On the induction of new fuzzy relations, new fuzzy operators and their aggregation
نویسندگان
چکیده
In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator, one from a fuzzy operator and a fuzzy relation and the other one from two fuzzy operators. The first one is an extension of the well-known fuzzy operator induced by a fuzzy relation through Zadeh’s compositional rule. Finally, we aggregate these operators through the quasi-arithmetic mean associated to a continuous Archimedean t-norm in order to compare the operator obtained by aggregating the generators with the operator obtained by the aggregation of the generated ones.
منابع مشابه
Negations and aggregation operators based on a new hesitant fuzzy partial ordering
Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~cite{GaCa:Pohfs}, in this paper a fuzzy disjunction ${D}$ on the set ${H}$ of finite and nonempty subsets of the unit interval and a t-conorm ${S}$ on the set $bar{{B}}$ of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negati...
متن کاملTrapezoidal intuitionistic fuzzy prioritized aggregation operators and application to multi-attribute decision making
In some multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. Fir...
متن کاملHesitant q-rung orthopair fuzzy aggregation operators with their applications in multi-criteria decision making
The aim of this manuscript is to present a new concept of hesitant q-rung orthopair fuzzy sets (Hq-ROFSs) by combining the concept of the q-ROFSs as well as Hesitant fuzzy sets. The proposed concept is the generalization of the fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and Pythagorean fuzzy sets as well as intuitionistic hesitant fuzzy sets (IHFSs) and hesitant Pythagorean fuz...
متن کاملA 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 کاملASSOCIATED PROBABILITY INTUITIONISTIC FUZZY WEIGHTED OPERATORS IN BUSINESS START-UP DECISION MAKING
In the study, we propose the Associated Probability Intuitionistic Fuzzy Weighted Averaging (As-P-IFWA) and the Associated Probability Intuitionistic Fuzzy Weighted Geometric (As-P-IFWG) aggregation operators with associated probabilities of a fuzzy measure presenting an uncertainty. Decision makers' evaluations are given as intuitionistic fuzzy values and are used as the arguments of the aggre...
متن کامل