muslims not to disrespect the qilādas. This order also reveals that the Qurʾān recognizes the qilāda tradition. Allāh’s Apostle (sallallaahu ‘alayhi wa sallam) and Ṣaḥāba are also known to continue this tradition.Summary: Ḥajj was the most important worship of the Arabs in the pre-Islamic period. Human and commodity mobility in the ḥajj had an important place in the life of the Meccans who lived in land unfit for agriculture. This fact is expressed as follows in Abraham’s (Ibrāhīm al-Khalīl) prayer: “Our Lord! Lo! I have settled some of my posterity in an uncultivable valley near unto Thy holy House, our Lord! That they may establish proper worship; so incline some hearts of men that they may yearn toward them, and provide Thou them with fruits in order that they may be thankful.” (Ibrahim 14:37) The Arabs who lived in various parts of the Arabian Peninsula used to come to Mecca during the ḥajj season and present their sacrifices. They also used to buy their needs from nearby markets. These markets were also places where traders had the opportunity to sell their products.Because the Arabian Peninsula is unfavorable in terms of climate and soil, many Arab tribes used to raid and attack other tribes to sustain their existence. It is even known that some Arabs proud of their raids. The attacks only used to stop in the ḥaram months (Dhū l-Qaʿdah, Dhū l-Ḥijjah, Muḥarram and Rajab). Because of the prohibition of fighting in the ḥaram months, the visitors used to visit the Kaʿba with confidence. Thanks to this truce, the trade goods carried by visitors used to reach to Mecca with confidence.It was possible that the visits outside of the ḥaram months were safe. However, it was necessary to follow some traditions in order to achieve this confidence. Visitors to the Kaʿba used to use some signs that they were visitors to the Kaʿba. One of these signs was qilāda (necklace) hanging on the neck or hump of the animal. The person wearing qilāda was Allāh’s guest, and his sacrifice was the property of Allāh. For this reason, no Arab would to dare to attack these visitors and property. Because of the Arab reverence for the Kaʿba, visitors wearing qilādas used to come to the Kaʿba and present their sacrifices throughout the year. The sacrifices had an important place in the livelihood of the poor.Qilādas were mostly used for visits outside the ḥaram months. The qilādas used to hang on the necks of the animals shipped to the Kaʿba as sacrifice. However, it is also known that qilādas are sometimes hung on hump. People who did not deliver sacrifices (animals) to the Kaʿba used to hang the qilāda his neck to show that he was a visitor to the Kaʿba. Similarly, it is known that people who sacrificed their animals on the Kaʿba hang the qilāda their neck on the way back. The qilādas fitted on the way to the Kaʿba were made of ropes spun from wool or hair. Sometimes horseshoes used to hang on these qilādas. Ḥarem plants (grass, tree bark) used to use in the qilādas on the way back.The Qurʾān orders Muslims not to disrespect the qilādas. This order also reveals that the Qurʾān recognizes the qilāda tradition. The word qalāid is mentioned twice in the Qurʾān: “O ye who believe violate not the sanctity of the symbols of Allāh, nor of the sacred month, nor of the animals brought for sacrifice, nor the qalāid, nor the people resorting to the sacred house, seeking of the Bounty and good pleasure of their Lord.” (Al Māʼidah 5:2), “Allāh made the Kaʿba, the sacred house, an asylum of security of men as also the sacred months, the animals for offerings, and the qalāid.” (Al Māʼidah 5:97) Considering the practices of the qilāda, it is understood that qilādas are a kind of visa. It is understood that all practices related to the visit to the Kaʿba, especially the ḥajj, have an aim to satisfy the material-spiritual needs of those who come there for the purpose of visiting and trading, as well as those who reside in the Kaʿba. Therefore, it will not be far away to say that qilādas can be used today for the same purpose. For example, labels, banderols, visas and passports can be used instead of ropes, horseshoes and plants. On the other hand, the meaning of the āyāt (verse) in which the word qalāid is mentioned is not limited to the Arabs. The same āyāt declare that qilādas are a development (qiyām) instrument for people. Therefore, the qilāda has a meaning potential beyond the 7th century and the inhabitants of this century. (shrink)

