For several decades now, social scientist interested in the relationship between education and so... more For several decades now, social scientist interested in the relationship between education and social stratification. The purpose of this study was to gain insight into the impact of cultural capital and sociology of classroom on students’ learning. The opinions of 152 university students regarding the influence of cultural capital, gender differences, students’ confidence and perception about teacher on students’ learning have shown some results which are not similar to conventional researches. This study raised questions about the extent to which sociology of classroom is significant to be studied for educational progress, and offers ideas for further researches in this area. Quantitative method of research was applied. A sample of 152 respondents was chosen by applying stratified and convenience sampling techniques from 23 Departments of University of Sargodha. The results of the study were diverse in comparison to conventional researches in this domain. It was found that gender ...
The present study was designed to identify the factors affecting the parents' attitude towar... more The present study was designed to identify the factors affecting the parents' attitude towards the skill development and job opportunities for their daughters. The study was conducted in Faisalabad district, which comprised of five tehsils. One tehsil was selected at random and five Union ...
Soft set theory is a general mathematical tool for dealing with
uncertain, fuzzy, not clearly de ... more Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly de ned objects.
Ten papers on characteristic function of a neutrosophic set, neutrosophic hypercompositional stru... more Ten papers on characteristic function of a neutrosophic set, neutrosophic hypercompositional structures, expanding Newton mechanics with neutrosophy, neutrosophic left almost semigroup, rough neutrosophic sets, soft neutrosophic ring, soft neutrosophic field, and similar topics. Contributors: F. Yuhua, A. A. Salama, F. Smarandache, S. A. Alblowi, M. Ali, M. Shabir, M. Naz, A. A. A. Agboola, S. A. Akinleye, M. Dhar, S. Broumi, P. Biswas, S. Pramanik, B. C. Giri, H. A. El-Ghareeb, A. M. Maine, V. Kandasamy, P. Sekar and J. Vidhyalakshmi.
In this paper we have extended neutrosophic LA-semigroup, neutrosophic sub LA-semigroup, neutroso... more In this paper we have extended neutrosophic LA-semigroup, neutrosophic sub LA-semigroup, neutrosophic ideals, neutosophic prime ideals, neutrosophic semiprime ideals, neutrosophic strong irreducible ideals to soft neutrosophic LA-semigroup,soft neutosophic sub LA-semigroup,soft neutrosophic ideals,soft neutrosophic prime ideals,soft neutrosophic semiprime ideals and soft strong irreducible neutrosophic ideals respectively. We have found some new notions related to the strong or pure part of neutrosophy and we give explaination with necessary illustrative examples. We have also given rigorious theorems and propositions. The notion of soft neutrosophic homomorphism is presented at the end.
— A complex fuzzy class is a set of fuzzy sets which is characterized by a pure complex fuzzy gra... more — A complex fuzzy class is a set of fuzzy sets which is characterized by a pure complex fuzzy grade of membership where both the real and imaginary parts are fuzzy functions. The values that a pure complex fuzzy grade of membership may receive all lie within the unite square or unit circle in the complex plane. In this paper, we investigate different operation properties and propose a distance measure for complex fuzzy classes. The distance of two complex fuzzy classes measures the difference between the memberships of the fuzzy sets in the two complex fuzzy classes as well as the difference between the memberships in the related fuzzy sets in the two complex fuzzy classes. -equalities of two complex fuzzy classes are then defined which mainly base on this distance measure. If the distance between two complex fuzzy classes is less than or equal to , then they are said to be -equal. This paper reveals that different operations between complex fuzzy classes can affect given -equalities of complex fuzzy classes. Further, an application of utilizing the concept of -equalities of complex fuzzy classes in stocks and mutual funds in the stock market is presented.
