Publication: The Origin of Fuzzy Extensions
Loading...
Full text at PDC
Publication Date
2015
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Citations
Exportar
Abstract
Many different kinds of sets have been defined within the framework of fuzzy sets . This paper focusses on those fuzzy set extensions that address the difficulties that experts find in order to build the membership values. In particular, we analyze type-2 fuzzy sets , interval-valued fuzzy sets , Atanassov’s intuitionistic fuzzy sets , or bipolar sets of type-2 and Atanassov’s interval-valued fuzzy sets. After stating a general approach to these extensions, we remark some structural problems in the extension problem and stress some applications for which the results obtained with extens
Description
UCM subjects
Unesco subjects
Keywords
Citation
L.A. Zadeh: Fuzzy sets, Inf. Control 8, 338–353 (1965)
J.A. Goguen: L-fuzzy sets, J. Math. Anal. Appl. 18, 145–174 (1967)
J.T. Cacioppo, W.L. Gardner, C.G. Berntson: Beyond bipolar conceptualizations and measures: The case of attitudes and evaluative space, Pers. Soc. Psychol. Rev. 1, 3–25 (1997)
R. Goldblatt: Topoi: The Categorial Analysis of Logic (North-Holland, Amsterdam 1979)
S.M. Lane, I. Moerfijk: Sheaves in Geometry and Logic (Springer, New York 1992)
G. Takeuti, S. Titani: Intuitionistic fuzzy logic and intuitionistic fuzzy set theory, J. Symb. Log. 49, 851–866 (1984)
D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk, H. Prade: Terminological difficulties in fuzzy set theory — The case of intuitionistic fuzzy sets, Fuzzy Sets Syst. 156(3), 485–491 (2005)
G. Birkhoff: Lattice Theory (American Mathematical Society, Providence 1973)
R. Willmott: Mean Measures in Fuzzy Power-Set Theory, Report No. FRP-6 (Dep. Math., Univ. Essex , Colchester 1979)
W. Bandler, L. Kohout: Fuzzy power sets, fuzzy implication operators, Fuzzy Sets Syst. 4, 13–30 (1980)
B. De Baets, E.E. Kerre, M. Gupta: The fundamentals of fuzzy mathematical morphology – part 1: Basic concepts, Int. J. Gen. Syst. 23(2), 155–171 (1995)
L.K. Huang, M.J. Wang: Image thresholding by minimizing the measure of fuzziness, Pattern Recognit. 29(1), 41–51 (1995)
H. Bustince, J. Montero, E. Barrenechea, M. Pagola: Semiautoduality in a restricted family of aggregation operators, Fuzzy Sets Syst. 158(12), 1360–1377 (2007)
T. Calvo, A. Kolesárová, M. Komorníková, R. Mesiar: Aggregation operators: Properties, classes and construction methods. In: Aggregation Operators New Trends and Applications, ed. by T. Calvo, G. Mayor, R. Mesiar (Physica, Heidelberg 2002) pp. 3–104
J. Fodor, M. Roubens: Fuzzy preference modelling and multicriteria decision support, Theory and Decision Library (Kluwer, Dordrecht 1994)
E.P. Klement, R. Mesiar, E. Pap: Triangular norms, trends in logic, Studia Logica Library (Kluwer, Dordrecht 2000)
L.A. Zadeh: Quantitative fuzzy semantics, Inf. Sci. 3, 159–176 (1971)
E.E. Kerre: A first view on the alternatives of fuzzy sets theory. In: Computational Intelligence in Theory and Practice, ed. by B. Reusch, K.-H. Temme (Physica, Heidelberg 2001) pp. 55–72
M. Mizumoto, K. Tanaka: Some properties of fuzzy sets of type 2, Inf. Control 31, 312–340 (1976)MATHMathSciNet
D. Dubois, H. Prade: Operations in a fuzzy-valued logic, Inf. Control 43(2), 224–254 (1979)
J. Harding, C. Walker, E. Walker: The variety generated by the truth value algebra of type-2 fuzzy sets, Fuzzy Sets Syst. 161, 735–749 (2010)
