Interval valued fuzzy sets based on normal forms. (English) Zbl 0618.94020

Turksen, I. B.

Fuzzy Sets Syst. 20, 191-210 (1986).

Interval valued fuzzy sets are proposed for the representation of combined concepts based on normal forms where linguistic connectives as well as variables are assumed to be fuzzy. It is shown that the proposed representation (1) exists for certain families of the conjugate pairs of t-norms and t-conorms; and (2) resolves some of the difficulties associated with particular interpretations of conjunction, disjunction, and implication in fuzzy set theories.

MSC:

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

Keywords:

interpretation of connectives; linguistic connectives; t-norms; t-conorms

References:

[1]	Osherson, D.N.; Smith, E.E., On the adequacy of prototype theory as a theory of concepts, Cognition, 9, 35-58, (1981)
[2]	Osherson, D.N.; Smith, E.E., Gradedness of conceptual combination, Cognition, 12, 299-318, (1982)
[3]	Prade, H., Approximate and plausible reasoning: the state of the art, ()
[4]	Schweizer, B.; Sklar, A., Statistical metric spaces, Pacific J. math., 10, 313-334, (1960) · Zbl 0091.29801
[5]	Schweizer, B.; Sklar, A., Associative functions and statistical triangle inequalities, Publ. math. debrecen, 8, 169-186, (1961) · Zbl 0107.12203
[6]	Schweizer, B.; Sklar, A., Associative functions and abstract semigroups, Publ. math. debrecen, 10, 69-81, (1963) · Zbl 0119.14001
[7]	Thole, U.; Zimmermann, H.-H.; Zysno, P., On the suitability of minimum and product operators for intersection of fuzzy sets, Fuzzy sets and systems, 2, 167-180, (1979) · Zbl 0408.94030
[8]	Turksen, I.B., Inference regions for fuzzy proposition, (), 137-148
[9]	Turksen, I.B., Fuzzy representation and inference with normal forms, () · Zbl 0846.03007
[10]	Turksen, I.B.; Yao, D.D.W., On bounds for fuzzy inference, (), 729-734
[11]	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
[12]	Weber, S., A general concept of fuzzy connectives, negations, and implications based on t-norms and t-conorms, Fuzzy sets and systems, 11, 115-134, (1983) · Zbl 0543.03013
[13]	Yager, R.R., On a general class of fuzzy connectives, Fuzzy sets and systems, 4, 235-242, (1980) · Zbl 0443.04008
[14]	Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
[15]	Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE trans. systems man cybernet., 28-44, (1973) · Zbl 0273.93002
[16]	Zadeh, L.A.; Zadeh, L.A.; Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning — I, I,, III, Inform. sci., Inform. sci., Inform. sci., 9, 43-80, (1975) · Zbl 0404.68075
[17]	Zadeh, L.A., Fuzzy sets, () · Zbl 0139.24606
[18]	Zadeh, L.A., A theory of approximate reasoning, () · Zbl 0397.68071
[19]	Zadeh, L.A., PRUF-A meaningful representation language for natural languages, Internat. J. man-machine stud., 10, 395-460, (1978) · Zbl 0406.68063
[20]	Zadeh, L.A., A note on prototype theory and fuzzy sets, Cognition, 12, 291-297, (1982)
[21]	Zadeh, L.A., A computation approach to fuzzy quantifiers in natural languages, Comput. math. appl., 9, 149-184, (1983) · Zbl 0517.94028
[22]	Zadeh, L.A., A computational theory of dispositions, (), 312-318
[23]	Zimmerman, H.-J., Results of empirical studies in fuzzy set theory, ()
[24]	Zimmerman, H.-H.; Zysno, P., Latent connectives in human decision making, Fuzzy sets and systems, 4, 37-51, (1980) · Zbl 0435.90009