In this study, we presented concept of neutrosophic cubic set by extending the concept of cubic s... more In this study, we presented concept of neutrosophic cubic set by extending the concept of cubic set to neutrosophic set. We also defined internal neutrosophic cubic set (INCS) and external neutrosophic cubic set (ENCS). Then, we proposed some new type of INCS and ENCS is called 1 3-INCS (or 2 3-ENCS), 2 3-INCS (or 1 3-ENCS). Then we study some of their relevant properties. Finally, we introduce an adjustable approach to NCS based decision making by similarity measure and an illustrative example is employed to show that they can be successfully applied to problems that contain uncertainties.
Fuzzy sets are the most significant tools to handle uncertain data while neutro-sophic sets are t... more Fuzzy sets are the most significant tools to handle uncertain data while neutro-sophic sets are the generalizations of fuzzy sets in the sense to handle uncertain, incomplete, inconsistent, indeterminate, false data. In this paper, we introduced fuzzy subspaces and neutrosophic subspaces (generalization of fuzzy subspaces) by applying group actions.Further, we define fuzzy transitivity and neutrosophic transitivty in this paper. Fuzzy orbits and neutrosophic orbits are introduced as well. We also studied some basic properties of fuzzy subspaces as well as neutrosophic subspaces.
Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, ... more Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difficulty, we introduce complex neutrosophic set. A complex neutrosophic set is a neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex-valued falsehood membership functions are the combination of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false amplitude term with phase term, respectively. Complex neutrosophic set is an extension of the neutrosophic set. Further set theoretic operations such as complement, union, intersection, complex neutrosophic product, Cartesian product, distance measure, and d-equalities of complex neutrosophic sets are studied here. A possible application of complex neutrosophic set is presented in this paper. Drawbacks and failure of the current methods are shown, and we also give a comparison of complex neutrosophic set to all such methods in this paper. We also showed in this paper the dominancy of complex neutrosophic set to all current methods through the graph.
In this paper we introduced mapping on neutrosophic soft expert sets through which we can study t... more In this paper we introduced mapping on neutrosophic soft expert sets through which we can study the images and inverse images of neutrosophic soft expert sets. Further, we investigated the basic operations and other related properties of mapping on neutrosophic soft expert sets in this paper.
In this paper, we introduce concept of bipolar neutrosophic set and its some operations. Also, we... more In this paper, we introduce concept of bipolar neutrosophic set and its some operations. Also, we propose score, certainty and accuracy functions to compare the bipolar neutrosophic sets. Then, we develop the bipolar neutrosophic weighted average operator (Aw) and bipolar neutrosophic weighted geometric operator (Gw) to aggregate the bipolar neutrosophic information. Furthermore, based on the (Aw) and (Gw) operators and the score, certainty and accuracy functions, we develop a bipolar neutrosophic multiple criteria decision-making approach, in which the evaluation values of alternatives on the attributes take the form of bipolar neutrosophic numbers to select the most desirable one(s). Finally, a numerical example of the method was given to demonstrate the application and effectiveness of the developed method.
The paper presents a VIPRO versatile, intelligent and mobile platform for robots, using an origin... more The paper presents a VIPRO versatile, intelligent and mobile platform for robots, using an original virtual projection method which involves the representation of modern mobile robots in a 3D virtual environment using a strong robotic simulator, an open architecture system and adaptive networks over the classical control system of the robot, developing intelligent control interfaces The advanced control technologies adapted to the robot environment such as neutrosophic control, robot Extenics control and robot haptic control are used. The obtained results lead to the conclusion that the VIPRO platform is to be integrated on the IT market as a new component alongside the existing ones, allowing a correct evaluation of robot behaviors in hazardous or challenging environments and high level real-time simulation in order to correctly model interactions among the robots and between the robots and the environment.
Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly de... more Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly dened objects.
In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and... more In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields.
The idea of neutrosophic code came into our mind at that time when we were reading the literature... more The idea of neutrosophic code came into our mind at that time when we were reading the literature about linear codes and we saw that, if there is data transfremation between a sender and a reciever. They want to send 11and 00 as codewords. They suppose 11 for true and 00 for false. When the sender sends these two codewords and the error occures. As a result the reciever recieved 01 or 10 instead of 11 and 00. This story give a way to the neutrosophic codes and thus we introduced neutrosophic codes over finite field in this paper.
