Fuzzy sets are used to express the experts’ preferences. For example, if criterion X moderately dominates criterion Y, then the fuzzy set (1, 3, 5), which represents suitable fuzziness, is entered in the row corresponding to X and the column corresponding to Y. Furthermore, the reciprocal ...
Dubois D. and Prade H. (1980b). New results about properties and semantics of fuzzy-set-theoretic operators,Fuzzy Sets: Theory and Applications to Policy Analysis and Information Systems(Wang P.P. and Chang S.K., eds.), Plenum Publ., 59–75. Google Scholar Dubois D. and Prade H. (1...
It can address uncertainty associated with vague concepts by allowing partial membership to a set (Zadeh, 1965; Fisher, 2000). When a spatial concept is characterized by vagueness—i.e., exurbanization—it should be represented using fuzzy boundaries rather than crisp discrete boundaries. Fuzzy ...
Let (𝛩, 𝒫(𝛩), 𝑃𝑜𝑠) denote a possibility space where 𝛩 is a non-empty set and 𝒫(𝛩) is the power set of 𝛩. For a fuzzy event H ⊆ P Θ 𝐻⊆𝒫(𝛩), P o s H 𝑃𝑜𝑠{𝐻} and N e c H 𝑁𝑒𝑐{𝐻} are the possibility and ...
In general, fuzzy inference is a method that interprets the values in the input vector and, based on some set of rules, assigns values to the output vector. Fuzzy Sets Fuzzy logic starts with the concept of a fuzzy set. Afuzzy setis a set without a crisp, clearly defined boundary. It...
If X is the universe of discourse and its elements are denoted by x, then a fuzzy set A in X is defined as a set of ordered pairs: A=x,µAx|x∈X where μA(x) is the membership function of x in A. All properties of the crisp set are also applicable for fuzzy sets except ...
program. They used mathematical techniques to verify certain hypotheses about the operation of GCPV systems by comparing simulated results with computed data. The research set out to answer pressing questions about the general implementation of PV systems, such as the technology needs for GCPVS and ...
Classical set theory establishes evident sharp (crisp or exact) boundaries with apparently no uncertainty associated (i.e., black–white, true–false, good–bad, etc.); contrarily, fuzzy set theory considers ambiguous boundaries (e.g., the gray color exists between black and white; describing ...
Also Intuitionistic fuzzy equivalence classes have been characterized with the help of (α, β)-cut of Intuitionistic fuzzy relations and finally for any Intuitionistic fuzzy equivalence relation on a finite set, we have given an upper bound of the number of values that the degree of......
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