Fuzzy sets in a approximate reasoning. I: Inference with possibility distributions. (English) Zbl 0722.03017

Dubois, Didier; Prade, Henri

Fuzzy Sets Syst. 40, No. 1, 143-202 (1991).

[Part II is reviewed below (see Zbl 0722.03018).]
This paper focuses on semantic approaches to approximate reasoning based on fuzzy sets, commonly exemplified by the generalized modus ponens, but also considers applications to current topics in Artificial Intelligence such as default reasoning and qualitative process modeling.

Reviewer: M.Matłoka (Poznań)

MSC:

03B52	Fuzzy logic; logic of vagueness
94D05	Fuzzy sets and logic (in connection with information, communication, or circuits theory)
68T30	Knowledge representation

Keywords:

semantic approaches to approximate reasoning based on fuzzy sets; generalized modus ponens; Artificial Intelligence; default reasoning; qualitative process modeling

Citations:

Zbl 0722.03018

References:

[1]	Aguilar-Martin, J.; López de Mántaras, R., The process of classification and learning the meaning of linguistic descriptors of concepts, (), 165-175
[2]	Ahlquist, J.E.; Ahlquist, J.E., Application of fuzzy implication to probe non-symmetric relations: part II, Fuzzy sets and systems, Fuzzy sets and systems, 25, 87-95, (1988) · Zbl 0645.62065
[3]	Arrazola, I.; Plainfossé, A.; Prade, H.; Testemale, C., Extrapolation of fuzzy values from incomplete data bases, Inform. systems, 14, 6, 487-492, (1989)
[4]	Baldwin, J.F., A new approach to approximate reasoning using a fuzzy logic, Fuzzy sets and systems, 2, 309-325, (1979) · Zbl 0413.03017
[5]	Baldwin, J.F., Fuzzy logic and approximate reasoning for mixed input arguments, Internat. J. man-machine stud., 11, 381-396, (1979) · Zbl 0413.03016
[6]	Baldwin, J.F., Fuzzy logic and fuzzy reasoning, Internat. J. man-machine stud., 11, 465-480, (1979) · Zbl 0418.03014
[7]	Baldwin, J.F.; Guild, N.C.F., Modelling controllers using fuzzy relations, Kybernetes, 9, 223-229, (1980) · Zbl 0452.93005
[8]	Baldwin, J.F.; Guild, N.C.F., Feasible algorithms for approximate reasoning using fuzzy logic, Fuzzy sets and systems, 3, 225-251, (1980) · Zbl 0435.03019
[9]	Baldwin, J.F.; Pilsworth, B.W., Fuzzy truth definition of possibility measure for decision classification, Internat. J. man-machine stud., 11, 447-463, (1979) · Zbl 0407.94021
[10]	Baldwin, J.F.; Pilsworth, B.W., A model of fuzzy reasoning through multi-valued logic and set theory, Internat. J. man-machine stud., 11, 351-380, (1979) · Zbl 0413.03015
[11]	Baldwin, J.F.; Pilsworth, B.W., Axiomatic approach to implication for approximate reasoning with fuzzy logic, Fuzzy sets and systems, 3, 193-219, (1980) · Zbl 0434.03021
[12]	Baldwin, J.F.; Zhou, S.Q., A fuzzy relational inference language, Fuzzy sets and systems, 14, 155-174, (1984) · Zbl 0575.68093
[13]	Bandler, W.; Kohout, L.J., Fuzzy power sets and fuzzy implication operators, Fuzzy sets and systems, 4, 13-30, (1980) · Zbl 0433.03013
[14]	Bandler, W.; Kohout, L.J., Semantics of implication operators and fuzzy relational products, Internat. J. man-machine stud., 12, 89-116, (1980) · Zbl 0435.68042
[15]	Bandler, W.; Kohout, L.J., The four modes of inference in fuzzy expert systems, (), 581-586
[16]	Bandler, W.; Kohout, L.J., The interrelations of the principal fuzzy logical operators, (), 767-780
[17]	Bellman, R.E.; Zadeh, L.A., Local and fuzzy logics, (), 103-165 · Zbl 0382.03017
[18]	Bonissone, P.P., A pattern recognition approach to the problem of linguistic approximation in system analysis, (), 793-798
[19]	Bouchon, B., Fuzzy inferences and conditional possibility distributions, Fuzzy sets and systems, 23, 33-41, (1987) · Zbl 0633.68100
