[1] J. Aczel, Lectures on Functional Equations and Their Applications, Academic press, New
York, London, 1966.
[2] C. Alsina, On a family of connectives for fuzzy sets, Fuzzy Sets and Systems, 16 (1985),
231-235.
[3] M. J. Asiain, H. Bustince, B. Bedregal, Z. Takac, M. Baczynski, D. Paternain and G. Dimuro,
About the Use of Admissible Order for Defining Implication Operators, Cham: Springer International
Publishing(2016), 353-362.
[4] M. J. Asiain, H. Bustince, R. Mesiar, A. Kolesarova and Z. Takac, Negations with respect to
admissible orders in the interval-valued fuzzy set theory, IEEE Transactions on Fuzzy Systems,
PP(99) (2017), 1{26.
[5] E. Barrenechea, J. Fernandez, M. Pagola, F. Chiclana and H. Bustince, Construction of
interval-valued fuzzy preference relations from ignorance functions and fuzzy preference re-
lations: application to decision making, Knowledge-Based Systems, 58 (2014), 33{44.
[6] B. Bedregal, On interval fuzzy negations, Fuzzy Sets and Systems, 161(17) (2010) 2290{2313.
[7] U. Bentkowska, B. Pekala, H. Bustince, J. Fernandez, A. Jurio and K. Balicki, N-reciprocity
property for interval-valued fuzzy relations with an application to group decision making prob-
lems in social networks, International Journal of Uncertainty, Fuzziness and Knowledge-Based
Systems, 25, Suppl. 1 (2017), 43{72.
[8] H. Bustince, M. Pagola, R. Mesiar, E. Hullermeier and F. Herrera, Grouping, overlap and gen-
eralized bientropic functions for fuzzy modeling of pairwise comparisons, IEEE Transactions
on fuzzy systems, 20(3) (2012), 405{415.
[9] G. Birkho, Lattice Theory, AMS Coll. Publ. 25, Providence, 1967.
[10] T. Calvo, On mixed De Morgan triplets, Fuzzy Sets and Systems, 50 (1992), 47-50.
[11] T. Calvo, B. De Baets and J. Fodor, The functional equations of Frank and Alsina for
uninorms and nullnorms, Fuzzy Sets and Systems, 120 (2001), 385-394.
[12] T. Calvo, A. Kolesarova, M. Komornikova and R. Mesiar, Aggregation operators: properties,
classes and construction methods, In: Calvo, T., et al. (eds.), Aggregation Operators New
trends and Applications, Physica-Verlag, Heidelberg(2002), 3{104.
[13] H. Chen and L. Zhou, An approach to group decision making with interval fuzzy preference
relations based on induced generalized continuous ordered weighted averaging operator, Expert
Systems with Applications, 38 (2011), 13432{13440.
[14] F. Chiclana, E. Herrera-Viedma, S. Alonso and R. A. M. Pereira, Preferences and consistency
issues in group decision making, in Bustince, H., at al. (eds.), Fuzzy Sets and Their Extensions:
Representation, Aggregation and Models, Springer-Verlag, Berlin, (2008), 219{237.
[15] F. Chiclana, F. Herrera and E. Herrera-Viedma, Integrating three representation models in
fuzzy multipurpose decision making based on fuzzy preference relations, Fuzzy Sets and Systems,
97(1) (1998), 33-48.
[16] B. De Baets, B. Van de Walle and E. Kerre, Fuzzy preference structures without incompara-
bility, Fuzzy Sets and Systems, 76(3) (1995), 333-348.
[17] G. Deschrijver, C. Cornelis and E. E. Kerre, On the Representation of Intuitonistic Fuzzy
t-Norms and t-Conorms, IEEE Trans. Fuzzy Syst., 12 (2004), 45{61.
[18] G. Deschrijver and E. Kerre, Aggregation Operators in Interval-valued Fuzzy and Atanassovs
Intuitionistic Fuzzy Set Theory, In: Bustince, H., et al. (eds.) Fuzzy Sets and their Extensions:
Representation, Aggregation and Models, Springer, (2008), 183{203.
