Orthopairs and granular computing

Aguirre F, Destercke S, Dubois D, Sallak M, Jacob C (2014) Inclusion-exclusion principle for belief functions. Int J Approx Reason 55(8):1708–1727

Amgoud L, Prade H (2013) A formal concept view of abstract argumentation. In: van der Gaag LC (ed) Proceedings 12th Eur. Conf. Symb. and Quant. Appr. to Reas. with Uncert. (ECSQARU’13), Utrecht, July 8–10, LNCS 7958, pp 1–12. Springer

Andreoli G (1959) Algebre di boole - algebre di insieme - algebre di livelli. Giornale di Matematiche di Battaglini vol LXXXVII, pp 3–22

Andreoli G (1961) Dicotomie e tricotomie (anelli booleani triadici ed algebre booleane a tre valori). Ricerca 11:1–10

Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

Atanassov KT (1999) Intuitionistic fuzzy sets, vol 35. Physica Verlag, Springer, Heidelberg

Atanassov KT (2012) On intuitionistic fuzzy sets theory, studies in fuzziness and soft computing, vol 283, Springer, Heidelberg

Belnap ND (1977) A useful four-valued logic. In: Dunn JM, Epstein G (eds) Modern uses of multiple-valued logic, D. Reidel Publishing Company, Dordrecht, pp 8–37

Béziau JY (2003) New light on the square of oppositions and its nameless corner. Log Investig 10:218–233

Béziau JY (2012) The power of the hexagon. Log Univ 6(1–2):1–43

Blamey S (1985) Partial logic. In: Gabbay DM, Guenthner F (eds) Handbook of philosophical logic, vol. 3, p 1–70. D. Reidel Publishing Company, Dordrecht

Blanché R (1953) Sur l’opposition des concepts. Theoria 19:89–130

Blanché R (1966) Structures intellectuelles. Essai sur l’Organisation Systématique des Concepts. Vrin, Paris

Cattaneo G, Ciucci D (2006) Basic intuitionistic principles in fuzzy set theories and its extensions (a terminological debate on Atanassov IFS). Fuzzy Sets Syst 157:3198–3219

Cattaneo G, Ciucci D, Dubois D (2011) Algebraic models of deviant modal operators based on de morgan and kleene lattices. Inf Sci 181(19):4075–4100

Cattaneo G, Manià A (1974) Abstract orthogonality and orthocomplementation. Proc Camb Philos Soc. 76:115–132

Ciucci D (2011) Orthopairs: a simple and widely used way to model uncertainty. Fundam Inform 108(3–4):287–304

Ciucci D (2014) Orthopairs in the 1960s: historical remarks and new ideas. In: Cornelis C, Kryszkiewicz M, Slezak D, Ruiz EM, Bello R, Shang L (eds) Proc RSCTC, LNCS, vol 8536, Cham

Ciucci D, Dubois D (2014) Three-valued logics, uncertainty management and rough sets. Trans Rough Sets 17:1–32

Ciucci D, Dubois D, Lawry J (2014) Borderline vs. unknown: comparing three-valued representations of imperfect information. Int J Approx Reason 55(9):1866–1889

Ciucci D, Dubois D, Prade H (2014) The structure of oppositions in rough set theory and formal concept analysis—toward a new bridge between the two settings. In: Beierle C, Meghini C (eds) Proceedings of the 8th international symposium on foundations of information and knowledge systems (FoIKS’14), Bordeaux, Mar. 3–7, LNCS, vol 8367. Springer, Cham, pp 154–173

Ciucci D, Dubois D, Prade P (2016) Structures of opposition induced by relations. Ann Math Artif Intell. doi: 10.1007/s10472-015-9480-8

Çoker D (1996) A note on intuitionistic sets and intuitionistic points. Turk J Math 20:343–351

Crosscombe M, Lawry J (2015) Exploiting vagueness for multi-agent consensus. In: Bai Q, Ren F, Zhang M, Ito T (eds) The Proceedings of the 2nd International Workshop on Smart Simulation and Modelling for Complex Systems at IJCAI 2015

Csajbók Z (2013) Approximation of sets based on partial covering. Trans Rough Sets 16:144–220

