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Journal articles on the topic 'Set valued theory'

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Published: 4 June 2021
Last updated: 12 February 2022

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1

Hajek, P., and Z. Hanikova. "Interpreting lattice-valued set theory in fuzzy set theory." Logic Journal of IGPL 21, no. 1 (July 18, 2012): 77–90. http://dx.doi.org/10.1093/jigpal/jzs023.

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2

Titani, Satoko. "A lattice-valued set theory." Archive for Mathematical Logic 38, no. 6 (August 1, 1999): 395–421. http://dx.doi.org/10.1007/s001530050134.

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3

Protasov, I. "Decompositions of set-valued mappings." Algebra and Discrete Mathematics 30, no. 2 (2020): 235–38. http://dx.doi.org/10.12958/adm1485.

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Let X be a set, BX denotes the family of all subsets of X and F:X→BX be a set-valued mapping such that x∈F(x), supx∈X|F(x)|<κ, supx∈X|F−1(x)|<κ for all x∈X and some infinite cardinal κ. Then there exists a family F of bijective selectors of F such that |F|<κ and F(x)={f(x):f∈F} for each x∈X. We apply this result to G-space representations of balleans.
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4

Papageorgiou, Nikolaos S. "Contributions to the theory of set valued functions and set valued measures." Transactions of the American Mathematical Society 304, no. 1 (January 1, 1987): 245. http://dx.doi.org/10.1090/s0002-9947-1987-0906815-3.

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5

Papageorgiou, Nikolaos S. "On the theory of Banach space valued multifunctions. 2. Set valued martingales and set valued measures." Journal of Multivariate Analysis 17, no. 2 (October 1985): 207–27. http://dx.doi.org/10.1016/0047-259x(85)90079-x.

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6

TANINO, Tetsuzo. "Theory and Applications of Set-Valued Mappings : Part1:Fundamental Properties of Set-Valued Mappings." Journal of Japan Society for Fuzzy Theory and Systems 13, no. 1 (2001): 11–19. http://dx.doi.org/10.3156/jfuzzy.13.1_11.

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7

DESCHRIJVER, GLAD, and CHRIS CORNELIS. "REPRESENTABILITY IN INTERVAL-VALUED FUZZY SET THEORY." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, no. 03 (June 2007): 345–61. http://dx.doi.org/10.1142/s0218488507004716.

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Interval-valued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0,1]-valued membership degrees are replaced by intervals in [0,1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended setting, it is both natural and appropriate to "reuse" ingredients from classical fuzzy set theory. In this paper, we compare different ways of representing operations on interval-valued fuzzy sets by corresponding operations on fuzzy sets, study their intuitive semantics, and relate them to an existing, purely order-theoretical approach. Our approach reveals, amongst others, that subtle differences in the representation method can have a major impact on the properties satisfied by the generated operations, and that contrary to popular perception, interval-valued fuzzy set theory hardly corresponds to a mere twofold application of fuzzy set theory. In this way, by making the mathematical machinery behind the interval-valued fuzzy set model fully transparent, we aim to foster new avenues for its exploitation by offering application developers a much more powerful and elaborate mathematical toolbox than existed before.
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8

O'Regan, Donal. "Generalized coincidence theory for set-valued maps." Journal of Nonlinear Sciences and Applications 10, no. 03 (March 4, 2017): 855–64. http://dx.doi.org/10.22436/jnsa.010.03.01.

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9

Nishimura, Hirokazu. "Heyting valued set theory and fibre bundles." Publications of the Research Institute for Mathematical Sciences 24, no. 2 (1988): 225–47. http://dx.doi.org/10.2977/prims/1195175197.

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10

Nishimura, Hirokazu. "Heyting valued set theory and Sato hyperfunctions." Publications of the Research Institute for Mathematical Sciences 22, no. 4 (1986): 801–11. http://dx.doi.org/10.2977/prims/1195177631.

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11

LÖWE, BENEDIKT, and SOURAV TARAFDER. "GENERALIZED ALGEBRA-VALUED MODELS OF SET THEORY." Review of Symbolic Logic 8, no. 1 (January 12, 2015): 192–205. http://dx.doi.org/10.1017/s175502031400046x.

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AbstractWe generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory.
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12

OZAWA, MASANAO. "ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY." Review of Symbolic Logic 10, no. 4 (June 5, 2017): 782–807. http://dx.doi.org/10.1017/s1755020317000120.