In this paper, Smarandache soft groupoids shortly (SS-groupoids) are introduced as a generalizati... more In this paper, Smarandache soft groupoids shortly (SS-groupoids) are introduced as a generalization of Smarandache Soft semigroups (SS-semigroups) . A Smarandache Soft groupoid is an approximated collection of Smarandache subgroupoids of a groupoid . Further, we introduced parameterized Smarandache groupoid and strong soft semigroup over a groupoid Smarandache soft ideals are presented in this paper. We also discussed some of their core and fundamental properties and other notions with sufficient amount of examples. At the end, we introduced Smarandache soft groupoid homomorphism.
Neutrosophic LA-semigroup is a midway structure between a neutrosophic groupoid and a commutative... more Neutrosophic LA-semigroup is a midway structure between a neutrosophic groupoid and a commutative neutrosophic semigroup. Rings are the old concept in algebraic structures. We combine the neutrosophic LA-semigroup and ring together to form the notion of neutrosophic LA-semigroup ring. Neutrosophic LAsemigroup ring is defined analogously to neutrosophic group ring and neutrosophic semigroup ring.
Multi-space is the notion combining different fields in to a unifying field, which is more applic... more Multi-space is the notion combining different fields in to a unifying field, which is more applicable in our daily life. In this paper, we introduced the notion of multi-soft space which is the approximated collection of the multi-subspaces of a multi-space . Further, we defined some basic operations such as union, intersection, AND, OR etc. We also investigated some properties of multi-soft spaces.
For several decades now, social scientist interested in the relationship between education and so... more For several decades now, social scientist interested in the relationship between education and social stratification. The purpose of this study was to gain insight into the impact of cultural capital and sociology of classroom on students’ learning. The opinions of 152 university students regarding the influence of cultural capital, gender differences, students’ confidence and perception about teacher on students’ learning have shown some results which are not similar to conventional researches. This study raised questions about the extent to which sociology of classroom is significant to be studied for educational progress, and offers ideas for further researches in this area. Quantitative method of research was applied. A sample of 152 respondents was chosen by applying stratified and convenience sampling techniques from 23 Departments of University of Sargodha. The results of the study were diverse in comparison to conventional researches in this domain. It was found that gender ...
The present study was designed to identify the factors affecting the parents' attitude towar... more The present study was designed to identify the factors affecting the parents' attitude towards the skill development and job opportunities for their daughters. The study was conducted in Faisalabad district, which comprised of five tehsils. One tehsil was selected at random and five Union ...
Soft set theory is a general mathematical tool for dealing with
uncertain, fuzzy, not clearly de ... more Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly de ned objects.
Ten papers on characteristic function of a neutrosophic set, neutrosophic hypercompositional stru... more Ten papers on characteristic function of a neutrosophic set, neutrosophic hypercompositional structures, expanding Newton mechanics with neutrosophy, neutrosophic left almost semigroup, rough neutrosophic sets, soft neutrosophic ring, soft neutrosophic field, and similar topics. Contributors: F. Yuhua, A. A. Salama, F. Smarandache, S. A. Alblowi, M. Ali, M. Shabir, M. Naz, A. A. A. Agboola, S. A. Akinleye, M. Dhar, S. Broumi, P. Biswas, S. Pramanik, B. C. Giri, H. A. El-Ghareeb, A. M. Maine, V. Kandasamy, P. Sekar and J. Vidhyalakshmi.
