Although Dubois and Prade’s fuzzy elements and gradual sets cannot be represented as objects or fuzzy predicates in first-order versions of known systems of propositional fuzzy logic, they can be represented in higher-order fuzzy logic. However, this logical representation does not simplify handling these notions, compared to informal semantic methods of traditional fuzzy mathematics. Finding a...

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...

Ranking fuzzy numbers plays an important role in data analysis, decision making optimization, forecasting etc. The last few decades have seen a large number of methods investigated for ranking fuzzy numbers. In this paper, a new approach is proposed for the ranking of generalized trapezoidal fuzzy numbers namely Haar ranking and is based on the approximate coefficients and detailed coefficients...

In recent years, there has been significant interest in the study of stability analysis and con‐ troller synthesis for Takagi-Sugeno(T-S) fuzzy systems, which has been used to approximate certain complex nonlinear systems [1]. Hence it is important to study their stability analysis and controller synthesis. A rich body of literature has appeared on the stability analysis and synthesis problems ...