J.M. Mendel, R.I. John: Type-2 fuzzy sets made simple, IEEE Trans. Fuzzy Syst. 10, 117–127 (2002)
J. Aisbett, J.T. Rickard, D.G. Morgenthaler: Type-2 fuzzy sets as functions on spaces, IEEE Trans. Fuzzy Syst. 18(4), 841–844 (2010)
G. Deschrijver, E.E. Kerre: On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision, Inf. Sci. 177, 1860–1866 (2007)M
G. Deschrijver, E.E. Kerre: On the relationship between some extensions of fuzzy set theory, Fuzzy Sets Syst. 133, 227–235 (2003)
D. Dubois, H. Prade: Fuzzy Sets and Systems: Theory and Applications (Academic, New York 1980)
G.J. Klir, B. Yuan: Fuzzy Sets and Fuzzy Logic: Theory and Applications (Prentice-Hall, New Jersey 1995)MATH
J.M. Mendel: Type-2 fuzzy sets for computing with words, IEEE Int. Conf. Granul. Comput., Atlanta (2006), GA 8-8
J.M. Mendel: Computing with words and its relationships with fuzzistics, Inf. Sci. 177(4), 988–1006 (2007)MathSciNet
J.M. Mendel: Historical reflections on perceptual computing, Proc. 8th Int. FLINS Conf. (FLINS'08) (World Scientific, Singapore 2008) pp. 181–187
J.M. Mendel: Computing with words: Zadeh, Turing, Popper and Occam, IEEE Comput. Intell. Mag. 2, 10–17 (2007)
H. Hagras: Type-2 FLCs: A new generation of fuzzy controllers, IEEE Comput. Intell. Mag. 2, 30–43 (2007)
H. Hagras: A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots, IEEE Trans. Fuzzy Syst. 12, 524–539 (2004)
R. Sepulveda, O. Castillo, P. Melin, A. Rodriguez-Diaz, O. Montiel: Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic, Inf. Sci. 177, 2023–2048 (2007)
X.S. Xia, Q.L. Liang: Crosslayer design for mobile ad hoc networks using interval type-2 fuzzy logic systems, Int. J. Uncertain. Fuzziness Knowl. Syst. 16(3), 391–408 (2008)
C.H. Wang, C.S. Cheng, T.T. Lee: Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN), IEEE Trans. Syst. Man Cybern. B 34(3), 14621477 (2004)
R. Sambuc: Fonction Φ-Flous, Application a l'aide au Diagnostic en Pathologie Thyroidienne, These de Doctorat en Medicine (Univ. Marseille, Marseille 1975)
K.U. Jahn: Intervall-wertige Mengen, Math. Nachr. 68, 115–132 (1975)
I. Grattan-Guinness: Fuzzy membership mapped onto interval and many-valued quantities, Z. Math. Log. Grundl. Math. 22, 149–160 (1976)
A. Dziech, M.B. Gorzalczany: Decision making in signal transmission problems with interval-valued fuzzy sets, Fuzzy Sets Syst. 23(2), 191–203 (1987)MathSciNet
M.B. Gorzalczany: A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets Syst. 21, 1–17 (1987)
M.B. Gorzalczany: An interval-valued fuzzy inference method. Some basic properties, Fuzzy Sets Syst. 31(2), 243–251 (1989)
I.B. Türksen: Interval valued fuzzy sets based on normal forms, Fuzzy Sets Syst. 20(2), 191–210 (1986)
I.B. Türksen, Z. Zhong: An approximate analogical reasoning schema based on similarity measures and interval-valued fuzzy sets, Fuzzy Sets Syst. 34, 323–346 (1990)
I.B. Türksen, D.D. Yao: Representation of connectives in fuzzy reasoning: The view through normal forms, IEEE Trans. Syst. Man Cybern. 14, 191–210 (1984)
J.L. Deng: Introduction to grey system theory, J. Grey Syst. 1, 1–24 (1989)
H. Bustince: Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets, Int. J. Approx. Reason. 23(3), 137–209 (2000)M
G. Deschrijver: The Archimedean property for t-norms in interval-valued fuzzy set theory, Fuzzy Sets Syst. 157(17), 2311–2327 (2006)
G. Deschrijver, C. Cornelis, E.E. Kerre: On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Trans. Fuzzy Syst. 12(1), 45–61 (2004)