[20]	Bouchon, B.; Bouchon, B., Stability of linguistic modifiers compatible with a fuzzy logic, (), 63-70 · Zbl 1155.68522
[21]	Bouchon, B.; Després, S.; Bouchon, B.; Després, S., Propagating of uncertainties and inaccuracies in knowledge-based system, (), 58-65, selected and extended contributions
[22]	Buckley, J.J.; Tucker, D., Extended fuzzy relations: application to fuzzy expert systems, Internat. J. approximate reasoning, 1, 177-195, (1987)
[23]	Buisson, J.C.; Farreny, H.; Prade, H., Mise en oeuvre de techniques de raisonnement approché dans un système expert — L’exemple de DIABETO-III, Innovation et technlogie en biologie et Médecine, 8, no. special 2, 71-89, (1987)
[24]	Buisson, J.C.; Farreny, H.; Prade, H.; Turnin, M.C.; Tauber, J.P.; Bayard, F., TOULMED, an inference engine which deals with imprecise and uncertain aspects of medical knowledge, (), 124-140
[25]	Cao, Z.Q.; Kandel, A., Applicability of some fuzzy implication operators, Fuzzy sets and systems, 31, 151-186, (1989)
[26]	Cat Ho, N.; Wechler, W., Hedge algebras: an algebraic approach to structure of sets of linguistic truth values, Fuzzy sets and systems, 35, 281-293, (1990) · Zbl 0704.03007
[27]	Cayrol, M.; Farreny, H.; Prade, H., Fuzzy pattern matching, Kybernetes, 11, 103-116, (1982)
[28]	Chatalic, P.; Dubois, D.; Prade, H., A system for handling relation dependencies in approximate reasoning, (), 495-502
[29]	Cox, R.T., Probability, frequency and reasonable expectation, Amer. J. phys., 14, 1-13, (1946) · Zbl 0063.01001
[30]	D’Ambrosio, B., Qualitative process theory using linguistic variables, (1989), Springer-Verlag Berlin
[31]	D’Ambrosio, B., Extending the mathematics in qualitative process theory, Internat. J. intelligent systems, 4, 55-80, (1989) · Zbl 0850.93070
[32]	Després, S., GRIF: a guide for representing fuzzy interfaces, (), 353-356
[33]	Di Nola, A.; Pedrycz, W.; Sessa, S., Fuzzy relation equations and algorithms of inference mechanism in expert systems, (), 355-367
[34]	Di Nola, A.; Pedrycz, W.; Sessa, S., An aspect of discrepancy in the implementation of modus ponens in the presence of fuzzy quantities, Internat. J. approximate reasoning, 3, 259-265, (1989) · Zbl 0676.68055
[35]	Di Nola, A.; Sessa, S.; Pedrycz, W.; Sanchez, E., Fuzzy relations equations and their applications to knowledge engineering, (1989), Kluwer Academic Publishers Dordrecht
[36]	Di Nola, A.; Sessa, S.; Pedrycz, W., Modus ponens for fuzzy data realized via equations with equality operators, Internat. J. intelligent systems, 5, 1-14, (1990) · Zbl 0703.03005
[37]	Ding, L.; Shen, Z.L.; Mukaidono, M., A new method for approximate reasoning, (), 179-185
[38]	Driankov, D., Inference with a single fuzzy conditional proposition, Fuzzy sets and systems, 24, 51-63, (1987) · Zbl 0635.03017
[39]	Dubois, D., Fuzzy knowledge in an artificial intelligence system for job-shop scheduling, (), 73-89
[40]	Dubois, D.; Lang, J.; Prade, H., Fuzzy sets in approximate reasoning, part 2: logical approaches, Fuzzy sets and systems, 40, 203-244, (1991), (this issue) · Zbl 0722.03018
[41]	Dubois, D.; Martin-Clouaire, R.; Prade, H., Practical computing in fuzzy logic, (), 11-34
[42]	Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press New York · Zbl 0444.94049
[43]	Dubois, D.; Prade, H., On distances between fuzzy points and their use for plausible reasoning, (), 300-303
[44]	Dubois, D.; Prade, H., Fuzzy logics and the generalized modus ponens revisited, Internat. J. cybernetics and systems, 15, 293-331, (1984) · Zbl 0595.03016
[45]	Dubois, D.; Prade, H., Fuzzy set-theoretic differences and inclusions and their use in the analysis of fuzzy equations, Control and cybernetics, 13, 3, 129-145, (1984) · Zbl 0549.03020