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AbstractIn 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo–Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti’s model with Boolean-valued models by constructing models based on general complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even nonpolynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti’s model and leads to a much more flexible approach to quantum set theory.
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13

Alkhazaleh, Shawkat. "n-Valued refined neutrosophic soft set theory." Journal of Intelligent & Fuzzy Systems 32, no. 6 (May 23, 2017): 4311–18. http://dx.doi.org/10.3233/jifs-16950.

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14

Gambino, Nicola. "Heyting-valued interpretations for Constructive Set Theory." Annals of Pure and Applied Logic 137, no. 1-3 (January 2006): 164–88. http://dx.doi.org/10.1016/j.apal.2005.05.021.

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15

DESCHRIJVER, GLAD. "ORDINAL SUMS IN INTERVAL-VALUED FUZZY SET THEORY." New Mathematics and Natural Computation 01, no. 02 (July 2005): 243–59. http://dx.doi.org/10.1142/s1793005705000172.

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Interval-valued fuzzy sets form an extension of fuzzy sets which assign to each element of the universe a closed subinterval of the unit interval. This interval approximates the "real", but unknown, membership degree. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. A method for constructing t-norms that satisfy the residuation principle is by using the ordinal sum theorem. In this paper, we construct the ordinal sum of t-norms on [Formula: see text], where [Formula: see text] is the underlying lattice of interval-valued fuzzy set theory, in such a way that if the summands satisfy the residuation principle, then the ordinal sum does too.
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16

Bader, Ralf. "A degree theory for set-valued maps with proximally ∞-connected values." Nonlinear Analysis: Theory, Methods & Applications 30, no. 5 (December 1997): 3081–91. http://dx.doi.org/10.1016/s0362-546x(97)00348-9.

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17

Flagg, R. C. "Epistemic set theory is a conservative extension of intuitionistic set theory." Journal of Symbolic Logic 50, no. 4 (December 1985): 895–902. http://dx.doi.org/10.2307/2273979.

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In [6] Gödel observed that intuitionistic propositional logic can be interpreted in Lewis's modal logic (S4). The idea behind this interpretation is to regard the modal operator □ as expressing the epistemic notion of “informal provability”. With the work of Shapiro [12], Myhill [10], Goodman [7], [8], and Ščedrov [11] this simple idea has developed into a successful program of integrating classical and intuitionistic mathematics.There is one question quite central to the above program that has remained open. Namely:Does Ščedrov's extension of the Gödel translation to set theory provide a faithful interpretation of intuitionistic set theory into epistemic set theory?In the present paper we give an affirmative answer to this question.The main ingredient in our proof is the construction of an interpretation of epistemic set theory into intuitionistic set theory which is inverse to the Gödel translation. This is accomplished in two steps. First we observe that Funayama's theorem is constructively provable and apply it to the power set of 1. This provides an embedding of the set of propositions into a complete topological Boolean algebra . Second, in a fashion completely analogous to the construction of Boolean-valued models of classical set theory, we define the -valued universe V(). V() gives a model of epistemic set theory and, since we use a constructive metatheory, this provides an interpretation of epistemic set theory into intuitionistic set theory.
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18

Komiya, Katsuhiro. "Equivariant critical point theory and set-valued genera." Kodai Mathematical Journal 18, no. 2 (1995): 344–50. http://dx.doi.org/10.2996/kmj/1138043430.

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19

Xiao, Feng, and Long Wang. "Asynchronous Rendezvous Analysis via Set-valued Consensus Theory." SIAM Journal on Control and Optimization 50, no. 1 (January 2012): 196–221. http://dx.doi.org/10.1137/100801202.

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20

O'Regan, Donal. "A General Coincidence Theory for Set-Valued Maps." Zeitschrift für Analysis und ihre Anwendungen 18, no. 3 (1999): 701–12. http://dx.doi.org/10.4171/zaa/907.

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21

Hernandez, E. G. "Boolean-Valued Models of Set Theory with Automorphisms." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 32, no. 7-9 (1986): 117–30. http://dx.doi.org/10.1002/malq.19860320704.

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22

Deschrijver, Glad. "Arithmetic operators in interval-valued fuzzy set theory." Information Sciences 177, no. 14 (July 2007): 2906–24. http://dx.doi.org/10.1016/j.ins.2007.02.003.