In the ḥadīth sources it is being conveyed that the companions (ṣaḥāba) refrained from asking questions to the Prophet. This situation is generally associated with the verse of sūrat al-Māʾida 5:101. An-Navvās b. Samʿān (d. 50/670), Abū Umāma al-Bāhilī (d. 86/705) and Anas b. Mālik (d. 93/711-12) are among the companions who consider this situation as the ban on the asking questions. The concern that asking questions may cause additional obligations that were not presumed to be obligatory also attracts attention (...) in these records. Keeping all numerous questions addressed to the Prophet in mind we may ask if there is a Prophetic prohibition on asking questions. We will seek an answer to this question, which constitutes the main axis of this article, especially in the framework of the narrations mentioned among the reasons of the al-Māʾida 101. We will evaluate the information concerned in their historical context and internal coherence inductively. Our investigation differs in this respect from the investigations, which dealt with the disapproval of excessive and unnecessary questions. As a result of our research, we think that it is possible to talk about a ban on asking questions about religious issues in the last three years of the Medina period. We will first discuss the dating and nature of this ban, from which only Bedouin and visitors who come to Madina were excluded. Then, we especially will evaluate the theological consequences of answer of the Prophet, which mentioned in the same context, of whether the pilgrimage is religious duty for every year. In the last part of the article, the prohibition of asking questions will be discussed in the light of Hans-Georg Gadamer’s principle “Der hermeneutische Vorrang der Frage”, which deals with the effect of the questions on the direction and nature of the answer.Summary: It is reported in Qurʾān and Ḥadīth that the Prophet Muḥammad (PBUH) was asked a lot of questions and he responded based on the revealed knowledge or his own. He did not like the questions which remain outside of the daily religious life like the questions whether he is able to know the end of the world or to show miracle. There are some reports which covey that the Prophet frowned upon some questions because they could cause new assignments or lead to complicate the existing ones. The Companions like an-Nawwās b- Samʿān (d. 50/670), Abū Umāma al-Bāhilī (d. 86/705) and Anas b. Mālik (d. 93/711-12) have been describing this situation as the ban of asking of religious implications.This issue which companions formulated exactly as the ban of the asking questions was regarded in research until now just as the depreciation of the Prophet upon the unnecessary questions. In this interpretation the idea played a role that the ban of the asking may not conform to the religious pedagogic of the Prophet and the real existence of a lot of asked questions contradict that. Therefore the imperative “do not ask” in al-Māʾida 5:101 (O believers, do not ask about things which, if made known to you, may vex you) were interpreted not as the prohibition of the asking questions in real sense, but as just the depreciation of the unnecessary questions.We argue that it is possible to talk about a prohibition of the asking questions in real sense. We are of the view that the asking to religious matters was prohibited in the last years of the Medina period. In a time of Madina period when the fundamental principles of Islam emerged the questions of companions let the Prophet think that they may lead to additional religious obligations. Therefore the Prophet warned his companions in these words: “Do not ask me about the details of the things which I do not mention to you” and “Allāh Taʿālā has remained silent about some things, out of compassion for you, not forgetfulness so do not seek after them.”The imperative “do not ask” in al-Māʾida 5:101 has to been understood in the light of the Prophet’s advice as quoted above. According to the expressions of the companions reported in hadith collections, it is obvious that the imperative “do not ask” signifies not only “do not ask unnecessary questions”, but “do not ask questions related to theology matters in general”.Anas b. Mālik served the Prophet nine or ten years and was not criticised by the Prophet anytime. A companion like Anas cannot have refrained from the asking questions because they may be unnecessary. Anas interpreted “ do not ask” in al-Māʾida 5:101 in words: “We were forbidden in the Qurʾān that we ask the Prophet anything". Anas’s observation reveals that the companions considered the “do not ask” in al-Māʾida 5:101 as a general prohibition for the questions to religious issue.According to our research