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International Journal of Neutrosophic Science
Volume 18 , Issue 1, PP: 99-116 , 2022 | Cite this article as | XML | Html |PDF

Title

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

Authors Names :   A. Rezaei   1 *     T. Oner   2     T. Katican   3     F. Smarandache   4     N. Gandotra   5  

1  Affiliation :  Department of Mathematics, Payame Noor University, P.O.Box. 19395-4697, Tehran, Iran

    Email :  rezaei@pnu.ac.ir


2  Affiliation :  Department of Mathematics, Ege University, 35100 Izmir, Turkey

    Email :  tahsin.oner@ege.edu.tr


3  Affiliation :  Department of Mathematics and Science, University of New Mexico, Gallup, UNM 87301, USA

    Email :  tugcektcn@gmail.com


4  Affiliation :  Department of Mathematics, Ege University, 35100 Izmir, Turkey.

    Email :  smarand@unm.edu


5  Affiliation :  Yogananda School of AI, Comput. Data Sci., Shoolini University, Solan 173229, Himachal Pradesh, India

    Email :  neerajgandotra@shooliniuniversity.com



Doi   :   https://doi.org/10.54216/IJNS.180109

Received: Aug. 30, 2021 Accepted: Jan 16, 2022

Abstract :

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough studies 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.

Keywords :

Neutrosophic sets; Plithogenic sets; Intuitionistic Fuzzy Sets

References :

[1]          E. Abo-El-Hamd, H. M. Shamma, M. Saleh, I. El-Khodary, Neutrosophic Logic Theory and Applications, Neutrosophic Sets and Systems, vol. 41, pp. 30–51, 2021.

[2]          A.A.A. Agboola, Introduction to NeutroGroups, International Journal of Neutrosophic Science, vol. 6, no. 1, pp. 41–47, 2020.

[3]          M. Al-Tahan, B. Davvaz, F. Smarandache and O. Anis, On Some NeutroHyperstructures, Symmetry, 13, 355. https://doi.org/10.3390/sym13040535

[4]          M. Al-Tahan, F. Smarandache, B. Davvaz, NeutroOrderedAlgebra: Applications to Semigroups, Neutrosophic Sets and Systems, vol. 39, pp. 133–147, 2021.

[5]          K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.20, pp. 87–96, 1986.

[6]          K. T. Atanassov, On intuitionistic fuzzy sets theory, Springer, vol. 283, 2012.

[7]          K. T. Atanassov, Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84), June 1983, (in Bulg.).

[8]          K. T. Atanassov and S. Stoeva, Intuitionistic fuzzy sets, Proc. of Polish Symp. on Interval & Fuzzy Mathematics, Poznan, pp. 23–26, August 1983.

[9]          K. T. Atanassov, Answer to Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade’s, H., paper :

Terminological difficulties in fuzzy set theory- the case of “intuitionistic fuzzy sets”, Fuzzy Sets and Systems 156(3), 496–499 (2005)

[10]       K. T. Atanassov and T. Trifonov, Towards combining two kinds of intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, vol. 11, no. 2, pp. 1–11, 2005. http://ifigenia.org/wiki/issue:nifs/11/2/01-11

[11]       K. T. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 31, no. 3, pp. 343–349, 1989.

[12]       K. T. Atanassov, Review and new results on intuitionistic fuzzy sets, Preprint, IM-MFAIS-1-88, Sofia, 1988.

[13]       K. T. Atanassov, On intuitionistic fuzzy sets research in Institute for Microsystems and some open problems in the intuitionistic fuzzy set theory, Ninetieth Session of the Nat. Seminar of Informatics of the Union of Bulg. Mathematicians and Fourth Scientific Session of the ”Mathematical Foundation Artificial Intelligence” Seminar, Sofia, Nov. 5, Preprint, IM-MFAIS-5-90, Sofia, pp. 7–14, 1990.

[14]       K. T. Atanassov, Remark on a temporal intuitionistic fuzzy logic, Second Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, March 30, Preprint, IM-MFAIS-I-90, pp. 1–5, 1990.