[46]	Dubois, D.; Prade, H., A theorem on implication functions defined from triangular norms, Stochastica, 8, 3, 267-279, (1984) · Zbl 0581.03016
[47]	Dubois, D.; Prade, H., Evidence measures based on fuzzy information, Automatica, 21, 5, 547-562, (1985) · Zbl 0596.62007
[48]	Dubois, D.; Prade, H., The generalized modus ponens under sup-MIN composition—A theoretical study, (), 217-232
[49]	Dubois, D.; Prade, H.; Farreny, H.; Martin-Clouaire, R.; Testemale, C.; Dubois, D.; Prade, H.; Farreny, H.; Martin-Clouaire, R.; Testemale, C., Possibility theory: an approach to computerized processing of uncertainty, (), (1988), Academic Press New York, with the collaboration of
[50]	Dubois, D.; Prade, H., Possibilistic inference under matrix form, (), 112-126
[51]	Dubois, D.; Prade, H., An alternative approach to the handling of subnormal possibility distributions — A critical comment on a proposal by yager, Fuzzy sets and systems, 24, 128, (1987)
[52]	Dubois, D.; Prade, H.; Dubois, D.; Prade, H., The principle of minimum specificity as a basis for evidential reasoning, (), 75-84
[53]	Dubois, D.; Prade, H., Upper and lower images of a fuzzy set induced by a fuzzy relation—A fresh look at fuzzy inference and diagnosis, Tech. report, LSI, univ. P. sabatier, Toulouse, France, no. 265, 36-76, (1987), To appear in Inform. Sci.
[54]	Dubois, D.; Prade, H., On fuzzy syllogisms, Computational intelligence, 4, 171-179, (1988)
[55]	Dubois, D.; Prade, H., Default reasoning and possibility theory, Artificial intelligence, 35, 243-257, (1988) · Zbl 0645.68108
[56]	Dubois, D.; Prade, H., On the combination of uncertain or imprecise pieces of information in rule-based systems — A discussion in the framework of possibility theory, Internat. J. approximate reasoning, 2, 65-87, (1988) · Zbl 0646.68112
[57]	Dubois, D.; Prade, H., An introduction to possibilistic and fuzzy logics, (), 288-326
[58]	Dubois, D.; Prade, H., Incomplete conjunctive information, Comput. math. app., 15, 10, 797-810, (1988) · Zbl 0709.94588
[59]	Dubois, D.; Prade, H., Handling uncertainty in expert systems: pitfalls, difficulties, remedies, (), 64-118
[60]	Dubois, D.; Prade, H., Measure-free conditioning, probability and non-monotonic reasoning, (), 1110-1114
[61]	Dubois, D.; Prade, H., Processing fuzzy temporal knowledge, IEEE trans. systems man cybernet, 19, 4, 729-744, (1989)
[62]	Dubois, D.; Prade, H., Order-of-magnitude reasoning with fuzzy relations, Revue d’intelligence artificielle, 3, 4, 69-94, (1989)
[63]	Dubois, D.; Prade, H., A typology of fuzzy “if…then…” rules, (), 782-785
[64]	Dubois, D.; Prade, H.; Dubois, D.; Prade, H., Fuzzy arithmetic in qualitative reasoning, (), 457-467 · Zbl 0605.03021
[65]	Dubois, D.; Prade, H., Resolution principles in possibilistic logic, Internat. J. approximate reasoning, 3, 1-21, (1990) · Zbl 0697.68083
[66]	Dubois, D.; Prade, H., Gradual inference rules in approximate reasoning, (), To appear in Inform. Sci. · Zbl 0736.68070
[67]	Dubois, D.; Prade, H., Inference in possibilistic hypergraphs, (), 228-230
[68]	Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, Internat. J. general systems, 17, 191-209, (1990) · Zbl 0715.04006
[69]	Dubois, D.; Prade, H.; Testemale, C., Weighted fuzzy pattern matching, Fuzzy sets and systems, 28, 313-331, (1988) · Zbl 0658.94026
[70]	Esragh, F.; Mamdani, E.H., A general approach to linguistic approximation, Internat. J. man-machine stud., 11, 501-519, (1979) · Zbl 0403.68075
[71]	Ezawa, Y., Homomorphism criteria of fuzzy multiple inference, (), 290-293
[72]	Ezhkova, I.V.; Pospelov, D.A.; Ezhkova, I.V.; Pospelov, D.A., Decision making on fuzzy premises—II. deduction schemes, Engineering cybernetics, Scripta comp. publ., 16, 2, 1-6, (1979), (translation of the Soviet J. Computer and Systems Sci.)
