On the construction of fuzzy preference structures

Abstract

In this paper, we analyse the generalization of the classical method of the construction of a preference structure from a reflexive binary relation to the case of fuzzy binary relations. According to our approach, there are two interesting fuzzy preference structures we can construct from a given reflexive fuzzy binary relation. These two fuzzy preference structures correspond to the two extreme solutions of the system of functional equations in the method of Fodor and Roubens. We also prove that only one of two fuzzy preference structures allows its fuzzy relation of strict preference to be transitive with respect to the -transform of the Lukasiewicz t-norm when the reflexive fuzzy relation it is constructed from is also transitive with respect to the same t-norm.

Construction of global fuzzy preference structures from two-parameter single-criterion fuzzy outranking relations

“…4. For each of them, the three conditions (1), (2) and (3) that a fuzzy preference structure must satisfy will be examined.…”

“…An important issue in fuzzy preference structures is the one related to their construction from a given reflexive fuzzy outranking relation [2,15,22]. One way of dealing with this issue consists of defining one of the three components of the fuzzy preference structure using a well-known t-norm such as the Łukasiewicz t-norm or min t-norm and then to define the two other components in such a way that the three components fulfil the conditions of a fuzzy preference structure.…”

Assessment of Strategic R&D Projects for Car Manufacturers Based on the Evidential Reasoning Approach

“…Firstly, the assessments on "theoretical standard" and "level of innovation" are aggregated to generate an intermediate assessment on E I (2) , as shown by equations (18), (19), (20), and (21) …”

“…Then, generate the assessment on "theoretical and innovation level" (E I(3) ) by aggregating E I (2) and the assessment on individual design: …”

“…Over the last 20 years, a lot of research has been conducted to develop methods for dealing with uncertain information. 1,2,5,16,18 The evidential reasoning (ER) approach was therefore introduced in 1990s 19,20,22,24 based on the Dempster-Shafer (D-S) theory 3,7 and decision theory. This approach is well-suited to addressing uncertain MADA problems with qualitative attributes in strategic R&D project assessment in a rational way since the concept of qualitative evaluation grades is imbedded in the assessment process and qualitative evaluation grades do not have to be quantified in the ER-based assessment aggregation.…”