Z. Xu, R.R. Yager: Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. Gen. Syst. 35, 417–433 (2006)
H. Bustince, J. Fernandez, A. Kolesárová, M. Mesiar: Generation of linear orders for intervals by means of aggregation functions, Fuzzy Sets Syst. 220, 69–77 (2013)
J. Montero, D. Gomez, H. Bustince: On the relevance of some families of fuzzy sets, Fuzzy Sets Syst. 158(22), 2429–2442 (2007)
H. Bustince, F. Herrera, J. Montero: Fuzzy Sets and Their Extensions: Representation Aggregation and Models (Springer, Berlin 2007)
W. Pedrycz: Shadowed sets: Representing and processing fuzzy sets, IEEE Trans. Syst. Man Cybern. B 28, 103–109 (1998)
W. Pedrycz, G. Vukovich: Investigating a relevance off uzzy mappings, IEEE Trans. Syst. Man Cybern. B 30, 249–262 (2000)
W. Pedrycz, G. Vukovich: Granular computing with shadowed sets, Int. J. Intell. Syst. 17, 173–197 (2002)M
J.M. Mendel: Advances in type-2 fuzzy sets and systems, Inf. Sci. 177, 84–110 (2007)
H. Bustince, J. Montero, M. Pagola, E. Barrenechea, D. Gomez: A survey of interval-valued fuzzy sets. In: Handbook of Granular Computing, ed. by W. Pedrycz (Wiley, New York 2008)
P. Burillo, H. Bustince: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets Syst. 78, 305–316 (1996)
A. Jurio, M. Pagola, D. Paternain, C. Lopez-Molina, P. Melo-Pinto: Interval-valued restricted equivalence functions applied on clustering techniques, Proc. Int. Fuzzy Syst. Assoc. World Congr. Eur. Soc. Fuzzy Log. Technol. Conf. (2009) pp. 831–836
E. Szmidt, J. Kacprzyk: Entropy for intuitionistic fuzzy sets, Fuzzy Sets Syst. 118(3), 467–477 (2001)MATHMathSciNet
H. Rezaei, M. Mukaidono: New similarity measures of intuitionistic fuzzy sets, J. Adv. Comput. Intell. Inf. 11(2), 202–209 (2007)
H. Bustince, M. Pagola, E. Barrenechea, J. Fernandez, P. Melo-Pinto, P. Couto, H.R. Tizhoosh, J. Montero: Ignorance functions. An application to the calculation of the threshold in prostate ultrasound images, Fuzzy Sets Syst. 161(1), 20–36 (2010)
D. Wu: Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: Overview and comparisons, IEEE Trans. Fuzzy Syst. 21(1), 80–99 (2013)
H. Bustince, M. Galar, B. Bedregal, A. Kolesárová, R. Mesiar: A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy set applications, IEEE Trans. Fuzzy Syst. 21(6), 1150–1162 (2013)
J. Sanz, H. Bustince, F. Herrera: Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning, Inf. Sci. 180(19), 3674–3685 (2010)
J. Sanz, A. Fernandez, H. Bustince, F. Herrera: A genetic tuning to improve the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets: Degree of ignorance and lateral position, Int. J. Approx. Reason. 52(6), 751–766 (2011)
J. Sanz, A. Fernandez, H. Bustince, F. Herrera: IIVFDT: Ignorance functions based interval-valued fuzzy decision tree with genetic tuning, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 20(Suppl. 2), 1–30 (2012)MathSciNet
J. Sanz, A. Fernandez, H. Bustince, F. Herrera: IVTURS: A linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection, IEEE Trans. Fuzzy Syst. 21(3), 399–411 (2013)
Z. Chi, H. Yan, T. Pham: Fuzzy Algorithms with Applications to Image Processing and Pattern Recognition (World Scientific, Singapore 1996)MATH
H. Ishibuchi, T. Yamamoto, T. Nakashima: Hybridization of fuzzy GBML approaches for pattern classification problems, IEEE Trans. Syst. Man Cybern. B 35(2), 359–365 (2005)