[73]	Fodor, J.C., Some remarks on fuzzy implication operations, Busefal, 38, 42-46, (1989)
[74]	Forbus, K.D., Qualitative processus theory, Artificial intelligence, 24, 85-168, (1984)
[75]	Freksa, C., Linguistic description of human judgments in expert systems and in the ‘soft’ sciences, (), 297-305
[76]	Fukami, S.; Mizumoto, M.; Tanaka, K., Some considerations on fuzzy conditional inference, Fuzzy sets and systems, 4, 243-273, (1980) · Zbl 0453.03022
[77]	Gaines, B.R., Foundations of fuzzy reasoning, Internat. J. man-machine stud., 6, 623-668, (1976) · Zbl 0342.68056
[78]	Giles, R., A formal system for fuzzy reasoning, Fuzzy sets and systems, 2, 233-257, (1979) · Zbl 0411.03018
[79]	()
[80]	Godo, L.; Jacas, J.; Valverde, L.; Godo, L.; Jacas, J.; Valverde, L., Fuzzy values in fuzzy logic, (), 829-832, Short version in · Zbl 0716.03014
[81]	Goguen, J.A., The logic of inexact concepts, Synthese, 19, 325-373, (1969) · Zbl 0184.00903
[82]	Gorzalczany, M.B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy sets and systems, 21, 1-17, (1987) · Zbl 0635.68103
[83]	Gorzalczany, M.B., An interval-valued fuzzy inference method — some basic properties, Fuzzy sets and systems, 31, 243-251, (1989)
[84]	Hall, L.O., On the fuzzy logic modes of inference: confirmation and denial, (), 24-26
[85]	Hall, L.O., The choice of ply operator in fuzzy intelligent systems, Fuzzy sets and systems, 34, 135-144, (1990) · Zbl 0689.68108
[86]	Hisdal, E., Conditional possibilities independence and non-interaction, Fuzzy sets and systems, 1, 283-297, (1978) · Zbl 0393.94050
[87]	Hisdal, E., The fuzzy “IF then ELSE” statement and interval-valued fuzzy sets of higher types, Internat. J. man-machine stud., 4, 385-455, (1981) · Zbl 0471.03013
[88]	Izumi, K.; Tanaka, H.; Asai, K., Adjointness of fuzzy systems, Fuzzy sets and systems, 20, 211-221, (1986) · Zbl 0633.03014
[89]	Kandel, A.; Peng, X.T.; Cao, Z.Q.; Wang, P.Z., Representation of concepts by factor spaces, (), 145-148 · Zbl 0797.68146
[90]	Kaufmann, A., Nouvelles logiques pour l’inteligence artificielle, (1987), Hermès Paris
[91]	Kickert, W.J.M., An example of linguistic modelling: the case of Mulder’s theory of power, (), 519-540
[92]	Kiszka, J.B.; Gupta, M.M.; Trojan, G.M., Multivariable fuzzy controller under Gödel’s implication, Fuzzy sets and systems, 34, 301-321, (1990)
[93]	Kiszka, J.B.; Kochanska, M.E.; Sliwinska, D.S., The influence of some fuzzy implication operators on the accuracy of a fuzzy model—part I, Fuzzy sets and systems, 15, 111-128, (1985) · Zbl 0581.94033
[94]	Kiszka, J.B.; Kochanska, M.E.; Sliwinska, D.S., The influence of some fuzzy implication operators on the accuracy of a fuzzy model—part II, Fuzzy sets and systems, 15, 223-240, (1985) · Zbl 0581.94034
[95]	Kruse, R.; Schwecke, E., Fuzzy reasoning in a multi-dimensional space of hypotheses, (), 147-151 · Zbl 0697.68086
[96]	Kruse, R.; Schwecke, E., On the treatment of cyclic dependencies in causal networks, (), 416-419
[97]	Kruse, R.; Schwecke, E., Fuzzy reasoning in a multidimensional space of hypotheses, Internat. J. approximate reasoning, 4, 47-68, (1990) · Zbl 0697.68086
[98]	Lakoff, G., Hedges: a study in meaning-criteria and the logic of fuzzy concepts, (), 2, 221-271, (1973)
[99]	Lebailly, J.; Martin-Clouaire, R.; Prade, H., Use of fuzzy logic in a rule-based system in petroleum geology, (), 125-144
[100]	Lesmo, L.; Saitta, L.; Torasso, P., Fuzzy production rules: a learning methodology, (), 181-198
[101]	Lowen, R., A fuzzy Lagrange interpolation theorem, Fuzzy sets and systems, 34, 33-38, (1990) · Zbl 0685.41005