In this paper we have extended neutrosophic LA-semigroup, neutrosophic sub LA-semigroup, neutroso... more In this paper we have extended neutrosophic LA-semigroup, neutrosophic sub LA-semigroup, neutrosophic ideals, neutosophic prime ideals, neutrosophic semiprime ideals, neutrosophic strong irreducible ideals to soft neutrosophic LA-semigroup,soft neutosophic sub LA-semigroup,soft neutrosophic ideals,soft neutrosophic prime ideals,soft neutrosophic semiprime ideals and soft strong irreducible neutrosophic ideals respectively. We have found some new notions related to the strong or pure part of neutrosophy and we give explaination with necessary illustrative examples. We have also given rigorious theorems and propositions. The notion of soft neutrosophic homomorphism is presented at the end.
— A complex fuzzy class is a set of fuzzy sets which is characterized by a pure complex fuzzy gra... more — A complex fuzzy class is a set of fuzzy sets which is characterized by a pure complex fuzzy grade of membership where both the real and imaginary parts are fuzzy functions. The values that a pure complex fuzzy grade of membership may receive all lie within the unite square or unit circle in the complex plane. In this paper, we investigate different operation properties and propose a distance measure for complex fuzzy classes. The distance of two complex fuzzy classes measures the difference between the memberships of the fuzzy sets in the two complex fuzzy classes as well as the difference between the memberships in the related fuzzy sets in the two complex fuzzy classes. -equalities of two complex fuzzy classes are then defined which mainly base on this distance measure. If the distance between two complex fuzzy classes is less than or equal to , then they are said to be -equal. This paper reveals that different operations between complex fuzzy classes can affect given -equalities of complex fuzzy classes. Further, an application of utilizing the concept of -equalities of complex fuzzy classes in stocks and mutual funds in the stock market is presented.
In this study, we presented concept of neutrosophic cubic set by extending the concept of cubic s... more In this study, we presented concept of neutrosophic cubic set by extending the concept of cubic set to neutrosophic set. We also defined internal neutrosophic cubic set (INCS) and external neutrosophic cubic set (ENCS). Then, we proposed some new type of INCS and ENCS is called 1 3-INCS (or 2 3-ENCS), 2 3-INCS (or 1 3-ENCS). Then we study some of their relevant properties. Finally, we introduce an adjustable approach to NCS based decision making by similarity measure and an illustrative example is employed to show that they can be successfully applied to problems that contain uncertainties.
Fuzzy sets are the most significant tools to handle uncertain data while neutro-sophic sets are t... more Fuzzy sets are the most significant tools to handle uncertain data while neutro-sophic sets are the generalizations of fuzzy sets in the sense to handle uncertain, incomplete, inconsistent, indeterminate, false data. In this paper, we introduced fuzzy subspaces and neutrosophic subspaces (generalization of fuzzy subspaces) by applying group actions.Further, we define fuzzy transitivity and neutrosophic transitivty in this paper. Fuzzy orbits and neutrosophic orbits are introduced as well. We also studied some basic properties of fuzzy subspaces as well as neutrosophic subspaces.
Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, ... more Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difficulty, we introduce complex neutrosophic set. A complex neutrosophic set is a neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex-valued falsehood membership functions are the combination of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false amplitude term with phase term, respectively. Complex neutrosophic set is an extension of the neutrosophic set. Further set theoretic operations such as complement, union, intersection, complex neutrosophic product, Cartesian product, distance measure, and d-equalities of complex neutrosophic sets are studied here. A possible application of complex neutrosophic set is presented in this paper. Drawbacks and failure of the current methods are shown, and we also give a comparison of complex neutrosophic set to all such methods in this paper. We also showed in this paper the dominancy of complex neutrosophic set to all current methods through the graph.
In this paper we introduced mapping on neutrosophic soft expert sets through which we can study t... more In this paper we introduced mapping on neutrosophic soft expert sets through which we can study the images and inverse images of neutrosophic soft expert sets. Further, we investigated the basic operations and other related properties of mapping on neutrosophic soft expert sets in this paper.