Dekker PJ (2015) Not only barbara. J Logic Lang Inf 24(2):95–129

Demey L (2012) Algebraic aspects of duality diagrams. In: Cox PT, Plimmer B, Rodgers PJ (eds) Proceedings of the 7th International Conference on Diagrammatic Representation and Inference (Diagrams’12), Canterbury, July 2-6, LNCS, vol 7352. Springer, Heidelberg, pp 300–302

Dubois D, Gottwald S, Hajek P, Kacprzyk J, Prade H (2005) Terminological difficulties in fuzzy set theory—the case of Intuitionistic Fuzzy Sets. Fuzzy Sets Syst 156:485–491

Dubois D, Prade H (1994) Conditional objects as nonmonotonic consequence relationships. IEEE Trans Syst Man Cybern 24(12):1724–1740

Dubois D, Prade H (2012a) From Blanché’s hexagonal organization of concepts to formal concept analysis and possibility theory. Log Univ 6:149–169

Dubois D, Prade H (2012b) Possibility theory and formal concept analysis: characterizing independent sub-contexts. Fuzzy Sets Syst 196:4–16

Dubois D, Prade H (2015a) Possibility theory and its applications: where do we stand? In: Kacprzyk J, Pedrycz W (eds) Springer Handbook of Computational Intelligence, Springer, Dordrecht, pp 31–60

Dubois D, Prade H (2015b) Gradual structures of oppositions. In: Esteva F, Magdalena L, Verdegay JL (eds) Enric Trillas: passion for fuzzy sets, studies in fuzziness and soft computing, vol 322. Springer, Cham, pp 79–91

Dubois D, Prade H, Smets P (2001) “Not impossible” vs. “guaranteed possible” in fusion and revision. In: Benferhat S, Besnard P (eds) Symbolic and quantitative approaches to reasoning with uncertainty, 6th European conference, ECSQARU 2001, Toulouse, France, September 19–21, 2001, Proceedings, LNCS, vol 2143. Springer, Berlin, London, pp 522–531

Fadini A (1962) Il calcolo delle classi in una logica a tre valori di verità. Giornale di Matematiche di Battaglini vol XC, pp 72–91

Fadini A (1962) Teoria degli elementi complessi nelle Algebre di Boole. Ann del Pontif Ist Super di Sci e Lett S. Chiara 12:223–243

Fitting M (1989) Bilattices and the theory of truth. J Philos Logic 18:225–256

Ganter B, Kuznetsov SO (2003) Hypotheses and version spaces. In: de Moor A, Lex W, Ganter B (eds) Conceptual structures for knowledge creation and communication, 11th International Conference on Conceptual Structures, ICCS 2003 Dresden, Germany, July 21–25, 2003 Proceedings, LNCS, 2746:83–95

Gentilhomme MY (1968) Les ensembles flous en linguistique. Cah de Linguist Theor et Appl Bucar 47:47–65

Grabisch M, Marichal JL, Mesiar R, Pap E (2009) Aggregation functions. Cambridge University Press, New York

Hacker E (1975) The octagon of opposition. Notre Dame J Form Logic 16:352–353

Kacprzyk J, Pedrycz W (eds) (2015) Springer handbook of computational intelligence, Springer, Dordrecht

Kleene SC (1952) Introduction to metamathematics. North-Holland Pub. Co., Amsterdam

Lawry J, Dubois D (2012) A bipolar framework for combining beliefs about vague propositions. In: Brewka G, Eiter T, McIlraith SA (eds) Proceedings of the thirteenth international conference on principles of knowledge representation and reasoning (KR 2012), Roma, Italy, pp 530–540

Lawry J, González Rodríguez I (2011) A bipolar model of assertability and belief. Int J Approx Reason 52(1):76–91

Lawry J, Tang Y (2012) On truth-gaps, bipolar belief and the assertability of vague propositions. Artif Intell 191–192:20–41

Miclet L, Prade H (2014) Analogical proportions and square of oppositions. In: Laurent A et al. (eds) Proceedings of the 15th international conference on information processing and management of uncertainty in knowledge-based systems, July 15–19, Montpellier, CCIS, vol 443. Springer, Cham, pp 324–334

Mitchell T (1982) Generalization as search. Artif Intell 18:203–226

Monteiro A (1980) Sur les algèbres de Heyting symétriques. Port Math 39:1–237

Moraschini T (2014) An algebraic study of exactness in partial contexts. Int J Approx Reason 55(1):457–468

