A THEORETICAL APPLICATION OF INTERVAL-VALUED TYPE 2 REPRESENTATION**Extracted from LB.Türkşmen and T.Bilgic “Interval-valued Strict Preference with Zadeh triples”, Fuzzy Sets and Systems 78 (1996) 183–195, and modified as needed.

This chapter models a strict preference relation from a given subjective weak preference relation of the decision maker by proposing that the strict preference so constructed should be represented by an interval valued relation that represents the second order imprecision which is the uncertainty of imprecise information.

Abstract

This chapter models a strict preference relation from a given subjective weak preference relation of the decision maker. Fuzzy relations and interval valued type 2 fuzzy sets based on fuzzy disjunctive canonical forms (FDCF) and fuzzy conjunctive canonical forms (FCCF) representations are used as basic tools in the modeling. The concept of strict preference is defined in terms of the weak preference and this construction introduces the second order imprecision. It is proposed that the strict preference so constructed should be represented by an interval valued relation that represents the second order imprecision which is the uncertainty of imprecise information. The rationale of this approach can be explained as follows: it can simply be started with an imprecise construct namely, the fuzzy weak preference of the decision maker. The basic assertion is that higher concepts constructed from imprecision preferences induce a second order imprecision. Finally, the length of the interval for strict preference can be thought as a measure of confidence on the initial preference that can give rise to cardinal models of completeness of information in preference structures.