DeMorgan systems on the unit interval

Algebraic Aspects of Fuzzy Sets and Fuzzy Logic

This paper is expository. It is mainly a survey of some of our work on the algebraic systems that arise in fuzzy set theory and logic. We include some of the proofs here and refer to the papers [18, 19, 20, 21, 22] for further details. Our point of view is the algebraic one: when are the various systems that arise isomorphic, and what are their symmetries (automorphisms)? The bulk of the materi...

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions

Operation Planning of Wind Farms with Pumped Storage Plants Based on Interval Type-2 Fuzzy Modeling of Uncertainties

The operation planning problem encounters several uncertainties in terms of the power system’s parameters such as load, operating reserve and wind power generation. The modeling of those uncertainties is an important issue in power system operation. The system operators can implement different approaches to manage these uncertainties such as stochastic and fuzzy methods. In this paper, new ...

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...

A Characterization of Triple Semigroup of Ternary Functions and Demorgan Triple Semigroup of Ternary Functions

We define algebras of triple semigroup and DeMorgan triple semigroup and by defining three Mann’s compositions and one unary operation on the set of 3-place(ternary) functions over some set, we construct a DeMorgan triple semigroup of 3-place (ternary) functions and so find an abstract characterization of this algebras.