[19] G. Deschrijver, Quasi-arithmetic means and OWA functions in interval-valued and
Atanassovs intuitionistic fuzzy set theory, in: Galichet, S., et al. (eds.), Proceedings of
EUSFLAT-LFA 2011, 18-22.07.2011, Aix-les-Bains, France, (2011), 506{513.
[20] P. Drygas and B. Pekala, Properties of Decomposable Operations on some Extension of the
Fuzzy Set Theory, In: Atanassov, K.T., Hryniewicz, O., Kacprzyk, J. et al. (eds.), Advances
in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, EXIT, Warsaw,
(2008), 105{118.
[21] J. Fodor and M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support
in Theory and Decision Library, Kluwer Academic Publishers, 1994.
[22] S. Freson, B. De Baets and H. De Meyer, Closing reciprocal relations w.r.t. stochastic
transitivity, Fuzzy Sets and Systems, 241 (2014), 2{26.
[23] M. B. Gorza lczany, A method of inference in approximate reasoning based on interval-valued
fuzzy sets, Fuzzy Sets Syst., 21(1) (1987), 1{17.
[24] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Acad. Publ., Dordrecht,
2000.
[25] M. Komornkova and R. Mesiar, Aggregation functions on bounded partially ordered sets and
their classification, Fuzzy Sets and Systems, 175 (2011), 48{56.
[26] F. Liu, W. G. Zhang and L. H. Zhang, A group decision making model based on a generalized
ordered weighted geometric average operator with interval preference matrices, Fuzzy Sets and
Systems, 246 (2014), 1{18.
[27] B. Llamazares and B. De Baets, Fuzzy strict preference relations compatible with fuzzy or-
derings, International Uncertainty Fuzziness and Knowledge-Based Systems, 18(1) (2010),
13{24.
[28] S. V. Ovchinnikov and M. Roubens, On strict preference relations, Fuzzy Sets and Systems,
43 (1991), 319-326.
[29] D. Paternain, A. Jurio, E. Barrenechea, H. Bustince, B. Bedregal and E. Szmidt, An alterna-
tive to fuzzy methods in decision-making problems, Expert Systems with Applications, 39(9)
(2012), 7729{7735.
[30] B. Pekala and U. Bentkowska, Generalized reciprocity property for interval-valued fuzzy set-
ting in some aspect of social network, IWIFSGN'2016 Fifteenth International Workshop on
Intuitionistic Fuzzy Sets and Generalized Nets, Warsaw, Poland, October 12{14, Springer,
2016.
[31] A. Pradera, G. Beliakov, H. Bustince and B. De Baets, A review of the relationships between
implication, negation and aggregation functions from the point of view of material implication,
Inf. Sci., 329 (2016), 357{380.
[32] M. Roubens and P. Vincke, Preference Modelling, Springer-Verlag, Berlin, 1985.
[33] R. Sambuc, Fonctions Ø-floues: Application a l'aide au diagnostic en pathologie thyroidi-
enne, Ph.D. Thesis, Universite de Marseille, France, 1975 (in French).
[34] J. Sanz, A. Fernandez, H. Bustince and F. Herrera, Improving the performance of fuzzy
rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning,
Information Sciences, 180(19) (2010), 3674{3685.
[35] J. Sanz, A. Fernandez, H. Bustince and F. Herrera, A genetic tuning to improve the perfor-
mance of fuzzy rule-based classification systems with intervalvalued fuzzy sets: degree of ig-
norance and lateral position, International Journal of Approximate Reasoning, 52(6) (2011),
751{766.
[36] I. B. Turksen and T. Bilgic, Interval-valued strict preference relations with Zadeh triples,
Fuzzy Sets and Systems, 78 (1996), 183{195.
[37] Z. Xu, On compatibility of interval fuzzy preference relations, Fuzzy Optimization and Decision
Making, 3 (2004), 217{225.
[38] G. L. Xu and F. Liu, An approach to group decision making based on interval multiplicative
and fuzzy preference relations by using projection, Applied Mathematical Modelling, 37 (2013),
3929{3943.
[39] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
[40] L. A. Zadeh, The Concept of a Linguistic Variable and its Application to Approximate
Reasoning-I, Information Sciences, 8 (1975), 199{249.