it seems this ban was promulgated in last three years of Medina Period, and Bedouin and visitors were excluded. Al-Nawwās b. Samʿān noticed that the ban of the asking questions was only for the residents in Medina: “I was in Medina one year. The reason why I did not stay in Medina was my wish to ask the Prophet a religious issue. So, whoever stayed in Medina was not permitted to ask the Prophet questions.” Abū Umāma al-Bāhilī interpreted the ban of the asking in al-Māʾida 5:101 as a general ban. He reported that the companions give a garment (burda) as gift to a Bedouin in order to let him ask the Prophet questions. The ban on asking questions in Medina was not related to unnecessary questions. It was indeed related to the questions that might have caused addition to already well-defined obligatory rulings in Islam. Accordingly, the questions became unnecessary because they were asked in the time of revelation. With the ban of the asking the Prophet questions accentuated that God and his Messenger are aware what necessary and what was not. It means that God can intervene if it is necessary. For that they do not need ask the Prophet. Aṭ-Ṭabarī, al-Qurṭubī, en-Nawawī, Ibn RaJab el-Ḥanbalī and Ibn Ḥajar al-ʿAsqalānī are the scholars who interpreted the ban of asking in this general sense.We especially will evaluate the theological consequences of the Prophet’s response, as reported in the sources: “ If I said yes, the pilgrimage will be a religious duty for every year.” Here one may not misconstrue that the Prophet could determine the religious obligations arbitrarily. He meant that the believers have to practice only that which were revealed to them. The Prophet wanted to teach his followers the principle that became essential rule of Islamic jurisprudence: “What is not forbidden is permitted”.The Prophet did not perform tarāwīḥ-prayer in congregation in the month of fasting due to the apprehension that it might become obligatory for the believers and they would not be able to follow it. In this human reaction of the Prophet we see that the Prophet did not consider himself as the founder of the Islamic norms. In this context the following questions are important: Does God consider the human questions when making something obligatory? Is God influenceable in terms of His orders? Ibn Ḥajar observes: The scholars of Ahl al-Sunnah accept the causality in terms of the Islamic norms. Accordingly something can become a religious norm because the humans asked about that. But God’s decision does not depend on the humans. God can consider human questions, if He so wills. (shrink)

This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with the following 99 co-authors (alphabetically ordered) from 26 countries: Ahmed B. Al-Nafee, Adesina Abdul Akeem Agboola, Akbar Rezaei, Shariful Alam, Marina Alonso, Fran Andujar, (...) Toshinori Asai, Assia Bakali, Azmat Hussain, Daniela Baran, Bijan Davvaz, Bilal Hadjadji, Carlos Díaz Bohorquez, Robert N. Boyd, M. Caldas, Cenap Özel, Pankaj Chauhan, Victor Christianto, Salvador Coll, Shyamal Dalapati, Irfan Deli, Balasubramanian Elavarasan, Fahad Alsharari, Yonfei Feng, Daniela Gîfu, Rafael Rojas Gualdrón, Haipeng Wang, Hemant Kumar Gianey, Noel Batista Hernández, Abdel-Nasser Hussein, Ibrahim M. Hezam, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Muthusamy Karthika, Nour Eldeen M. Khalifa, Madad Khan, Kifayat Ullah, Valeri Kroumov, Tapan Kumar Roy, Deepesh Kunwar, Le Thi Nhung, Pedro López, Mai Mohamed, Manh Van Vu, Miguel A. Quiroz-Martínez, Marcel Migdalovici, Kritika Mishra, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohammed Alshumrani, Mohamed Loey, Muhammad Akram, Muhammad Shabir, Mumtaz Ali, Nassim Abbas, Munazza Naz, Ngan Thi Roan, Nguyen Xuan Thao, Rishwanth Mani Parimala, Ion Pătrașcu, Surapati Pramanik, Quek Shio Gai, Qiang Guo, Rajab Ali Borzooei, Nimitha Rajesh, Jesús Estupiñan Ricardo, Juan Miguel Martínez Rubio, Saeed Mirvakili, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, Ahmed A. Salama, Nirmala Sawan, Gheorghe Săvoiu, Ganeshsree Selvachandran, Seok-Zun Song, Shahzaib Ashraf, Jayant Singh, Rajesh Singh, Son Hoang Le, Tahir Mahmood, Kenta Takaya, Mirela Teodorescu, Ramalingam Udhayakumar, Maikel Y. Leyva Vázquez, V. Venkateswara Rao, Luige Vlădăreanu, Victor Vlădăreanu, Gabriela Vlădeanu, Michael Voskoglou, Yaser Saber, Yong Deng, You He, Youcef Chibani, Young Bae Jun, Wadei F. Al-Omeri, Hongbo Wang, Zayen Azzouz Omar. (shrink)

This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, (...) T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang. (shrink)