An interpretation of intuitionistic fuzzy sets is proposed based on random set theory and prototype theory. The extension of fuzzy labels are modelled by lower and upper random set neighbourhoods, identifying those element of the universe within an uncertain distance threshold of a set of prototypical elements. These neighbourhoods are then generalised to compound fuzzy descriptions generated a...

in this note, by considering the notions of the intuitionistic general l-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{l}$, there exists a minimal intuitionistic general l-fuzzy automaton recognizing $mathcal{l}$.we prove that the minimal intuitionistic general l-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...

Intuitionistic preference relations are becoming increasingly important in the field of group decision making since they present a flexible and simple way to the experts to provide their preference relations, while at the same time allowing them to accommodate a certain degree of hesitation inherent to all decision making processes. In this contribution, we prove the mathematical equivalence be...

Intuitionistic fuzzy sets are generalized fuzzy sets whose elements are characterized by a membership, as well as a non-membership value. The membership value indicates the degree of belongingness, whereas the nonmembership value indicates the degree of non-belongingness of an element to that set. The utility of intuitionistic fuzzy sets theory in computer vision is increasingly becoming appare...

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and...

Uninorms are a generalization of t-norms and tconorms for which the neutral element is an element of [0,1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0,1) to either 0 or 1. In reallife applications, this kind of aggregation may be counter-intuitive. Atanassov’s i...

in this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. moreover, some basicoperations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebrawith respect to these operations. afterwards, the a...

The extension of rough set model is an important research direction in rough set theory. The aim of this paper is to present a new extension. At the first, we introduce a pair of dual intuitionistic fuzzy operators (Θ,Φ). And some important properties are examined about these these operators. Moreover, θ-lower and φ-upper approximation operators are defined, by using the operators, and a novel ...

In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

Keywords: Fuzzy DEA Intuitionistic fuzzy DEA Optimistic and pessimistic performance Ranking methods Bank branch efficiency a b s t r a c t Intuitionistic fuzzy set (IFS) is an extension of fuzzy set and an approach to define a fuzzy set where available information is not sufficient to define an imprecise concept by means of a conventional fuzzy set. The existing fuzzy DEA (FDEA) models for meas...