In this paper, we introduce concept of bipolar neutrosophic set and its some operations. Also, we... more In this paper, we introduce concept of bipolar neutrosophic set and its some operations. Also, we propose score, certainty and accuracy functions to compare the bipolar neutrosophic sets. Then, we develop the bipolar neutrosophic weighted average operator (Aw) and bipolar neutrosophic weighted geometric operator (Gw) to aggregate the bipolar neutrosophic information. Furthermore, based on the (Aw) and (Gw) operators and the score, certainty and accuracy functions, we develop a bipolar neutrosophic multiple criteria decision-making approach, in which the evaluation values of alternatives on the attributes take the form of bipolar neutrosophic numbers to select the most desirable one(s). Finally, a numerical example of the method was given to demonstrate the application and effectiveness of the developed method.
The paper presents a VIPRO versatile, intelligent and mobile platform for robots, using an origin... more The paper presents a VIPRO versatile, intelligent and mobile platform for robots, using an original virtual projection method which involves the representation of modern mobile robots in a 3D virtual environment using a strong robotic simulator, an open architecture system and adaptive networks over the classical control system of the robot, developing intelligent control interfaces The advanced control technologies adapted to the robot environment such as neutrosophic control, robot Extenics control and robot haptic control are used. The obtained results lead to the conclusion that the VIPRO platform is to be integrated on the IT market as a new component alongside the existing ones, allowing a correct evaluation of robot behaviors in hazardous or challenging environments and high level real-time simulation in order to correctly model interactions among the robots and between the robots and the environment.
Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly de... more Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly dened objects.
In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and... more In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields.
The idea of neutrosophic code came into our mind at that time when we were reading the literature... more The idea of neutrosophic code came into our mind at that time when we were reading the literature about linear codes and we saw that, if there is data transfremation between a sender and a reciever. They want to send 11and 00 as codewords. They suppose 11 for true and 00 for false. When the sender sends these two codewords and the error occures. As a result the reciever recieved 01 or 10 instead of 11 and 00. This story give a way to the neutrosophic codes and thus we introduced neutrosophic codes over finite field in this paper.
In this paper, Smarandache soft groupoids shortly (SS-groupoids) are introduced as a generalizati... more In this paper, Smarandache soft groupoids shortly (SS-groupoids) are introduced as a generalization of Smarandache Soft semigroups (SS-semigroups) . A Smarandache Soft groupoid is an approximated collection of Smarandache subgroupoids of a groupoid . Further, we introduced parameterized Smarandache groupoid and strong soft semigroup over a groupoid Smarandache soft ideals are presented in this paper. We also discussed some of their core and fundamental properties and other notions with sufficient amount of examples. At the end, we introduced Smarandache soft groupoid homomorphism.
Neutrosophic LA-semigroup is a midway structure between a neutrosophic groupoid and a commutative... more Neutrosophic LA-semigroup is a midway structure between a neutrosophic groupoid and a commutative neutrosophic semigroup. Rings are the old concept in algebraic structures. We combine the neutrosophic LA-semigroup and ring together to form the notion of neutrosophic LA-semigroup ring. Neutrosophic LAsemigroup ring is defined analogously to neutrosophic group ring and neutrosophic semigroup ring.
Multi-space is the notion combining different fields in to a unifying field, which is more applic... more Multi-space is the notion combining different fields in to a unifying field, which is more applicable in our daily life. In this paper, we introduced the notion of multi-soft space which is the approximated collection of the multi-subspaces of a multi-space . Further, we defined some basic operations such as union, intersection, AND, OR etc. We also investigated some properties of multi-soft spaces.