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23

Hamel, Andreas H. "A Duality Theory for Set-Valued Functions I: Fenchel Conjugation Theory." Set-Valued and Variational Analysis 17, no. 2 (April 25, 2009): 153–82. http://dx.doi.org/10.1007/s11228-009-0109-0.

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24

Belluce, L. P. "Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory." Canadian Journal of Mathematics 38, no. 6 (December 1, 1986): 1356–79. http://dx.doi.org/10.4153/cjm-1986-069-0.

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In classical two-valued logic there is a three way relationship among formal systems, Boolean algebras and set theory. In the case of infinite-valued logic we have a similar relationship among formal systems, MV-algebras and what is called Bold fuzzy set theory. The relationship, in the latter case, between formal systems and MV-algebras has been known for many years while the relationship between MV-algebras and fuzzy set theory has hardly been studied. This is not surprising. MV-algebras were invented by C. C. Chang [1] in order to provide an algebraic proof of the completeness theorem of the infinitevalued logic of Lukasiewicz and Tarski. Having served this purpose (see [2]), the study of these algebras has been minimal, see for example [6], [7]. Fuzzy set theory was also being born around the same time and only in recent years has its connection with infinite-valued logic been made, see e.g. [3], [4], [5]. It seems appropriate then, to take a further look at the structure of MV-algebras and their relation to fuzzy set theory.
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25

Alkhazaleh, Shawkat, and Abdul Razak Salleh. "Generalised Interval-Valued Fuzzy Soft Set." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/870504.

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We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.
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26

KUTTLER, KENNETH L., and MEIR SHILLOR. "SET-VALUED PSEUDOMONOTONE MAPS AND DEGENERATE EVOLUTION INCLUSIONS." Communications in Contemporary Mathematics 01, no. 01 (February 1999): 87–123. http://dx.doi.org/10.1142/s0219199799000067.

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We develop the theory of evolution inclusions for set-valued pseudomonotone maps. The problems we investigate are [Formula: see text] where B=B(t) is a linear operator that may vanish and A is a set-valued pseudomonotone operator. We prove the existence of unique solutions of such, possibly degenerate, problems.We apply the theory to the problem of dynamic frictional contact with a slip dependent friction coefficient and prove the existence of its unique weak solution.This theory opens the way for the investigation of sophisticated dynamical models in mechanics and frictional contact problems.
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27

XIAO, Di. "Generalization rough set theory and real-valued attributes reduction." Journal of Computer Applications 28, no. 6 (August 20, 2008): 1420–23. http://dx.doi.org/10.3724/sp.j.1087.2008.01420.

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28

Agarwal, R. P., and D. O'Regan. "Fixed-point theory for closed inward set valued maps." Mathematical and Computer Modelling 32, no. 11-13 (December 2000): 1305–10. http://dx.doi.org/10.1016/s0895-7177(00)00205-3.

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29

Khalil, Ahmed Mostafa, Sheng-Gang Li, Fei You, and Sheng-Quan Ma. "More on “n-valued refined neutrosophic soft set theory”." Journal of Intelligent & Fuzzy Systems 36, no. 3 (March 26, 2019): 2757–63. http://dx.doi.org/10.3233/jifs-18647.

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30

Awang, Azzah, Mumtaz Ali, and Lazim Abdullah. "Hesitant Bipolar-Valued Neutrosophic Set: Formulation, Theory and Application." IEEE Access 7 (2019): 176099–114. http://dx.doi.org/10.1109/access.2019.2946985.

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31

TANINO, Tetsuzo. "Theory and Applications of Set-Valued Mappings : Part 3:Applications of Set-Valued Mappings to Dynamical Systems, Game Theory and so on." Journal of Japan Society for Fuzzy Theory and Systems 13, no. 3 (2001): 234–42. http://dx.doi.org/10.3156/jfuzzy.13.3_10.

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32

Bernardes, N. C., A. Peris, and F. Rodenas. "Set-Valued Chaos in Linear Dynamics." Integral Equations and Operator Theory 88, no. 4 (August 2017): 451–63. http://dx.doi.org/10.1007/s00020-017-2394-6.

