A Short History Of Fuzzy Intuitionistic Fuzzy Neutrosophic And Plithogenic Sets

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A short history of fuzzy, intuitionistic fuzzy, neutrosophic and plithogenic sets

A. Rezaei,T. Oner,T. Katican,F. Smarandache,N. Gandotra
A short history of fuzzy intuitionistic fuzzy neutrosophic and plithogenic sets Book PDF

Author : A. Rezaei,T. Oner,T. Katican,F. Smarandache,N. Gandotra
Publisher : Infinite Study
Page : 19 pages
File Size : 43,8 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 8210379456XXX

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A short history of fuzzy, intuitionistic fuzzy, neutrosophic and plithogenic sets by A. Rezaei,T. Oner,T. Katican,F. Smarandache,N. Gandotra Pdf

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements are characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets.

Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited

Florentin Smarandache
Plithogenic Set an Extension of Crisp Fuzzy Intuitionistic Fuzzy and Neutrosophic Sets Revisited Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 14 pages
File Size : 55,6 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 8210379456XXX

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Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited by Florentin Smarandache Pdf

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined between each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life.

Collected Papers. Volume X

Florentin Smarandache
Collected Papers Volume X Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 1006 pages
File Size : 46,5 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 8210379456XXX

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Collected Papers. Volume X by Florentin Smarandache Pdf

This tenth volume of Collected Papers includes 86 papers in English and Spanish languages comprising 972 pages, written between 2014-2022 by the author alone or in collaboration with the following 105 co-authors (alphabetically ordered) from 26 countries: Abu Sufian, Ali Hassan, Ali Safaa Sadiq, Anirudha Ghosh, Assia Bakali, Atiqe Ur Rahman, Laura Bogdan, Willem K.M. Brauers, Erick González Caballero, Fausto Cavallaro, Gavrilă Calefariu, T. Chalapathi, Victor Christianto, Mihaela Colhon, Sergiu Boris Cononovici, Mamoni Dhar, Irfan Deli, Rebeca Escobar-Jara, Alexandru Gal, N. Gandotra, Sudipta Gayen, Vassilis C. Gerogiannis, Noel Batista Hernández, Hongnian Yu, Hongbo Wang, Mihaiela Iliescu, F. Nirmala Irudayam, Sripati Jha, Darjan Karabašević, T. Katican, Bakhtawar Ali Khan, Hina Khan, Volodymyr Krasnoholovets, R. Kiran Kumar, Manoranjan Kumar Singh, Ranjan Kumar, M. Lathamaheswari, Yasar Mahmood, Nivetha Martin, Adrian Mărgean, Octavian Melinte, Mingcong Deng, Marcel Migdalovici, Monika Moga, Sana Moin, Mohamed Abdel-Basset, Mohamed Elhoseny, Rehab Mohamed, Mohamed Talea, Kalyan Mondal, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Ihsan, Muhammad Naveed Jafar, Muhammad Rayees Ahmad, Muhammad Saeed, Muhammad Saqlain, Muhammad Shabir, Mujahid Abbas, Mumtaz Ali, Radu I. Munteanu, Ghulam Murtaza, Munazza Naz, Tahsin Oner, ‪Gabrijela Popović, Surapati Pramanik, R. Priya, S.P. Priyadharshini, Midha Qayyum, Quang-Thinh Bui, Shazia Rana, Akbara Rezaei, Jesús Estupiñán Ricardo, Rıdvan Sahin, Saeeda Mirvakili, Said Broumi, A. A. Salama, Flavius Aurelian Sârbu, Ganeshsree Selvachandran, Javid Shabbir, Shio Gai Quek, Son Hoang Le, Florentin Smarandache, Dragiša Stanujkić, S. Sudha, Taha Yasin Ozturk, Zaigham Tahir, The Houw Iong, Ayse Topal, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Rizha Vitania, Luige Vlădăreanu, Victor Vlădăreanu, Ștefan Vlăduțescu, J. Vimala, Dan Valeriu Voinea, Adem Yolcu, Yongfei Feng, Abd El-Nasser H. Zaied, Edmundas Kazimieras Zavadskas.

Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set

Florentin Smarandache
Neutrosophic Set A Generalization of The Intuitionistic Fuzzy Set Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 10 pages
File Size : 55,7 Mb
Release : 2010-08-23
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set by Florentin Smarandache Pdf

In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.