Neutrosophic Theory means Neutrosophy applied in many
fields in order to solve problems related t... more Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy considers every entity <A> together with its opposite or negation <antiA>, and with their spectrum of neutralities <neutA> in between them (i.e. entities supporting neither <A> nor <antiA>). Where <neutA>, which of course depends on <A>, can be indeterminacy, neutrality, tie (game), unknown, vagueness, contradiction, ignorance, incompleteness, imprecision, etc. Hence, in one hand, the Neutrosophic Theory is based on the triad <A>, <neutA>, and <antiA>. In the other hand, Neutrosophic Theory studies the indeterminacy in general, labelled as I, with In = I for n ≥1, and mI + nI = (m+n)I, in neutrosophic structures developed in algebra, geometry, topology etc. This volume contains 45 papers, written by the author alone or in collaboration with the following co-authors: Mumtaz Ali, Said Broumi, Sukanto Bhattacharya, Mamoni Dhar, Irfan Deli, Mincong Deng, Alexandru Gal, Valeri Kroumov, Pabitra Kumar Maji, Maikel Leyva-Vazquez, Feng Liu, Pinaki Majumdar, Munazza Naz, Karina Perez-Teruel, Rıdvan Sahin, A. A. Salama, Muhammad Shabir, Rajshekhar Sunderraman, Luige Vladareanu, Magdalena Vladila, Stefan Vladutescu, Haibin Wang, Hongnian Yu, Yan-Qing Zhang.
In this book, we define several new neutrosophic algebraic structures and their related propertie... more In this book, we define several new neutrosophic algebraic structures and their related properties. The main focus of this book is to study the important class of neutrosophic rings such as neutrosophic LA-semigroup ring, neutrosophic loop ring, neutrosophic groupoid ring and so on. We also construct their generalization in each case to study these neutrosophic algebraic structures ina broader sense. The indeterminacy element “ I ” give rise to a more bigger algebraic structure than the classical algebraic structures. It mainly classifies the algebraic structures in three catagories such as: neutrosophic algebraic structures, strong neutrosophic algebraic structures, and classical algebraic structures respectively. This reveals the fact that a classical algebraic structure is a part of the neutrosophic algebraic structures. This open a new way for the researchers to think in a broader way to visualize these vast neutrosophic algebraic structures.
In this book, the authors define several new types of soft neutrosophic algebraic structures over... more In this book, the authors define several new types of soft neutrosophic algebraic structures over neutrosophic algebraic structures and we study their generalizations. These soft neutrosophic algebraic structures are basically parameterized collections of neutrosophic sub-algebraic structures of the neutrosophic algebraic structure. An important feature of this book is that they introduce the soft neutrosophic group ring, soft neutrosophic semigroup ring with its generalization, and soft mixed neutrosophic N-algebraic structure over neutrosophic group ring, then the neutrosophic semigroup ring and mixed neutrosophic N-algebraic structure respectively.
In this book the authors introduce and study the following notions: Neutrosophic Crisp Points, Ne... more In this book the authors introduce and study the following notions: Neutrosophic Crisp Points, Neutrosophic Crisp Relations, Neutrosophic Crisp Sets, Neutrosophic Set Generated by Ng (Characteristic Function), α‐cut Level for Neutrosophic Sets, Neutrosophic Crisp Continuous Function, Neutrosophic Crisp Compact Spaces, Neutrosophic Crisp Nearly Open Sets, Neutrosophic Crisp Ideals, Neutrosophic Crisp Filter, Neutrosophic Crisp Local Functions, Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals, Neutrosophic Crisp L‐Openness and Neutrosophic Crisp L‐Continuity, Neutrosophic Topological Region, Neutrosophic Closed Set and Neutrosophic Continuous Function, etc. They compute the distance between neutrosophic sets and extend it to Neutrosophic Hesitancy Degree. The authors also generalize the Crisp Topological Space and Intuitionistic Topological Space to the notion of Neutrosophic Crisp Topological Space. At the end, they present applications to Neutrosophic Database, and show a security scheme based on Public Key Infrastructure (PKI) using Neutrosophic Logic Manipulation. The authors utilize neutrosophic sets in order to analyze social networks data conducted through learning activities, and for the Geographical Information Systems (GIS) they employ fundamental concepts and properties of a Neutrosophic Spatial Region.