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33

ZENG, WENYI, YU SHI, and HONGXING LI. "REPRESENTATION THEOREM OF INTERVAL-VALUED FUZZY SET." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14, no. 03 (June 2006): 259–69. http://dx.doi.org/10.1142/s0218488506003996.

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In this paper, we introduce the concept of interval-valued nested set on the universal set X, propose two representation theorems and equivalent classification theorem of interval-valued fuzzy set. These works can be used in setting up the basic theory of interval-valued fuzzy set.
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34

TANINO, Tetsuzo. "Theory and Applications of Set-Valued Mappings : Part 2:Derivatives of Set-Valued Mappings and Applications to Optimization." Journal of Japan Society for Fuzzy Theory and Systems 13, no. 2 (2001): 146–54. http://dx.doi.org/10.3156/jfuzzy.13.2_18.

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35

Zong, Gaofeng, Zengjing Chen, and Yuting Lan. "Fubini-Like Theorem of Real-Valued Choquet Integrals for Set-Valued Mappings." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 24, no. 03 (June 2016): 387–403. http://dx.doi.org/10.1142/s0218488516500197.

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The purpose of this paper is to establish a Fubini-like theorem of real-valued Choquet integrals for set-valued mappings in the frame of capacity theory. To this, we introduce the comonotonic random sets and slice-comonotonic set-valued mappings, which to make good use of the comonotonic additivity of Choquet integrals.
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36

Germina, K. A., Kumar Abhishek, and K. L. Princy. "Further results on set-valued graphs." Journal of Discrete Mathematical Sciences and Cryptography 11, no. 5 (October 2008): 559–66. http://dx.doi.org/10.1080/09720529.2008.10698208.

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37

Zhang, Yu, and Tao Chen. "Minimax problems for set-valued mappings with set optimization." Numerical Algebra, Control & Optimization 4, no. 4 (2014): 327–40. http://dx.doi.org/10.3934/naco.2014.4.327.

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38

Kaczynski, Tomasz. "Conley index for set-valued maps: from theory to computation." Banach Center Publications 47, no. 1 (1999): 57–65. http://dx.doi.org/10.4064/-47-1-57-65.

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39

Moon, T. K., and S. E. Budge. "Classification using set-valued Kalman filtering and Levi's decision theory." IEEE Transactions on Systems, Man, and Cybernetics 24, no. 2 (1994): 313–19. http://dx.doi.org/10.1109/21.281429.

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40

Deschrijver, Glad. "Additive and Multiplicative Generators in Interval-Valued Fuzzy Set Theory." IEEE Transactions on Fuzzy Systems 15, no. 2 (April 2007): 222–37. http://dx.doi.org/10.1109/tfuzz.2006.879999.

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41

Sun, Bingzhen, Weimin Ma, and Zengtai Gong. "Dominance-based rough set theory over interval-valued information systems." Expert Systems 31, no. 2 (May 7, 2013): 185–97. http://dx.doi.org/10.1111/exsy.12022.

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42

Yiarayong, Pairote. "On interval-valued fuzzy soft set theory applied to semigroups." Soft Computing 24, no. 5 (January 7, 2020): 3113–23. http://dx.doi.org/10.1007/s00500-019-04655-3.

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43

Gong, Zengtai, Bingzhen Sun, and Degang Chen. "Rough set theory for the interval-valued fuzzy information systems." Information Sciences 178, no. 8 (April 2008): 1968–85. http://dx.doi.org/10.1016/j.ins.2007.12.005.

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44

Wang, Ting, Hang Zhang, and Yan-long Zhao. "Parameter Estimation Based on Set-valued Signals: Theory and Application." Acta Mathematicae Applicatae Sinica, English Series 35, no. 2 (April 2019): 255–63. http://dx.doi.org/10.1007/s10255-019-0822-x.

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45

GUO, R. "A REPAIRABLE SYSTEM MODELLING: COMBINING GREY SYSTEM THEORY WITH INTERVAL-VALUED FUZZY SET THEORY." International Journal of Reliability, Quality and Safety Engineering 12, no. 03 (June 2005): 241–66. http://dx.doi.org/10.1142/s0218539305001811.