NEUTROSOPHIC SET – A GENERALIZATION OF THE INTUITIONISTIC FUZZY SET

Florentin SMARANDACHE
NEUTROSOPHIC SET A GENERALIZATION OF THE INTUITIONISTIC FUZZY SET Book PDF

Author : Florentin SMARANDACHE
Publisher : Infinite Study
Page : 10 pages
File Size : 42,6 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 8210379456XXX

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NEUTROSOPHIC SET – A GENERALIZATION OF THE INTUITIONISTIC FUZZY SET by Florentin SMARANDACHE Pdf

In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.

Plithogenic sets and their application in decision making

S. Gomathy,D. Nagarajan,S. Broumi,M. Lathamaheswari
Plithogenic sets and their application in decision making Book PDF

Author : S. Gomathy,D. Nagarajan,S. Broumi,M. Lathamaheswari
Publisher : Infinite Study
Page : 17 pages
File Size : 54,8 Mb
Release : 2020-12-01
Category : Mathematics
ISBN : 8210379456XXX

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Plithogenic sets and their application in decision making by S. Gomathy,D. Nagarajan,S. Broumi,M. Lathamaheswari Pdf

This paper aims to test whether Plithogenic aggregation operation is more effective than other sets in its accuracy, while decision making. In order to obtain a better accuracy, the Plithogenic aggregation operation such as Fuzzy set [FS], Intuitionistic fuzzy set [IFS] and Neutrosophic set [NS] used tnorm and tconorm. An illustration is examined in this paper to prove the result of better accuracy using plithogenic aggregation operators in decision making.

Plithogeny, Plithogenic Set, Logic, Probability, and Statistics

Florentin Smarandache
Plithogeny Plithogenic Set Logic Probability and Statistics Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 143 pages
File Size : 55,7 Mb
Release : 2017-10-01
Category : Mathematics
ISBN : 8210379456XXX

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Plithogeny, Plithogenic Set, Logic, Probability, and Statistics by Florentin Smarandache Pdf

We introduce for the first time the concept of plithogeny in philosophy and, as a derivative, the concepts of plithogenic set / logic / probability / statistics in mathematics and engineering – and the degrees of contradiction (dissimilarity) between the attributes’ values that contribute to a more accurate construction of plithogenic aggregation operators and to the plithogenic relationship of inclusion (partial ordering).

Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview

Said Broumi ,Mohamed Talea,Assia Bakali,Florentin Smarandache,Deivanayagampillai Nagarajan,Malayalan Lathamaheswari,Mani Parimala
Shortest path problem in fuzzy intuitionistic fuzzy and neutrosophic environment an overview Book PDF

Author : Said Broumi ,Mohamed Talea,Assia Bakali,Florentin Smarandache,Deivanayagampillai Nagarajan,Malayalan Lathamaheswari,Mani Parimala
Publisher : Infinite Study
Page : 8 pages
File Size : 47,9 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview by Said Broumi ,Mohamed Talea,Assia Bakali,Florentin Smarandache,Deivanayagampillai Nagarajan,Malayalan Lathamaheswari,Mani Parimala Pdf

In the last decade, concealed by uncertain atmosphere, many algorithms have been studied deeply to workout the shortest path problem. In this paper, we compared the shortest path problem with various existing algorithms. Finally, we concluded the best algorithm for certain environment.

Advances of Standard and Nonstandard Neutrosophic Theories

Florentin Smarandache
Advances of Standard and Nonstandard Neutrosophic Theories Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 308 pages
File Size : 43,9 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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Advances of Standard and Nonstandard Neutrosophic Theories by Florentin Smarandache Pdf

In this book, we approach different topics related to neutrosophics, such as: Neutrosophic Set, Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set, Picture Fuzzy Set, Ternary Fuzzy Set, Pythagorean Fuzzy Set, Atanassov’s Intuitionistic Fuzzy Set of second type, Spherical Fuzzy Set, n-HyperSpherical Neutrosophic Set, q-Rung Orthopair Fuzzy Set, truth-membership, indeterminacy-membership, falsehood-nonmembership, Regret Theory, Grey System Theory, Three-Ways Decision, n-Ways Decision, Neutrosophy, Neutrosophication, Neutrosophic Probability, Refined Neutrosophy, Refined Neutrosophication, Nonstandard Analysis; Extended Nonstandard Analysis; Open and Closed Monads to the Left/Right; Pierced and Unpierced Binads; and so on.