[15]       K. T. Atanassov, G. Gargov and C. Georgiev, Remark on intuitionistic fuzzy Modus Ponens, Second Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, March 30, Preprint, IM-MFAIS-I-90, pp. 10–13, 1990.

[16]       K. T. Atanassov, Intuitionistic fuzzy constraint logic programming, Preprint, MRL-I-92, Sofia, 1992.

[17]       K. T. Atanassov, Constraint logic programming and intuitionistic fuzzy logics, BUSEFAL, vol. 56, pp. 98–107, 1993.

[18]       K. T. Atanassov, One variant of the intuitionistic fuzzy relations, First Sci. Session of the ” Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, October 10, Preprint IM-MFAIS-7-89, pp. 1–3, 1989.

[19]       K. T. Atanassov, Generalized nets and their fuzzings, AMSE Review, vol. 2, no. 3, pp. 39–49, 1985.

[20]       K. T. Atanassov, Second type intuitionistic fuzzy generalized nets, AMSE Review, vol. 17, no.1, 5-8, 1991.

[21]       K. T. Atanassov, Algorithms of the functioning of the second type of intuitionistic fuzzy generalized nets, Advances in Modelling & Analysis, A, vol. 32, no. 1-2, pp. 57–61, 1997.

[22]       K. T. Atanassov and S. Stoeva, Intuitionistic fuzzy programs, Proc. of the Second Polish Symp. on Interval & Fuzzy Mathematics, Poznan, Sept. pp. 13–16, 1986.

[23]       K. T. Atanassov, Intuitionistic fuzzy sets and expert estimations, BUSEFAL, vol. 55, pp. 67–71, 1993.

[24]       K. T. Atanassov, Remark on intuitionistic fuzzy expert systems, BUSEFAL, vol. 59, pp. 71–76, 1994.

[25]       K. T. Atanassov, Intuitionistic fuzzy sets and expert estimations, II, BUSEFAL, vol. 59, pp. 64–69, 1994.

[26]       K. T. Atanassov, Intuitionistic fuzzy systems, BUSEFAL, vol. 58, pp. 92–96, 1994.

[27]       K. T. Atanassov and C. Georgiev, Intuitionistic fuzzy Prolog, Fuzzy sets and Systems, vol. 53, no.1, pp. 121–128, 1993.

[28]       K. T. Atanassov, H. Georgiev, A. Drumev and I. Kazalarski, Intuitionistic fuzzy PROLOG, Preprint, IM-MFAIS-5-89, Sofia, 1989.

[29]       K. T. Atanasov, Intuitionistic fuzzy sets: theory and applications, Physica-Verlag, 1999.

[30]       K. T. Atanasov, Intuitionistic fuzzy sets over different universes, Second Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, March 30 1990, Prepr. IM-MFAIS-I-90, pp. 6–9.

[31]       K. T. Atanasov, Temporal intuitionistic fuzzy sets, Comptes Rendus de l’ Academie Bulgare des Sciences, Tome 44, No. 7, pp. 5–7, 1991.

[32]       K. T. Atanasov, A second type of intuitionistic fuzzy sets, BUSEFAL, Vol. 56, pp. 66–70, 1993.

[33]       K. T. Atanasov, Two variants of intuitonistic fuzzy propositional calculus, Preprint IM-MFAIS-5-88, Sofia, 1988.

[34]       K. T. Atanasov, Two variants of intuitionistic fuzzy modal logic, Preprint IMMFAIS-3-89, Sofia, 1989.

[35]       K. T. Atanassov and G. Gargov, Intuitionistic fuzzy logic, Compt. rend. Acad. bulg. Sci., Tome 43, no. 3, pp. 9–12, 1990.

[36]       K. T. Atanassov, Index matrix representation of the intuitionistic fuzzy graphs, 5th Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, Oct. 5, Preprint MRL-MFAIS-1094, Sofia, pp. 36–41, 1994.

[37]       K. T. Atanassov, Remark on the concept intuitionistic fuzzy relation, Fifth Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, October 5, Preprint, MRL-MFAIS-10-94, Sofia, pp. 42–46, 1994.