J. Dombi, Z. Gera: Rule based fuzzy classification using squashing functions, J. Intell. Fuzzy Syst. 19(1), 3–8 (2008)
R. Alcalá, J. Alacalá-Fdez, F. Herrera: A proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection, IEEE Trans. Fuzzy Syst. 15(4), 616–635 (2007)
R. Alcalá, J. Alacalá-Fdez, M. Graco, F. Herrera: Rule base reduction and genetic tuning of fuzzy systems based on the linguistic 3-tuples representation, Soft Comput. 11(5), 401–419 (2007)
J. Quinlan: C4.5: Programs for Machine Learning (Morgan Kaufmann, San Mateo 1993)
C.Z. Janikow: Fuzzy decision trees: Issues and methods, IEEE Trans. Syst. Man Cybern. B 28(1), 1–14 (1998)
J. Alacalá-Fdez, R. Alcalá, F. Herrera: A fuzzy association rule-based classification model for high-dimensional problems with genetic rule selection and lateral tuning, IEEE Trans. Fuzzy Syst. 19(5), 857–872 (2011)
J. Hühn, E. Hüllermeier: FURIA: An algorithm for unordered fuzzy rule induction, Data Min. Knowl. Discov. 19(3), 293–319 (2009)
E. Barrenechea, H. Bustince, B. De Baets, C. Lopez-Molina: Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images, IEEE Trans. Fuzzy Syst. 19(5), 819–830 (2011)
H. Bustince, P.M. Barrenechea, J. Fernandez, J. Sanz: “Image thresholding using type II fuzzy sets.” Importance of this method, Pattern Recognit. 43(9), 3188–3192 (2010)
H. Bustince, E. Barrenechea, M. Pagola, J. Fernandez: Interval-valued fuzzy sets constructed from matrices: Application to edge detection, Fuzzy Sets Syst. 60(13), 1819–1840 (2009)
M. Galar, F. Fernandez, G. Beliakov, H. Bustince: Interval-valued fuzzy sets applied to stereo matching of color images, IEEE Trans. Image Process. 20, 1949–1961 (2011)
M. Pagola, C. Lopez-Molina, J. Fernandez, E. Barrenechea, H. Bustince: Interval type-2 fuzzy sets constructed from several membership functions. Application to the fuzzy thresholding algorithm, IEEE Trans. Fuzzy Syst. 21(2), 230–244 (2013)
H.R. Tizhoosh: Image thresholding using type-2 fuzzy sets, Pattern Recognit. 38, 2363–2372 (2005)
M.E. Yuksel, M. Borlu: Accurate segmentation of dermoscopic images by image thresholding based on type-2 fuzzy logic, IEEE Trans. Fuzzy Syst. 17(4), 976–982 (2009)
C. Shyi-Ming, W. Hui-Yu: Evaluating students answer scripts based on interval-valued fuzzy grade sheets, Expert Syst. Appl. 36(6), 9839–9846 (2009)
F. Liu, H. Geng, Y.-Q. Zhang: Interactive fuzzy interval reasoning for smart web shopping, Appl. Soft Comput. 5(4), 433–439 (2005)
C. Byung-In, C.-H.R. Frank: Interval type-2 fuzzy membership function generation methods for pattern recognition, Inf. Sci. 179(13), 2102–2122 (2009)MATH
H.M. Choi, G.S. Min, J.Y. Ahn: A medical diagnosis based on interval-valued fuzzy sets, Biomed. Eng. Appl. Basis Commun. 24(4), 349–354 (2012)
J.M. Mendel, H. Wu: Type-2 fuzzistics for symmetric interval type-2 fuzzy sets: Part 1: Forward problems, IEEE Trans. Fuzzy Syst. 14(6), 781–792 (2006)
D. Wu, J.M. Mendel: A vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets, Inf. Sci. 178(2), 381–402 (2008)
A. Jurio, H. Bustince, M. Pagola, A. Pradera, R.R. Yager: Some properties of overlap and grouping functions and their application to image thresholding, Fuzzy Sets Syst. 229, 69–90 (2013)
K.T. Atanassov: Intuitionistic fuzzy sets, VII ITKRs Session, Central Sci.-Tech. Libr. Bulg. Acad. Sci., Sofia (1983) pp. 1684–1697, (in Bulgarian)
K.T. Atanassov: Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20, 87–96 (1986)