Plithogenic Soft Set

Shawkat Alkhazaleh
Plithogenic Soft Set Book PDF

Author : Shawkat Alkhazaleh
Publisher : Infinite Study
Page : 19 pages
File Size : 50,8 Mb
Release : 2020-03-03
Category : Mathematics
ISBN : 8210379456XXX

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Plithogenic Soft Set by Shawkat Alkhazaleh Pdf

In 1995, Smarandache initiated the theory of neutrosophic set as new mathematical tool for handling problems involving imprecise, indeterminacy, and inconsistent data. Molodtsov initiated the theory of soft set as a new mathematical tool for dealing with uncertainties, which traditional mathematical tools cannot handle. He has showed several applications of this theory for solving many practical problems in economics, engineering, social science, medical science, etc.

Extension of Soft Set to Hypersoft Set, and then to Plithogenic Hypersoft Set

Florentin Smarandache
Extension of Soft Set to Hypersoft Set and then to Plithogenic Hypersoft Set Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 4 pages
File Size : 43,8 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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Extension of Soft Set to Hypersoft Set, and then to Plithogenic Hypersoft Set by Florentin Smarandache Pdf

In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic

Florentin Smarandache
Neutrosophic Logic A Generalization of the Intuitionistic Fuzzy Logic Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 7 pages
File Size : 54,6 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 8210379456XXX

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Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic by Florentin Smarandache Pdf

In this paper one generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The differences between IFL and NL (and the corresponding intuitionistic fuzzy set and neutrosophic set) are pointed out.

Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making

Shio Gai Quek,Ganeshsree Selvachandran,Florentin Smarandache,J. Vimala,Son Hoang Le ,Quang-Thinh Bui,Vassilis C. Gerogiannis
Entropy Measures for Plithogenic Sets and Applications in Multi Attribute Decision Making Book PDF

Author : Shio Gai Quek,Ganeshsree Selvachandran,Florentin Smarandache,J. Vimala,Son Hoang Le ,Quang-Thinh Bui,Vassilis C. Gerogiannis
Publisher : Infinite Study
Page : 17 pages
File Size : 50,6 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making by Shio Gai Quek,Ganeshsree Selvachandran,Florentin Smarandache,J. Vimala,Son Hoang Le ,Quang-Thinh Bui,Vassilis C. Gerogiannis Pdf

Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic sets have been introduced.

A Novel MCDM Method Based on Plithogenic Hypersoft Sets under Fuzzy Neutrosophic Environment

Muhammad Rayees Ahmad,Muhammad Saeed ,Usman Afzal,Miin-Shen Yang
A Novel MCDM Method Based on Plithogenic Hypersoft Sets under Fuzzy Neutrosophic Environment Book PDF

Author : Muhammad Rayees Ahmad,Muhammad Saeed ,Usman Afzal,Miin-Shen Yang
Publisher : Infinite Study
Page : 23 pages
File Size : 42,8 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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A Novel MCDM Method Based on Plithogenic Hypersoft Sets under Fuzzy Neutrosophic Environment by Muhammad Rayees Ahmad,Muhammad Saeed ,Usman Afzal,Miin-Shen Yang Pdf

In this paper, we advance the study of plithogenic hypersoft set (PHSS).We present four classifications of PHSS that are based on the number of attributes chosen for application and the nature of alternatives or that of attribute value degree of appurtenance. These four PHSS classifications cover most of the fuzzy and neutrosophic cases that can have neutrosophic applications in symmetry. We also make explanations with an illustrative example for demonstrating these four classifications.

Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications

Mohammed A. Al Shumrani,Selçuk Topal,Florentin Smarandache,Cenap Ozel
Covering Based Rough Fuzzy Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications Book PDF

Author : Mohammed A. Al Shumrani,Selçuk Topal,Florentin Smarandache,Cenap Ozel
Publisher : Infinite Study
Page : 8 pages
File Size : 52,7 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications by Mohammed A. Al Shumrani,Selçuk Topal,Florentin Smarandache,Cenap Ozel Pdf

In recent years, mathematical orientations on real-life problems', which continue to increase, began to make a significant impact. Information systems for many decision-making problems consist of uncertain, incomplete, indeterminate and indiscernible structures and components. Classical set theory and interpretation methods fail to represent, express and solve the problems of these types or cause to make wrong decisions. For this reason, in this study, we provide definitions and methods to present information and problem representations in more detail and precision. This paper introduces three new topologies called covering-based rough fuzzy, covering-based rough intuitionistic fuzzy and covering-based rough neutrosophic nano topology. Some fundamental definitions such as open set, closed set, interior, closure and basis are given. Neutrosophic definitions and properties are mainly investigated. We give some real life applications of covering-based rough neutrosophic nano topology in the final part of the paper and an explanatory example of decision making application by defining core point.