[38]       R. E. Bellman, R. Kalaba and L. A. Zadeh, Abstraction and pattern classification, J. Math. Anal. Appl., vol. 13, pp. 1–7, 1966.

[39]       M. Black, “Vagueness”, [Phil. of Science], vol. 4, pp. 427–455. Reprinted in Language and Philosophy: Studies in Method, Cornell University Press, Ithaca and London, pp. 23–58, 1949. Also in Int. J. of General Systems, vol. 17, pp. 107–128, 1990.

[40]       A. Borumand Saeid, Y. B. Jun, Neutrosophic sub-algebras of BCK/BCI-algebras based on neutrosophic points, Annals of Fuzzy Mathematics and Informatics, vol.14, pp. 87–97, 2017.

[41]       L.E.J. Brouwer, Collected Works, vol. 1, North Holland, Amsterdam, 1975.

[42]       P. Burillo and H. Bustince, Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 79, pp. 403-–405, 1996.

[43]       P. Burillo and H. Bustince, Algebraic structures for intuitionistic fuzzy sets, Fifth Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, October 5, 1994, Preprint, MRLMFAIS-10-94, Sofia, pp. 1–13, 1994.

[44]       P. Burillo and H. Bustince, Numerical measurements of information on intuitionistic fuzzy sets and interval-valued fuzzy sets (Φ−fuzzy), Fifth Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, October 5, 1994, Preprint MRL-MFAIS-10-94, Sofia, pp. 14–26, 1994.

[45]       H. Bustince, Correlation of interval-valued intuitionistic fuzzy sets, Fifth Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, October 5, 1994, Preprint MRL-MFAIS-I0-94, Sofia, pp. 27–35, 1994.

[46]       H. Bustince, Construction of intuitionistic fuzzy relations with predetermined properties, Fuzzy Sets and Systems, vol. 109, pp. 379–403, 2000.

[47]       L. Chwistek, The limits of science, Routledge and Kegan Paul, London, 1948.

[48]       T. Ciftcibasi and D. Altunay, Two-sided (intuitionistic) fuzzy reasoning, IEEE Trans. Systems Man Cybernet, vol. A-28, pp. 662–677, 1998.

[49]       I. M. Copilowish, Border-line cases, vagueness, and ambiguity, Phil. of Science, vol. 6, pp. 181–195, 1939.

[50]       S. K. De, R. Biswas and A. R. Roy, Some operations on intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 114, pp. 477–484, 2000.

[51]       S. K. De, R. Biswas and A. R. Roy, An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems, vol. 117, pp. 209–213, 2001.

[52]       L. I. Dengfeng, Fuzzy multiattribute decision making models and methods with incomplete information, Fuzzy Sets and Systems, vol. 106, no. 2, pp. 113–119, 1999.

[53]       L. I. Dengfeng, Fuzzy multi objective many-person decision-makings and games, National Defense Industry Press, Beijing, 2003.

[54]       L. I. Dengfeng and C. Cheng, New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions, Pattern Recognition Lett., vol. 23, no. 1–3, pp. 221–225, 2002.

[55]       G. Deschrijver and E. E. Kerre, On the composition of intuitionistic fuzzy relations, Fuzzy sets and Systems, vol. 136, no. 3, pp. 333–361, 2003.

[56]       D. Dubois D., H. Prade and R. R. Yager (Eds.), Fuzzy information engineering: a guided tour of applications, John Wiley & Sons, New York, 1997.

[57]       D. Dubois D., H. Prade and R. R. Yager (Eds.), Readings in Fuzzy Sets and Intelligent Systems, Morgan Kaufman, San Mateo, CA, 1993.

[58]       D. Dubois, W. Ostasiewicz and H. Prade, Fuzzy sets: history and basic notions, Fundamentals of fuzzy sets, Springer, Boston, MA, pp. 21–124, 2000.

[59]       D. Dubois and H. Prade, Possibility theory, 1988.

[60]       D. Dubois and H. Prade, Fuzzy sets and systems- theory and applications, Academic Press, New York, 1980.

