zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Inequality relation between fuzzy numbers and its use in fuzzy optimization. (English) Zbl 0574.04005
The inequality relation between two fuzzy numbers is investigated. A certain type of such a relation motivated by practical interpretation is proposed, and its correspondence with the usual lattice-type relation generated by the extended maximum and minimum operators and its possible interpretation are discussed. The concept of R-L fuzzy number is introduced, the class of all R-L fuzzy numbers covering practically the whole set of normal convex fuzzy numbers. Comparing two R-L fuzzy numbers of the same type, the relation introduced in the paper may be replaced by four ordinary inequalities. This fact may be taken advantage of in optimization problems with linear fuzzy constraints.

MSC:
 03E20 Other classical set theory (logic) 91B06 Decision theory
Full Text:
References:
 [1] Dubois, D.; Prade, H.: Systems of linear fuzzy constraints. Fuzzy sets and systems 3, 37-48 (1980) · Zbl 0425.94029 [2] Dubois, D.; Prade, H.: Ranking fuzzy numbers in the setting of possibility theory. Inform. sci. 30, 183-224 (1983) · Zbl 0569.94031 [3] Freeling, A. N. S.: Fuzzy sets and decision analysis. IEEE trans. Systems man cybernet. 10, 341-354 (1980) [4] Mizumoto, M.; Tanaka, K.: Some properties of fuzzy numbers. Advances in fuzzy set theory and applications, 153-164 (1979) [5] Negoita, C. V.: The current interest in fuzzy optimization. Fuzzy sets and systems 6, 261-269 (1981) · Zbl 0465.90091