جستجوی مقالات مرتبط با کلیدواژه « aggregation operation » در نشریات گروه « علوم پایه »
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Probabilistic hesitant fuzzy set (PHFS) is a fruitful concept that adds to hesitant fuzzy set (HFS) the term of probability which is able to retain more information than the usual HFS. Here, we demonstrate that the existing definitions of PHFS are not still reasonable, and therefore, we first improve the PHFS definition. By endowing the set and algebraic operations with a new re-definition of PHFS, we propose a class of T-norm-based and S-norm-based operations for PHFSs together with a number of aggregation operators. Eventually, on the basis of the new operators, the effectiveness and practicality of re-defined PHFS will be tested using {three} multiple criteria decision making (MCDM) problems concerning the automotive industry safety evaluation, the evaluation of Chines hospitals andthe evaluation of alternatives in an investment company.
Keywords: hesitant fuzzy set, Probabilistic hesitant fuzzy set, Aggregation operation, Multiple Criteria Decision Making} -
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 negations $N_n$ on ${H}$ and $mu_n$ on $bar{{B}}$ are proposed. Particularly, their De Morgan's laws are investigated with respect to binary operations ${C}$ and ${D}$ on ${H}$, as well as ${T}$ and {S} on $bar{{B}}$ respectively, where ${C}$ is a commutative fuzzy conjunction on $({H},leq_H)$ and ${T}$ is a t-norm on $(bar{{B}},leq_B)$. Finally, the new hesitant fuzzy aggregation operators are presented on ${H}$ and $bar{{B}}$ and their more general forms are given. Moreover, the validity of the aggregation operations is illustrated by a numerical example on decision making.
Keywords: Hesitant fuzzy sets, Finite subsets of the unit interval, Partial ordering, t-conorm, Negation, Aggregation operation}
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