[61]       D. Dubois and H. Prade, New results about properties and semantics of fuzzy-set-theoretic operators, fuzzy sets: theory and applications to policy analysis and information systems, (Wang P.P. and Chang S.K., eds.), Plenum Publ., pp. 59–75, 1980.

[62]       D. Dubois, S. Gottwald, P. Hajek, and J. Kacprzyk, H. Prade, Terminological difficulties in fuzzy set theory - the case of “intuitionistic fuzzy sets”, Fuzzy Sets and Systems, vol. 156, no. 3, pp. 485–491, 2005.

[63]       A. A. Fraenkel, Y. A. Bar-Hillel and A. Levy, Foundations of set theory, North-Holland, 1973.

[64]       W. L. Gau and D. J. Buehrer, Vague sets, IEEE Trans. Systems Man Cybernet, vol. 23, pp. 610–614, 1993.

[65]       G. Gargov and K. Atanassov, Two results in intuitionistic fuzzy logic, Compt. rend. Acad. bulg. Sci., Tome 45, no. 12, pp. 29–3l, 1992.

[66]       G. Gargov, Notes on the intuitionistic fuzzy predicate logic, First Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, October 10, Preprint, IM-MFAIS-7-89, pp. 19–21, 1989.

[67]       C. Georgiev and K. T. Atanassov, A possibility for incorporating constraints into intuitionistic fuzzy PROLOG, First Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, October 10, Preprint, IM-MFAIS-7-89, pp. 22–23, 1989.

[68]       C. Georgiev, Variant of the combination of evidence in the framework of intuitionistic fuzziness, Second Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, March 30, Prepr. IM-MFAIS-1-90, pp. 22–24, 1990.

[69]       K. Georgiev,               A             simplification        of            the          neutrosophic        sets,        neutrosophic        logic        and    intuitionistic          fuzzy       sets,        Notes      on           Intuitionistic          Fuzzy      Sets,        vol.          11,          no.          2,    pp.          28–31,   2005. http://ifigenia.org/wiki/issue:nifs/11/2/28-31

[70]       M. Gorzalczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, vol. 21, no. 1, pp. 1–17, 1987.

[71]       S. Gottwald, Fuzzy sets theory: some aspects of the early development, aspects of vagueness, (Skala H.J., Termini S. and Trillas E., eds.), D. Reidel, pp. 13–29. 1984.

[72]       S. Gottwald, Fuzzy sets and fuzzy logic- foundations of applications from a mathematical point of view, Vieweg, Wiesbaden, Germany, 1993.

[73]       M. M. Gupta, Fuzzy-ism, the first decade, Fuzzy Automate and Decision Processes (Gupta M.M., Saridis G.N. and Gaines B.R., eds.), North-Holland, Amsterdam, pp. 5–10, 1977.

[74]       L. Hadjyiski and N. Kamburov, Program package for calculations of intuitionistic fuzzy sets, First Sci. Session of the ”Mathematical Fundation of Artificial Intelligence” Seminar, Sofia, October 10, Preprint, IM-MFAIS-7-89, pp. 24–25, 1989.

[75]       P. Hajek, Metamathematics of fuzzy logic, Springer Science & Business Media, 4, 2013.´

[76]       C. G. Hempel, Vagueness and logic, Phil. of Science, vol. 6, pp. 163–180, 1939.

[77]       A. Heyting, Intuitionism. An Introduction, North-Holland, Amsterdam, 1956.

[78]       G. E. Hughes and M. J. Cresswell, An Introduction to modal logic, Methuen, London, 1968.

[79]       Y. B. Jun, F. Smarandache, Florentin and H. Bordbar, Neutrosophic N−structures applied to BCK/BCIalgebras, Information, vol. 8, no. 128, pp. 1–12, 2017.

[80]       A. Kandel, Fuzzy mathematical techniques with applications, Addison Wesley Publ. Corp., Reading, 1986.

[81]       M. Khan, S. Anis, F. Smarandache and Y.B. Jun, Neutrosophic N-structures and their applications in semigroups, 2017, Infinite Study.