W.L. Gau, D.J. Buehrer: Vague sets, IEEE Trans. Syst. Man Cybern. 23(2), 610–614 (1993)MATH
H. Bustince, P. Burillo: Vague sets are intuitionistic fuzzy sets, Fuzzy Sets Syst. 79(3), 403–405 (1996)
H. Bustince, E. Barrenechea, P. Pagola: Generation of interval-valued fuzzy and Atanassov's intuitionistic fuzzy connectives from fuzzy connectives and from $K_{{\alpha}}$ operators: Laws for conjunctions and disjunctions, amplitude, Int. J. Intell. Syst. 32(6), 680–714 (2008)
K.T. Atanassov, G. Gargov: Interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst. 31(3), 343–349 (1989)
J. Ye: Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment, Eur. J. Oper. Res. 205(1), 202–204 (2010)MATH
F. Herrera, E. Herrera-Viedma: Linguistic decision analysis: Steps for solving decision problems under linguistic information, Fuzzy Sets Syst. 115, 67–82 (2000)
L. Baccour, A.M. Alimi, R.I. John: Similarity measures for intuitionistic fuzzy sets: State of the art, J. Intell. Fuzzy Syst. 24(1), 37–49 (2013)
E. Szmidt, J. Kacprzyk, P. Bujnowski: Measuring the amount of knowledge for Atanassovs intuitionistic fuzzy sets, Lect. Notes Comput. Sci. 6857, 17–24 (2011)
N.R. Pal, H. Bustince, M. Pagola, U.K. Mukherjee, D.P. Goswami, G. Beliakov: Uncertainties with Atanassov's intuitionistic fuzzy sets: fuzziness and lack of knowledge, Inf. Sci. 228, 61–74 (2013)
U. Dudziak, B. Pekala: Equivalent bipolar fuzzy relations, Fuzzy Sets Syst. 161(2), 234–253 (2010)MATHMathSciNet
Z. Xu: Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators, Knowl. Syst. 24(6), 749–760 (2011)
Z. Xu, H. Hu: Projection models for intuitionistic fuzzy multiple attribute decision making, Int. J. Inf. Technol. Decis. Mak. 9(2), 257–280 (2010)
Z. Xu: Priority weights derived from intuitionistic multiplicative preference relations in decision making, IEEE Trans. Fuzzy Syst. 21(4), 642–654 (2013)
X. Zhang, Z. Xu: A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making, Fuzzy Optim. Decis. Mak. 11(2), 135–146 (2012)
T. Chen: Multi-criteria decision-making methods with optimism and pessimism based on Atanassov's intuitionistic fuzzy sets, Int. J. Syst. Sci. 43(5), 920–938 (2012)MATH
S.K. Biswas, A.R. Roy: An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets Syst. 117, 209–213 (2001)
I. Bloch: Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology, Inf. Sci. 181(10), 2002–2015 (2011)
P. Melo-Pinto, P. Couto, H. Bustince, E. Barrenechea, M. Pagola, F. Fernandez: Image segmentation using Atanassov's intuitionistic fuzzy sets, Expert Syst. Appl. 40(1), 15–26 (2013)
P. Couto, A. Jurio, A. Varejao, M. Pagola, H. Bustince, P. Melo-Pinto: An IVFS-based image segmentation methodology for rat gait analysis, Soft Comput. 15(10), 1937–1944 (2011)
K.T. Atanassov: Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper Terminological difficulties in fuzzy set theory – The case of Intuitionistic fuzzy sets, Fuzzy Sets Syst. 156(3), 496–499 (2005)
D. Dubois, H. Prade: An introduction to bipolar representations of information and preference, Int. J. Intell. Syst. 23, 866–877 (2008)
D. Dubois, H. Prade: An overview of the asymmetric bipolar representation of positive and negative information in possibility theory, Fuzzy Sets Syst. 160(10), 1355–1366 (2009)
W.R. Zhang: NPN fuzzy sets and NPN qualitative algebra: a computational framework for bipolar cognitive modeling and multiagent decision analysis, IEEE Trans. Syst. Man Cybern. B 26(4), 561–574 (1996)