[102]	Magrez, P.; Smets, P., Epistemic necessity, possibility, and truth—tools for dealing with imprecision and uncertainty in fuzzy knowledge-based systems, Internat. J. approximate reasoning, 3, 35-57, (1989) · Zbl 0665.68078
[103]	Magrez, P.; Smets, P., Fuzzy modus ponens: a new model suitable for applications in knowledge-based systems, Internat. J. intelligent systems, 4, 181-200, (1989) · Zbl 0672.03010
[104]	Mamdani, E.H., Application of fuzzy logic to approximate reasoning using linguistic systems, IEEE trans. comput., 26, 1182-1191, (1977) · Zbl 0397.94025
[105]	Martin-Clouaire, R., Semantics and computation of the generalized modus ponens: the long paper, Internat. J. approximate reasoning, 3, 195-217, (1989) · Zbl 0689.94006
[106]	Martin-Clouaire, R., Use of possibility theory in real reasoning systems, (), 786-789
[107]	Mizumoto, M., Note on the arithmetic rule by zadeh for fuzzy conditional inference, Cybernetics and systems, 12, 247-306, (1981) · Zbl 0472.03018
[108]	Mizumoto, M., Fuzzy inference using MAX-γ composition in the compositional rule of inference, (), 67-76
[109]	Mizumoto, M., Fuzzy conditional inference under MAX-⊙ composition, Inform. sci., 27, 183-209, (1982) · Zbl 0521.03013
[110]	Mizumoto, M., Extended fuzzy reasoning, (), 71-85
[111]	Mizumoto, M.; Fukami, S.; Tanaka, K., Some methods of fuzzy reasoning, (), 253-283
[112]	Mizumoto, M.; Zimmermann, H.J., Comparison of fuzzy reasoning methods, Fuzzy sets and systems, 8, 253-283, (1982) · Zbl 0501.03013
[113]	Mogre, A.; McLaren, R.; Keller, J., An approach to approximate reasoning using linguistic truth qualification, (), 563-566
[114]	Negoita, C.V.; Ralescu, D., Applications of fuzzy sets to systems analysis, () · Zbl 0326.94002
[115]	Nguyen, H.T., On conditional possibility distributions, Fuzzy sets and systems, 1, 299-309, (1978) · Zbl 0423.94052
[116]	Nordvik, J.P.; Smets, P.; Magrez, P.; Nordvik, J.P.; Smets, P.; Magrez, P., Fuzzy qualitative modeling, (), 231-238 · Zbl 0672.03010
[117]	Novak, V., Automatic generation of verbal comments on results of mathematical modelling, (), 55-68
[118]	Novak, V., Fuzzy sets and their applications, (1989), Adam Hilger Bristol-Philadelphia · Zbl 0683.94018
[119]	Oh, K.W.; Bandler, W., Properties of fuzzy implication operators, Internat. J. approximate reasoning, 1, 273-285, (1987) · Zbl 0653.68105
[120]	Pawlak, Z., Rough sets, Internat. J. comput. inform. sci., 11, 341-356, (1982) · Zbl 0501.68053
[121]	Pearl, J., Fusion, propagation, and structuring in belief networks, Artificial intelligence, 29, 13, 241-288, (1986) · Zbl 0624.68081
[122]	Petieau, A.M.; Moreau, A.; Willaeys, D.; Petieau, A.M.; Moreau, A.; Willaeys, D., Putting into practice Moreau’s extended generalized modus ponens, (), 373-384
[123]	Prade, H., Nomenclature of fuzzy measures, (), 7-25
[124]	Prade, H., Compatibilité, qualification, modification, niveau de précision, Busefal, 4, 71-78, (1980)
[125]	Prade, H., Modal semantics and fuzzy set theory, (), 232-246
[126]	Prade, H., Modèles mathématiques de l’imprécis et de l’incertain en vue d’applications au raisonnement naturel, Doctorat d’etat thesis, université P. sabatier, Toulouse, (1982) · Zbl 0491.68092
[127]	Prade, H., A computational approach to approximate and plausible reasoning with applications to expert systems, IEEE trans. pattern analysis machine intelligence, 7, 3, 260-283, (1985) · Zbl 0565.68089
[128]	Prade, H., Reasoning with fuzzy default values, (), 191-197