[82]       A. Kaplan and H. F. Schott, A calculus for empirical classes, Methods, vol. III, pp. 165–188, 1951.

[83]       A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, Fundamental Theoretical Elements, Academic Press, 1, New York, 1975.

[84]       G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic- theory and applications, Prentice Hall, Upper Saddle River, NJ, 1995.

[85]       G. J. Klir and B. Yuan, Fuzzy sets, Fuzzy logic, and fuzzy systems-selected papers by Lotfi A. Zadeh, World Scientific, Singapore, 1996.

[86]       G. J. Klir and T. A. Folger, Fuzzy sets, uncertainty, and information, Prentice Hall, Englewook Cliffs, NJ, 1988.

[87]       G. J. Klir, U. H. St Clair and B. Yuan, Fuzzy set theory- foundations and applications, Prentice Hall, Englewook Cliffs, NJ, 1997.

[88]       N. Kondakov, Logical Dictionary, Moskow, Nauka, 1971, (in Russian).

[89]       R. Kruse, J. Gebhardt and F. Klawonn, Foundations of fuzzy systems, Wiley, New York, 1994.

[90]       G. Lakoff, Women, fire, and dangerous things - what categories reveal about the mind, University of Chicago Press, Chicago, 1987.

[91]       S. Lesniewski, Podstawy ogolnej teorii mnogosci, Prace Polskiego Kola Naukowego w Moskwie, 2, Moscow, 1916.

[92]       S. Lesniewski, Collected works, Polish Scientific Publishers, Warszawa, 1992.

[93]       D. F. Li, Multiattribute decision making models and methods using intuitionistic fuzzy sets, Journal of computer and System Sciences, vol. 70, no. 1, pp. 73–85.

[94]       D. F. Li, Fuzzy Multi objective Many Person Decision Makings and Games, National Defense Industry Press, Beijing, 2003 (in Chinese).

[95]       D. F. Li, Decision and game theory in management with intuitionistic fuzzy sets, vol. 308, pp. 1–441, Berlin, Springer, 2014.

[96]       R. Lowen, Fuzzy set theory- basic concepts, techniques and bibliography, Kluwer Academic Publ., Dordrecht, 1996.

[97]       D. H. Mellor, Experimental error and deductibility, Phil. of Science, vol. 32, pp. 102–122, 1965.

[98]       D. H. Mellor, Inexactness and explanation, Phil. of Science, vol. 33, pp. 345–359, 1966.

[99]       K. Menger, Ensembles flous et fonctions aleatoires, Comptes Rendus de l’Academie des Sciences de´ Paris, vol. 232, pp. 2001–2003, 1951.

[100]    C. V. Negoita and D. A. Ralescu, Applications of fuzzy sets to systems analysis, Interdisciplinary Systems Research Series, Birkhaeuser, Basel & Stuttgart and Halsted Press, 11, New York, 1975.

[101]    H. T. Nguyen and E. A. Walker, A first course in fuzzy logic, CRC Press, New York, 1996.

[102]    V. Novak, Fuzzy sets and their applications, Adam Hilger, Bristol, UK, 1986.

[103]    T. Oner, T, Katican and A. Borumand Saeid, Neutrosophic N−structures on Sheffer stroke Hilbert algebras, Neutrosophic Sets and Systems, in press, 2021.

[104]    T. Oner, T, Katican and A. Rezaei, Neutrosophic N−structures on strong Sheffer stroke non-associative MV-algebras, Neutrosophic Sets and Systems, vol. 40, pp. 235–252, 2021.

[105]    W. Ostasiewicz, Uncertainty and vagueness, Advances in fuzzy sets and applications, (Tofan I., Gil Aluja J., Costinescu O. and Teodorescu H.N., Eds.), Iasi, 1992.

[106]    W. Ostasiewicz, Half a century of fuzzy sets, Supplement to Kybernetika, vol. 28, pp. 17–20, 1992. (Proc. of the Inter. Symp. on Fuzzy Approach to Reasoning and Decision Making, Bechyne, Czechoslovakia, June 25-29, 1990).

