Z-Numbers and Type-2 Fuzzy Sets: A Representation Result
نویسندگان
چکیده
Traditional [0, 1]-based fuzzy sets were originally invented to describe expert knowledge expressed in terms of imprecise (“fuzzy”) words from natural language. To make this description more adequate, several generalizations of the traditional [0, 1]-based fuzzy sets have been proposed, among them type-2 fuzzy sets and Z-numbers. The main objective of this paper is to study the relation between these two generalizations. As a result of this study, we show that if we apply data processing to Z-numbers, then we get type-2 sets of special type – that we call monotonic. We also prove that every monotonic type-2 fuzzy set can be represented as a result of applying an appropriate data processing algorithm to some Z-numbers. 1 Z-Numbers and Type-2 Fuzzy Sets: Formula-
منابع مشابه
A NOVEL TRIANGULAR INTERVAL TYPE-2 INTUITIONISTIC FUZZY SETS AND THEIR AGGREGATION OPERATORS
The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws. Furthermore, based on these operators, an approach to mul...
متن کاملMULTI-ATTRIBUTE DECISION MAKING METHOD BASED ON BONFERRONI MEAN OPERATOR and possibility degree OF INTERVAL TYPE-2 TRAPEZOIDAL FUZZY SETS
This paper proposes a new approach based on Bonferroni mean operator and possibility degree to solve fuzzy multi-attribute decision making (FMADM) problems in which the attribute value takes the form of interval type-2 fuzzy numbers. We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two interval trapezoidal type-2 fuz...
متن کاملA Multi-Criteria Analysis Model under an Interval Type-2 Fuzzy Environment with an Application to Production Project Decision Problems
Using Multi-Criteria Decision-Making (MCDM) to solve complicated decisions often includes uncertainty, which could be tackled by utilizing the fuzzy sets theory. Type-2 fuzzy sets consider more uncertainty than type-1 fuzzy sets. These fuzzy sets provide more degrees of freedom to illustrate the uncertainty and fuzziness in real-world production projects. In this paper, a new multi-criteria ana...
متن کاملThe generation of fuzzy sets and the~construction of~characterizing functions of~fuzzy data
Measurement results contain different kinds of uncertainty. Besides systematic errors andrandom errors individual measurement results are also subject to another type of uncertainty,so-called emph{fuzziness}. It turns out that special fuzzy subsets of the set of real numbers $RR$are useful to model fuzziness of measurement results. These fuzzy subsets $x^*$ are called emph{fuzzy numbers}. The m...
متن کاملHorizontal representation of a hesitant fuzzy set and its application to multiple attribute decision making
The main aim of this paper is to present a novel method for ranking hesitant fuzzy sets (HFSs) based on transforming HFSs into fuzzy sets (FSs). The idea behind the method is an interesting HFS decomposition which is referred here to as the horizontal representation in the current study. To show the validity of the proposed ranking method, we apply it to solve a multi-attribute decision-making ...
متن کامل