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A fundamental but impossible to be addressed problem in repairable system modelling is how to estimate the system repair improvement (or damage) effects because of the large-sample requirements from the standard statistical inference theory. On the other hand, repairable system operating and maintenance data are often imprecise and vague and therefore Type I fuzzy sets defined by point-wise membership functions are often used for the modelling repairable systems. However, it is more logical and natural to argue that Type II fuzzy sets defined by interval-valued membership function, called interval-valued fuzzy sets (IVFS), should be used in characterizing the underlying mechanism of repairable system. In this paper, we explore a small-sample based GM(1,1) modelling approach rooted in the grey system theory to extract the system intrinsic functioning times from the seemly lawless functioning-failure time records and thus to estimate the repair improvement (damage) effects. We further explore the role of interval-valued fuzzy sets theory in the analysis of the system underlying mechanism. We develop a framework of the GM(1,1)-IVFS mixed reliability analysis and illustrate our idea by an industrial example.
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46

Guan, Qing, and Jian He Guan. "Knowledge Acquisition of Interval Set-Valued Based on Granular Computing." Applied Mechanics and Materials 543-547 (March 2014): 2017–23. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.2017.

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The technique of a new extension of fuzzy rough theory using partition of interval set-valued is proposed for granular computing during knowledge discovery in this paper. The natural intervals of attribute values in decision system to be transformed into multiple sub-interval of [0,1]are given by normalization. And some characteristics of interval set-valued of decision systems in fuzzy rough set theory are discussed. The correctness and effectiveness of the approach are shown in experiments. The approach presented in this paper can also be used as a data preprocessing step for other symbolic knowledge discovery or machine learning methods other than rough set theory.
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47

Lee, Byung Soo, M. Firdosh Khan, and Salahuddin. "Fuzzy nonlinear set-valued variational inclusions." Computers & Mathematics with Applications 60, no. 6 (September 2010): 1768–75. http://dx.doi.org/10.1016/j.camwa.2010.07.007.

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48

Sedighi Hafshejani, J., A. R. Naghipour, and M. R. Rismanchian. "Integer-valued polynomials over block matrix algebras." Journal of Algebra and Its Applications 19, no. 03 (March 21, 2019): 2050053. http://dx.doi.org/10.1142/s021949882050053x.

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In this paper, we state a generalization of the ring of integer-valued polynomials over upper triangular matrix rings. The set of integer-valued polynomials over some block matrix rings is studied. In fact, we consider the set of integer-valued polynomials [Formula: see text] for each [Formula: see text], where [Formula: see text] is an integral domain with quotient field [Formula: see text] and [Formula: see text] is a block matrix ring between upper triangular matrix ring [Formula: see text] and full matrix ring [Formula: see text]. In fact, we have [Formula: see text]. It is known that the sets of integer-valued polynomials [Formula: see text] and [Formula: see text] are rings. We state some relations between the rings [Formula: see text] and the partitions of [Formula: see text]. Then, we show that the set [Formula: see text] is a ring for each [Formula: see text]. Further, it is proved that if the ring [Formula: see text] is not Noetherian then the ring [Formula: see text] is not Noetherian, too. Finally, some properties and relations are stated between the rings [Formula: see text], [Formula: see text] and [Formula: see text].
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49

Nachtegae, Mike, Peter Sussner, Tom Mélange, and Etienne E. Kerre. "Modelling Numerical and Spatial Uncertainty in GrayscaleImage Capture Using Fuzzy Set Theory." Journal of Advanced Computational Intelligence and Intelligent Informatics 13, no. 5 (September 20, 2009): 529–36. http://dx.doi.org/10.20965/jaciii.2009.p0529.

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In this paper, we will discuss interval-valued and intuitionistic fuzzy sets as a model for grayscale images, taking into account the uncertainty regarding the measured grayscale values, which in some cases is also related to the uncertainty regarding the spatial position of an object in an image. We will demonstrate the practical potential of this image model by introducing an interval-valued morphological theory and by illustrating its application with some examples. The results show that the uncertainty that is present during the image capture not only can be modelled, but can also be propagated such that the information regarding the uncertainty is never lost.
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50

He, Yiran. "The Tikhonov Regularization Method for Set-Valued Variational Inequalities." Abstract and Applied Analysis 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/172061.

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This paper aims to establish the Tikhonov regularization theory for set-valued variational inequalities. For this purpose, we firstly prove a very general existence result for set-valued variational inequalities, provided that the mapping involved has the so-called variational inequality property and satisfies a rather weak coercivity condition. The result on the Tikhonov regularization improves some known results proved for single-valued mapping.
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