[107]    W. Ostasiewicz, Pioneers of fuzziness, Busefal, vol. 46, pp. 4–15, 1991.

[108]    W. Pedrycz and F. Gomide, An introduction to fuzzy sets- analysis and design, MIT Press, Cambridge, Ma, 1998.

[109]    C. S. Peirce, Collected Papers of Charles Sanders Peirce, C. Hartshorne and P. Weiss, eds., Harvard University Press, Cambridge, MA, 1931.

[110]    S. Petkov and K. T. Atanassov, Intuitionistic fuzzy reasoning and expert systems on the example of the CONTEXT tool, Preprint IM-MFAIS-6-88, Sofia, 1988.

[111]    S. Petkov and K. T. Atanassov, Generalized net model of the fuzzy reasoning in the context expert system tool, Proc. of the XX Spring Conf. of the Union of Bulg. Math., Varna, Drujba, April 1991, pp. 336–340.

[112]    N. Rescher, Introduction to logic, St. Martins Press, New York, 1964.

[113]    B. Russell, Vagueness, Austr. J. of Philosophy, vol. 1, pp. 84–92, 1923.

[114]    B. Russell, The problem of philosophy, Williams & Norgate, London, 1934.

[115]    B. Rolf, Topics on vagueness, Ph. D. Thesis, University of Lund, Sweden, 1981.

[116]    M. S¸ahin, A. Kargın and M. A. C¸oban, Fixed point theorem for neutrosophic triplet partial metric space, Symmetry, vol. 10, no. 7, pp. 240, 2018.

[117]    A. Rezaei, F. Smarandache, On Neutro-BE-algebras and Anti-BE-algebras, International Journal of Neutrosophic Science, vol. 4, no. 1, pp. 8–15, 2020.

[118]    A. Rezaei, F. Smarandache and S. Mirvakili, Applications of (Neutro / Anti) Sophications to Semihypergroups, Journal of Mathematics, Vol. 2021, Article ID 6649349, 7 pages. https://doi.org/10.1155/2021/66493492021.

[119]    F. Smarandache, NeutroAlgebra is a Generalization of Partial Algebra, International Journal of Neutrosophic Science, vol. 2, no. 1, pp. 08–17, 2020.

[120]    F. Smarandache, Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited), Neutrosophic Sets and Systems, vol. 31, pp. 1–16, 2020.

[121]    F. Smarandache, Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic nSuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical- / Neutro- / Anti-) HyperAlgebra, Neutrosophic Sets and Systems, vol. 33, pp. 290–296, 2020.

[122]    F. Smarandache, Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures, in Advances of Standard and Nonstandard Neutrosophic Theories, Pons Publishing House Brussels, Belgium, Ch. 6, pp. 240–265, 2019.

[123]    F. Smarandache, Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited, t Neutrosophic Sets and Systems, vol. 21, pp. 153–166, 2018.

[124]    F. Smarandache, Symbolic Neutrosophic Theory, Europa Nova asbl Clos du Parnasse, 3E 1000, Bruxelles Belgium, 2015.

[125]    F. Smarandache, A unifying field in logics. neutrosophy: Neutrosophic probability, set and logic, American Research Press, Rehoboth, 1999.

[126]    F. Smarandache, Neutrosophy / Neutrosophic Probability, Set, and Logic, American Research Press, 1998.

[127]    F. Smarandache, Neutrosophic set a generalization of the intuitionistic fuzzy set, International journal of pure and applied mathematics, vol. 24, no. 3, pp. 287–297, 2005.

[128]    S. Stoeva and K. T. Atanassov, V -fizzy Petri nets and reduced V-fuzzy Generalized nets, AMSE Review, vol. 3, no. 3, pp. 1–5, 1986.

[129]    D. Stoyanova, A variant of a cartesian product over intuitionistic fuzzy sets, Second Sci. Session of the” Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, March 30, Preprint, IM-MFAIS-190, pp. 43–45, 1990.

[130]    D. Stoyanova, Algebraic structures of intuitionistic fuzzy sets, Third Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, June 12, Preprint, IM-MFAIS-2-90, Part 1, pp. 19–21, 1990.