[129]	Prade, H., Raisonner avec des règles d’inférence graduelle—une approche basée sur LES ensembles flous, Revue d’intelligence artificielle, 2, 2, 29-44, (1988)
[130]	()
[131]	Prade, H.; Testemale, C.; Prade, H.; Testemale, C., Representation of soft constraints and fuzzy attribute values by means of possibility distributions in databases, (), 213-229, Final version
[132]	Qian, D.Q.; Lu, Y.Z., A strategy of problem solving in a fuzzy reasoning network, Fuzzy sets and systems, 33, 137-154, (1989) · Zbl 0679.68179
[133]	Raiman, O., Order of magnitude reasoning, (), 118-124
[134]	Ramer, A., Conditional possibility measures, (), 412-415
[135]	Reiter, R., A logic for default reasoning, Artificial intelligence, 13, 81-132, (1980) · Zbl 0435.68069
[136]	Ruspini, E.H., A new approach to clustering, Inform. and control, 15, 22-32, (1969) · Zbl 0192.57101
[137]	Sanchez, E., On possibility-qualification in natural languages, Inform. sci., 15, 45-76, (1978) · Zbl 0437.03011
[138]	Sanchez, E., On truth-qualification in natural languages, (), 1233-1236
[139]	Sanchez, E., Importance in knowledge systems, Inform. systems, 14, 6, 455-464, (1989)
[140]	()
[141]	Shafer, G., A mathematical theory of evidence, (1976), Princeton University Press Princeton, NJ · Zbl 0359.62002
[142]	Shafer, G.; Shenoy, P.P.; Mellouli, K., Propagating belief functions in qualitative Markov trees, Internat. J. approximate reasoning, 1, 349-400, (1987) · Zbl 0641.68158
[143]	Shafer, G.; Shenoy, P.P., Local computation in hypertrees, ()
[144]	de O. Silva, O.; de R. e Souza, C., Changing the fuzzy rule of detachment, (), 267-271
[145]	Smets, P.; Magrez, P., Implication in fuzzy logic, Internat. J. approximate reasoning, 1, 327-347, (1987) · Zbl 0643.03018
[146]	Soula, G.; Sanchez, E., Soft deduction rules in medical diagnostic processes, (), 77-88
[147]	Sugeno, M.; Nishida, M., Fuzzy control of model car, Fuzzy sets and systems, 16, 103-113, (1985)
[148]	Sugeno, M.; Takagi, T., Multi-dimensional fuzzy reasoning, Fuzzy sets and systems, 9, 313-325, (1983) · Zbl 0513.94035
[149]	Tanaka, H.; Tsukiyama, T.; Asai, K., A fuzzy system model based on the logical structure, (), 257-274
[150]	Tong, R.M.; Efstathiou, J., A critical assessment of truth functional modification and its use in approximate reasoning, Fuzzy sets and systems, 7, 103-108, (1982) · Zbl 0483.03017
[151]	Trillas, E.; Valverde, L., On some functionally expressible implications for fuzzy set theory, (), 173-190
[152]	Trillas, E.; Valverde, L., On mode and implication in approximate reasoning, (), 157-166
[153]	Trillas, E.; Valverde, L., On implication and indistinguishability in the setting of fuzzy logic, (), 198-212
[154]	Trillas, E.; Valverde, L., On inference in fuzzy logic, (), 294-297
[155]	Tsukamoto, Y., An approach to fuzzy reasoning method, (), 137-149
[156]	Turksen, I.B., Interval valued fuzzy sets based on normal forms, Fuzzy sets and systems, 20, 191-210, (1986) · Zbl 0618.94020
[157]	Turksen, I.B., Four methods of approximate reasoning with interval-valued fuzzy sets, Internat. J. approximate reasoning, 3, 121-142, (1989) · Zbl 0666.68083
[158]	Turksen, I.B.; Yao, D.D.W., Representation of connectives in fuzzy reasoning: the view through normal forms, IEEE trans. systems man cybernet., 14, 146-151, (1984) · Zbl 0547.03021
[159]	Turksen, I.B.; Zhong, Z., An approximate analogical reasoning approach based on similarity measures, IEEE trans. systems man cybernet., 18, 6, 1049-1056, (1988)