In this book we introduce a new procedure called α-Discounting Method for Multi-Criteria Decision... more In this book we introduce a new procedure called α-Discounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-DMCDM is afterwards generalized to a set of preferences that can be transformed into a system of linear and/or non-linear homogeneous and/or non-homogeneous equations and/or inequalities. The general idea of α-D MCDM is to assign non-null positive parameters α1, α2, …, αp to the coefficients in the right-hand side of each preference that diminish or increase them in order to transform the above linear homogeneous system of equations which has only the null-solution, into a system having a particular non-null solution. After finding the general solution of this system, the principles used to assign particular values to all parameters α’s is the second important part of α-D, yet to be deeper investigated in the future. In the current book we propose the Fairness Principle, i.e. each coefficient should be discounted with the same percentage (we think this is fair: not making any favoritism or unfairness to any coefficient), but the reader can propose other principles. For consistent decision-making problems with pairwise comparisons, α- Discounting Method together with the Fairness Principle give the same result as AHP. But for weak inconsistent decision-making problem, α-Discounting together with the Fairness Principle give a different result from AHP. Many consistent, weak inconsistent, and strong inconsistent examplesare given in this book.
READUP BUILDUP. Thync is the third volume of α- instant readings put up by Florentin Smarandache.... more READUP BUILDUP. Thync is the third volume of α- instant readings put up by Florentin Smarandache. Although the style of the reading logs is uniform in the three volumes so far (rough and ready, kernel-extracting, absence of any secondary remarks, and thus masking the author-summarizator), this one address only technical issues from two topics of interest for the author (information fusion / data mining), unlike in previous eclectic books. Notes are taken directly from the source language (one language in this log, more languages before), and there are not abrupt transitions anymore in the selection of information. All works annotated here are from authoritative scientific sources, no more popularizers or debasers. The title of the volume is an aftereffect of juxtaposition of the verb think, and the noun syncronization, resulting in an incentive - unveiled from the first chapter of readings: Think in sync! Far from being just a call to thinking synchronously, the notes speak about communication as activity-together, where the interlocutors share information. Very likely, it resides right here the drive for publication of the instant readings series: to share. Besides, of course, multiple other layers of connotation (demonstrative or paideuma-tic), the reading series resemble an allegorical car, a carriage packed with books and bookmarks, which the author-summarizator shook of ideas. For personal use, but as well for a possible satisfaction of a possible spectator, necessarily perceived as a passer in a hurry, with no aptitude to dawdling around.
This book is a translation from Romanian of "Probleme Compilate şi Rezolvate de Geometrie şi Trig... more This book is a translation from Romanian of "Probleme Compilate şi Rezolvate de Geometrie şi Trigonometrie" (University of Kishinev Press, Kishinev, 169 p., 1998), and includes problems of 2D and 3D Euclidean geometry plus trigonometry, compiled and solved from the Romanian Textbooks for 9th and 10th grade students, in the period 1981-1988, when I was a professor of mathematics at the "Petrache Poenaru" National College in Balcesti, Valcea (Romania), Lycée Sidi El Hassan Lyoussi in Sefrou (Morocco), then at the "Nicolae Balcescu" National College in Craiova and Dragotesti General School (Romania), but also I did intensive private tutoring for students preparing their university entrance examination. After that, I have escaped in Turkey in September 1988 and lived in a political refugee camp in Istanbul and Ankara, and in March 1990 I immigrated to United States. The degree of difficulties of the problems is from easy and medium to hard. The solutions of the problems are at the end of each chapter. One can navigate back and forth from the text of the problem to its solution using bookmarks. The book is especially a didactical material for the mathematical students and instructors.
