in this work, we define a fuzzy soft set theory and its related properties. we then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.

The problem of choosing an appropriate total order is crucial for many applications that make use of extensions of fuzzy sets. In this work we introduce the concept of an admissible order as a total order that extends the usual partial order between intervals. We propose a method to build these admissible orders in terms of two aggregation functions and we prove that some of the most used examp...

In this work we construct linear orders between pairs of intervals by using aggregation functions. We apply these orders in a decision-making problem where the experts provide their opinions by means of interval-valued fuzzy sets.

In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets,...

The aim of this work is to study N−dual structures of representable implications generated from a set M of aggregation functions and pairs of mutual dual functions, founded on the isomorphism between the unit interval and special instances of the Goguen’s L-fuzzy sets. We discuss under which conditions representable functions preserve the main properties of their N−dual interval approach.

Fuzzy Sets theory has been applied in many fields to handle uncertainty, which can be reflected on the membership degree of the objects belonging to a set. Moreover, Hesitant Fuzzy Sets are useful whenever there is indecision among several possible values for the preferences over objects in the process of decision-making. In this sense, the aim of this work is to consider the notion of aggregat...

The study of linearly compensated hybrid connectives H = λC +(1−λ)C̄, where C is a t-norm and C̄ represents the dual connective of C, to define aggregation operators for fuzzy classifications is a key point not only in fuzzy sets theory but also in learning processes. Although these operators are not associative, the fact that they can be decomposed into associative functions easily gives rise to...

Consideration sets provide a standard tool for the exploration of consumer choice. It is appropriate to analyze it as a fuzzy set because not all the brands of a certain category of products or services that belong to it are considered of the same importance. In this work we propose an alternative operationalization of the aggregate fuzzy consideration set. It is based on a new approach for lin...

In the paper we study a method extending fuzzy measures on the set N = {1, . . . , n} to n-ary aggregation functions on the interval [0, 1]. The method is based on a fixed suitable n-ary aggregation function and the Möbius transform of the considered fuzzy measure. This approach generalizes the wellknown Lovász and Owen extensions of fuzzy measures. We focus our attention on the special class o...

The choice of an aggregation function is a common problem in Multi Attribute Decision Making (MADM) systems. The Method of Imprecision (MoI) is a formal theory for the manipulation of preliminary design information that represents preferences among design alternatives with the mathematics of fuzzy sets. The MoI formulates the preliminary design problem as a MADM problem. To date, two aggregatio...