[160]	Turksen, I.B.; Zhong, Z., An approximate analogical reasoning schema based on similarity measures and interval-valued fuzzy sets, Fuzzy sets and systems, 34, 323-346, (1990)
[161]	Valverde, L.; Trillas, E., On modus ponens in fuzzy logic, (), 294-301
[162]	Vandenberghe, R.; Van Schooten, A.; De Caluwe, R.; Kerre, E.E., Some practical aspects of fuzzy database techniques: an example, Inform. systems, 14, 6, 465-472, (1989)
[163]	Wang, P.Z., Factor spaces and knowledge representation, (), 62-79
[164]	Wang, P.Z.; Sugeno, M., The factors field and background structure for fuzzy subsets, Fuzzy mathematics (China), 2, 45-52, (1982)
[165]	Weber, S., A general concept of fuzzy connectives, negations and implications based on t-norms and t-co-norms, Fuzzy sets and systems, 11, 115-134, (1983) · Zbl 0543.03013
[166]	Weiss, J.J.; Donnell, M.L., A general purpose policy capturing device using fuzzy production rules, (), 589-604
[167]	()
[168]	Wenstøp, F., Deductive verbal models of organizations, Internat. J. man-machine stud., 8, 293-311, (1976) · Zbl 0361.68139
[169]	Wenstøp, F., Exploring linguistic consequences of assertions in social sciences, (), 501-518
[170]	Whalen, T.; Schott, B., Issues in fuzzy production systems, Internat. J. man-machine stud., 19, 57-71, (1983)
[171]	Whalen, T.; Schott, B., Alternative logics for approximate reasoning in expert systems: a comparative study, Internat. J. man-machine stud., 22, 327-346, (1985)
[172]	Whalen, T.; Schott, B., Presumption and prejudice in logical inference, Internat. J. approximate reasoning, 3, 359-382, (1989)
[173]	Whalen, T.; Schott, B., Usuality in fuzzy set logic, (), 575-577
[174]	Willmott, R., Two fuzzier implication operators in the theory of fuzzy power sets, Fuzzy sets and systems, 4, 31-36, (1980) · Zbl 0433.03014
[175]	Willmott, R., On the transitivity of implication and equivalence in some many-valued logics, (), 253-262
[176]	Wu, W.M., Fuzzy reasoning and fuzzy relational equations, Fuzzy sets and systems, 20, 67-78, (1986) · Zbl 0629.94031
[177]	Yager, R.R., An approach to inference in approximate reasoning, Internat. J. man-machine stud., 13, 323-338, (1980)
[178]	Yager, R.R., Generalized probabilities of fuzzy events from fuzzy belief structures, Inform. sci., 28, 45-62, (1982) · Zbl 0525.60006
[179]	Yager, R.R., Some questions related to linguistic variables, Busefal, 10, 54-65, (1982) · Zbl 0524.94037
[180]	Yager, R.R., Querying knowledge base systems with linguistic information via knowledge trees, Internat. J. man-machine stud., 19, 73-95, (1983)
[181]	Yager, R.R., Some relationships between possibility, truth and certainty, Fuzzy sets and systems, 11, 151-156, (1983) · Zbl 0524.94038
[182]	Yager, R.R., Quantified propositions in a linguistics logic, Internat. J. man-machine stud., 9, 195-227, (1983) · Zbl 0522.03013
[183]	Yager, R.R., An introduction to applications of possibility theory, Human systems management, 3, 246-269, (1983)
[184]	Yager, R.R., Approximate reasoning as a basis for rule-based expert systems, IEEE trans. systems man and cybernet., 14, 4, 636-643, (1984) · Zbl 0555.68066
[185]	Yager, R.R., On different classes of linguistic variables defined via fuzzy subsets, Kybernetes, 13, 103-110, (1984) · Zbl 0544.03008
[186]	Yager, R.R., Strong truth and rules of inference in fuzzy logic and approximate reasoning, Cybernetics and systems, 16, 23-63, (1985) · Zbl 0592.03013
[187]	Yager, R.R., Knowledge trees in complex knowledge bases, Fuzzy sets and systems, 15, 45-64, (1985) · Zbl 0565.68091
[188]	Yager, R.R., Reasoning with uncertainty for expert systems, (), 1295-1297