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uncertain, fuzzy, not clearly de ned objects.
distance measure, and d-equalities of complex neutrosophic
sets are studied here. A possible application of complex neutrosophic set is presented in this paper. Drawbacks and failure of the current methods are shown, and we also give a comparison of complex neutrosophic set to all such methods in this paper. We also showed in this paper the dominancy of complex neutrosophic set to all current methods through the graph.
uncertain, fuzzy, not clearly de ned objects.
distance measure, and d-equalities of complex neutrosophic
sets are studied here. A possible application of complex neutrosophic set is presented in this paper. Drawbacks and failure of the current methods are shown, and we also give a comparison of complex neutrosophic set to all such methods in this paper. We also showed in this paper the dominancy of complex neutrosophic set to all current methods through the graph.
fields in order to solve problems related to indeterminacy.
Neutrosophy considers every entity <A> together with its
opposite or negation <antiA>, and with their spectrum of
neutralities <neutA> in between them (i.e. entities supporting neither <A> nor <antiA>). Where <neutA>, which of course depends on <A>, can be indeterminacy,
neutrality, tie (game), unknown, vagueness, contradiction,
ignorance, incompleteness, imprecision, etc.
Hence, in one hand, the Neutrosophic Theory is based on
the triad <A>, <neutA>, and <antiA>. In the other hand, Neutrosophic Theory studies the indeterminacy in general, labelled as I, with In = I for n ≥1, and mI + nI = (m+n)I, in neutrosophic structures developed in algebra, geometry, topology etc.
This volume contains 45 papers, written by the author
alone or in collaboration with the following co-authors:
Mumtaz Ali, Said Broumi, Sukanto Bhattacharya, Mamoni
Dhar, Irfan Deli, Mincong Deng, Alexandru Gal, Valeri
Kroumov, Pabitra Kumar Maji, Maikel Leyva-Vazquez, Feng
Liu, Pinaki Majumdar, Munazza Naz, Karina Perez-Teruel,
Rıdvan Sahin, A. A. Salama, Muhammad Shabir, Rajshekhar
Sunderraman, Luige Vladareanu, Magdalena Vladila,
Stefan Vladutescu, Haibin Wang, Hongnian Yu, Yan-Qing
Zhang.
The general idea of α-D MCDM is to assign non-null positive parameters
α1, α2, …, αp to the coefficients in the right-hand side of each preference that diminish or increase them in order to transform the above linear homogeneous system of equations which has only the null-solution, into a system having a particular non-null solution. After finding the general
solution of this system, the principles used to assign particular values to all parameters α’s is the second important part of α-D, yet to be deeper investigated in the future.
In the current book we propose the Fairness Principle, i.e. each
coefficient should be discounted with the same percentage (we think this is
fair: not making any favoritism or unfairness to any coefficient), but the
reader can propose other principles.
For consistent decision-making problems with pairwise comparisons, α-
Discounting Method together with the Fairness Principle give the same
result as AHP.
But for weak inconsistent decision-making problem, α-Discounting together with the Fairness Principle give a different result from AHP. Many consistent, weak inconsistent, and strong inconsistent examplesare given in this book.
style of the reading logs is uniform in the three volumes so far (rough and ready, kernel-extracting, absence of any
secondary remarks, and thus masking the author-summarizator), this one address only technical issues from two
topics of interest for the author (information fusion / data mining), unlike in previous eclectic books. Notes are taken directly from the source language (one language in this log,
more languages before), and there are not abrupt transitions anymore in the selection of information. All works
annotated here are from authoritative scientific sources, no more popularizers or debasers. The title of the volume is an aftereffect of juxtaposition of the verb think, and the noun syncronization, resulting in an incentive - unveiled from the first
chapter of readings: Think in sync! Far from being just a call to thinking synchronously, the notes speak about communication as activity-together, where the interlocutors share information. Very likely, it resides right here the drive for publication of the
instant readings series: to share. Besides, of course, multiple other layers of connotation (demonstrative or paideuma-tic), the reading series resemble an allegorical car, a carriage
packed with books and bookmarks, which the author-summarizator shook of ideas. For personal use, but as well
for a possible satisfaction of a possible spectator, necessarily perceived as a passer in a hurry, with no aptitude to
dawdling around.