W.R. Zhang: Bipolar logic and bipolar fuzzy partial orderings for clustering and coordination, Proc. 6th Joint Conf. Inf. Sci. (2002) pp. 85–88
P. Grzegorzewski: On some basic concepts in probability of IF-events, Inf. Sci. 232, 411–418 (2013)MATHMathSciNet
H. Bustince, P. Burillo: Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst. 74(2), 237–244 (1995)
J. Wu, F. Chiclana: Non-dominance and attitudinal prioritisation methods for intuitionistic and interval-valued intuitionistic fuzzy preference relations, Expert Syst. Appl. 39(18), 13409–13416 (2012)
Z. Xu, Q. Chen: A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy bonferroni means, J. Syst. Sci. Syst. Eng. 20(2), 217–228 (2011)
J. Ye: Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets, Appl. Math. Model. 36(9), 4466–4472 (2012)
A. Aygunoglu, B.P. Varol, V. Cetkin, H. Aygun: Interval-valued intuitionistic fuzzy subgroups based on interval-valued double t-norm, Neural Comput. Appl. 21(1), S207–S214 (2012)
M. Fanyong, Z. Qiang, C. Hao: Approaches to multiple-criteria group decision making based on interval-valued intuitionistic fuzzy Choquet integral with respect to the generalized lambda-Shapley index, Knowl. Syst. 37, 237–249 (2013)
W. Wang, X. Liu, Y. Qin: Interval-valued intuitionistic fuzzy aggregation operators 14, J. Syst. Eng. Electron. 23(4), 574–580 (2012)
K. Hirota: Concepts of probabilistic sets, Fuzzy Sets Syst. 5, 31–46 (1981)
R.R. Yager: On the theory of bags, Int. J. Gen. Syst. 13, 23–37 (1986)
S. Miyamoto: Multisets and fuzzy multisets. In: Soft Computing and Human-Centered Machines, ed. by Z.-Q. Liu, S. Miyamoto (Springer, Berlin 2000) pp. 9–33
Y. Shang, X. Yuan, E.S. Lee: The n-dimensional fuzzy sets and Zadeh fuzzy sets based on the finite valued fuzzy sets, Comput. Math. Appl. 60, 442–463 (2010)MATHMathSciNet
B. Bedregal, G. Beliakov, H. Bustince, T. Calvo, R. Mesiar, D. Paternain: A class of fuzzy multisets with a fixed number of memberships, Inf. Sci. 189, 1–17 (2012)
A. Amo, J. Montero, G. Biging, V. Cutello: Fuzzy classification systems, Eur. J. Oper. Res. 156, 459–507 (2004)
J. Montero: Arrow`s theorem under fuzzy rationality, Behav. Sci. 32, 267–273 (1987)
A. Mesiarová, J. Lazaro: Bipolar Aggregation operators, Proc. AGOP2003, Al-calá de Henares (2003) pp. 119–123
A. Mesiarová-Zemánková, R. Mesiar, K. Ahmad: The balancing Choquet integral, Fuzzy Sets Syst. 161(17), 2243–2255 (2010)
A. Mesiarová-Zemánková, K. Ahmad: Multi-polar Choquet integral, Fuzzy Sets Syst. 220, 1–20 (2013)MATH
W.R. Zhang, L. Zhang: YinYang bipolar logic and bipolar fuzzy logic, Inf. Sci. 165(3/4), 265–287 (2004)
W.R. Zhang: YinYang Bipolar T-norms and T-conorms as granular neurological operators, Proc. IEEE Int. Conf. Granul. Comput., Atlanta (2006) pp. 91–96
F. Smarandache: A unifying field in logics: Neutrosophic logic, Multiple-Valued Logic 8(3), 385–438 (2002)
V. Torra: Hesitant fuzzy sets, Int. J. Intell. Syst. 25, 529539 (2010)
V. Torra, Y. Narukawa: On hesitant fuzzy sets and decision, Proc. Conf. Fuzzy Syst. (FUZZ IEEE) (2009) pp. 1378–1382
D. Molodtsov: Soft set theory. First results, Comput. Math. Appl. 37, 19–31 (1999)
P.K. Maji, R. Biswas, R. Roy: Fuzzy soft sets, J. Fuzzy Math. 9(3), 589–602 (2001)
Z. Pawlak: Rough sets, Int. J. Comput. Inf. Sci. 11, 341–356 (1982)
D. Dubois, H. Prade: Rough fuzzy-sets and fuzzy rough sets, Int. J. Gen. Syst. 17(3), 191–209 (1990)