[189]	Yager, R.R., A note on projections of conditional possibility distributions in approximate reasoning, () · Zbl 0599.94020
[190]	Yager, R.R., A modification of the certainty measure to handle subnormal distributions, Fuzzy sets and systems, 20, 317-324, (1986) · Zbl 0618.94021
[191]	Yager, R.R., Toward a general theory of reasoning with uncertainty—part I: nonspecificity and fuzziness, Internat. J. intelligent systems, 1, 45-67, (1986) · Zbl 0641.68154
[192]	Yager, R.R., Using approximate reasoning to represent default knowledge, Artificial intelligence, 31, 99-112, (1987) · Zbl 0624.68083
[193]	Yager, R.R., Toward a theory of conjunctive variables, Internat. J. general systems, 13, 203-227, (1987)
[194]	Yager, R.R., On the knowledge structure of multi-solution variables, including quantified statements, Internat. J. approximate reasoning, 1, 23-70, (1987) · Zbl 0639.68107
[195]	Yager, R.R.; Yager, R.R., Possibilistic qualification and default rules, (), 41-57 · Zbl 1014.68145
[196]	Yager, R.R., A generalized view of non-monotonic knowledge: a set-theoretic perspective, Internat. J. general systems, 14, 251-265, (1988) · Zbl 1200.68228
[197]	Yager, R.R., Set based representations of conjunctive and disjunctive knowledge, Inform. sci., 41, 1-22, (1988) · Zbl 0626.68073
[198]	Yager, R.R., On considerations of credibility of evidence, () · Zbl 0787.68096
[199]	Yager, R.R., Connectives and quantifiers in fuzzy sets, Fuzzy sets and systems, 40, 39-75, (1991), (this issue) · Zbl 0725.03033
[200]	Yager, R.R.; Larsen, H.L., On discovering potential inconsistencies in validating uncertain knowledge bases by reflecting on the input, () · Zbl 0793.68150
[201]	Zadeh, L.A., Quantitative fuzzy semantics, Inform. sci., 3, 159-176, (1971) · Zbl 0218.02057
[202]	Zadeh, L.A., A fuzzy set-theoretic interpretation of linguistic hedges, J. cybernet., 2, 4-34, (1972)
[203]	Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE trans. systems man cybernet., 3, 28-44, (1973) · Zbl 0273.93002
[204]	Zadeh, L.A., Calculus of fuzzy restrictions, (), 1-39 · Zbl 0327.02018
[205]	Zadeh, L.A.; Zadeh, L.A.; Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning, parts 1-3, Inform. sci., Inform. sci., Inform. sci., 9, 43-80, (1975) · Zbl 0404.68075
[206]	Zadeh, L.A., A fuzzy-algorithmic approach to the definition of complex or imprecise concepts, Internat. J. man-machine stud., 8, 249-291, (1976) · Zbl 0332.68068
[207]	Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
[208]	Zadeh, L.A., PRUF — a meaning representation language for natural languages, Internat. J. man-machine stud., 10, 395-460, (1978) · Zbl 0406.68063
[209]	Zadeh, L.A., A theory of approximate reasoning, (), 149-194
[210]	Zadeh, L.A., Fuzzy sets and information granularity, (), 3-18 · Zbl 0377.04002
[211]	Zadeh, L.A., A computational approach to fuzzy quantifiers in natural languages, Comput. math. appl., 9, 149-184, (1983) · Zbl 0517.94028
[212]	Zadeh, L.A., The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy sets and systems, 11, 199-227, (1983) · Zbl 0553.68049
[213]	Zadeh, L.A., Syllogistic reasoning in fuzzy logic and its application to reasoning with dispositions, IEEE trans. systems man cybernet., 15, 754-763, (1985) · Zbl 0593.03033
[214]	Zadeh, L.A., A computational theory of dispositions, Internat. J. intelligent systems, 2, 39-63, (1987) · Zbl 0641.68153
[215]	Zimmermann, H.J., Fuzzy sets, decision making, and expert systems, (1987), Kluwer Academic Publ Dordrecht-Boston