Murinová P, Novák V (2013) The analysis of the generalized square of opposition. In: Montero J, Pasi G, Ciucci D (eds) Proceedings of the 8th conference of the european society for fuzzy logic and technology (EUSFLAT’13), Milano, September 11–13. Atlantis Press

Murinová P, Novák V (2014) Analysis of generalized square of opposition with intermediate quantifiers. Fuzzy Sets Syst 242:89–113

Pagliani P, Chakraborty M (2008) A geometry of approximation, Springer, Dordrecht

Pawlak Z (1982) Rough sets. Int J Comp Inf Sci 11:341–356

Pedrycz W (1998) Shadowed sets: representing and processing fuzzy sets. IEEE Trans Syst Man Cybern Part B Cybern 28(1):103–109

Pedrycz W (2005) Granular computing with shadowed sets. Springer, Berlin 23–32

Pedrycz W (2009) From fuzzy sets to shadowed sets: interpretation and computing. Int J Intell Syst 24:48–61

Pedrycz W, Vukovich G (2002) Granular computing with shadowed sets. Int J Intell Syst 17:173–197

Prade H, Serrurier M (2008) Bipolar version space learning. Int J Intell Syst 23:1135–1152

Qi J, Wei L, Yao Y (2014) Three-way formal concept analysis. In: Miao D, Pedrycz W, Slezak D, Peters G, Hu Q, Wang R (eds) Rough sets and knowledge technology - 9th International Conference, RSKT 2014, Shanghai, China, October 24–26, 2014, Proceedings, LNCS, 8818:732–741

Reichenbach H (1952) The syllogism revised. Philos Sci 19(1):1–16

Reichenbach H (1954) Philosophic foundations of quantum mechanics. University of California Press, Berkeley

Shapiro S (2006) Vagueness in context. Oxford University Press, Oxford

Smessaert H, Demey L (2014) Logical geometries and information in the square of oppositions. J Logic Lang Inf 23(4):527–565

Sobocinski B (1952) Axiomatization of a partial system of three-value calculus of propositions. J Comp Syst 1:23–55

Vakarelov D (1977) Notes on n-lattices and constructive logic with strong negation. Stud Log 36:109–125

Vetterlein T (2015) Logic of prototypes and counterexamples: possibilities and limits. In: The Proceedings of 16th World Congress of the International Fuzzy Systems Association (IFSA), p 697–704

Walker E (1994) Stone algebras, conditional events, and three valued logic. IEEE Trans Syst Man Cybern 24(12):1699–1707

Wu J, Chiclana F, Herrera-Viedma E (2015) Trust based consensus model for social network in an incomplete linguistic information context. Appl Soft Comp 35:827–839

Yao JT, Vasilakos AV, Pedrycz W (2013) Granular computing: perspectives and challenges. IEEE Trans Cybern 43(6):1977–1989

Yao Y (1993) Interval-set algebra for qualitative knowledge representation. In: Proceedings of the Fifth international Conference on Computing and Information p 370–374

Yao YY (1998) Constructive and algebraic methods of the theory of rough sets. J Inf Sci 109:21–47

Yao Y (2009a) Interval sets and interval-set algebras. In: Proceedings of the 8th IEEE international conference on cognitive informatics pp 307–314

Yao Y (2009b) Three-way decision: an interpretation of rules in rough set theory. In: Wen P, Li Y, Polkowski L, Yao Y, Tsumoto S, Wang G (eds) Rough sets and knowledge technology, 4th International conference, RSKT 2009, Gold Coast, Australia, July 14–16, 2009. Proceedings, LNCS, vol 5589. Springer, Heidelberg, pp 642–649

Yao Y (2013) Granular computing and sequential three-way decisions. In: Lingras P, Wolski M, Cornelis C, Mitra S, Wasilewski P (eds) RSKT, Lecture notes in computer science 8171:16–27

Yao Y (2015) Rough sets and three-way decisions. In: Ciucci D, Wang G, Mitra S, Wu W (eds) RSKT proceedings, LNCS, vol 9436

Yao Y, Lingras P, Wang R, Miao D (2009) Interval set cluster analysis: a re-formulation. In: Proceedings of the RSFDGrC 2009, LNCS, 5908:398–405

Yao Y, Zhang N, Miao D, Xu F (2012) Set-theoretic approaches to granular computing. Fundam Inform 115(2–3):247–264