[131]    D. Stoyanova, Algebraic structures of fuzzy sets, Third Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, June 12, Preprint IM-MFAIS-2-90, Part 1, pp. 15–18, 1990.

[132]    D. Stoyanova, Sets from (α,β)-level generated by an intuitionistic fuzzy sets, Ninetieth Session of the Nat. Seminar of Informatics of the Union of Bulg. Mathematicians and Fourth Scientific Session of the ”Mathematical Foundation Artificial Intelligence” Seminar, Sofia, Nov. 5, Preprint, IM-MFAIS-5-90, Sofia, pp. 40–42, 1990.

[133]    D. Stoyanova and K. T. Atanassov, Relations between operators, defined over intuitionistic fuzzy sets, Second Sci. Session of the ”Mathematical Foundation of Artificial Intelligence” Seminar, Sofia, March 30, Preprint, IM-MFAIS-I-90, pp. 46–49, 1990.

[134]    E. Szmidt and J. Kacprzyk, Entropy for intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 118, pp. 467–477, 2001.

[135]    E. Szmidt and J. Kacprzyk, Intuitionistic fuzzy sets in group decision making, NIFS, vol. 2, no. 1, pp. 15–32, 1996.

[136]    E. Szmidt and J. Kacprzyk, Remarks on some applications of intuitionistic fuzzy sets in decision making, NIFS, vol. 2, no. 3, pp. 22–31, 1996.

[137]    E. Szmidt and J. Kacprzyk, Group decision making via intuitionistic fuzzy sets, FUBEST’96, Sofia, Bulgaria, October 9–11, pp. 107–112, 1996.

[138]    E. Szmidt and J. Kacprzyk, Intuitionistic fuzzy sets for more realistic group decision making, International Conference on Transition to Advanced Market Institutions and Economies, Warsaw, June 18–21, pp. 430–433, 1997.

[139]    E. Szmidt and J. Kacprzyk, Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 114, pp. 505–518, 2001.

[140]    G. Takeuti and S. Titani, Intuitionistic fuzzy logic and intuitionistic fuzzy set theory, The Journal of Symbolic Logic, vol. 49, no. 3, pp. 851–866, 1984.

[141]    T. Terano, K. Asai and M. Sugeno, Fuzzy systems theory and its applications, Academic Press, 1987.

[142]    N. Turanli and D. Coker, Fuzzy connectedness in intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, vol. 116, pp. 369–375, 2000.

[143]    D. Van Dalen (ed.), Brouwer’s Cambridge Lectures on Intuitionism, Cambridge Univ. Press, Cambridge, 1981.

[144]    H. Weyl, The ghost of modality, Philosophical essays in memory of Edmund Husserl, Cambridge, MA, pp. 278–303, 1940.

[145]    L. Wittgenstein, Philosophical investigations, Macmillan, New York, 1953.

[146]    R. R. Yager, S. Ovchinnikov, R. M. Tong and H. T. Nguyen (Eds.), Fuzzy sets and applications: selected papers by L. A. Zadeh, Wiley, New York, 1987.

[147]    C. Young, The algebra of many-valued quantities, Mathematische Annalen, vol. 104, pp. 260–290, 1931.

[148]    L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8, no. 3, pp. 338–353, 1965.

[149]    L. A. Zadeh, , Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. on Systems, Man and Cybernetics, vol. 3, pp. 28–44, 1973.

[150]    H. J. Zimmermann, Fuzzy sets theory- and its applications, Kluwer/Nijhoff Publ., Boston, 1985. Second revised edition, Kluwer Academic Publ., Boston, 1991. Third revised edition, 1996.


Cite this Article as :
A. Rezaei , T. Oner , T. Katican , F. Smarandache , N. Gandotra, A short history of fuzzy, intuitionistic fuzzy, neutrosophic and plithogenic sets, International Journal of Neutrosophic Science, Vol. 18 , No. 1 , (2022) : 99-116 (Doi   :  https://doi.org/10.54216/IJNS.180109)