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...

Consistency of preference relations is associated with the study of the transitivity property. In this paper, we analyze the properties to be verified by a function, T , in order to obtain the value of preference of the alternative xi over the alternative xk when we already have the values of the preference of xi over xj , and of xj over xk. As a consequence, we define T -additive transitivity ...

The problem of embedding incomplete into complete relations has been an important topic of research in the context of crisp relations and their applications. Several variations of the acclaimed Szpilrajn’s theorem have been provided, inclusive of the case when some order conditions between elements are imposed on the extension. We extend the analysis of that topic by Alcantud to the fuzzy case....

Equivalence relations and orderings are key concepts of mathematics. For both types of relations, formulations within the framework of fuzzy relations have been proposed already in the early days of fuzzy set theory. While similarity (indistinguishability) relations have turned out to be very useful tools, e.g. for the interpretation of fuzzy partitions and fuzzy controllers, the utilization of...

In decision making, consistency in fuzzy preference relations is associated with the study of transitivity property. While using additive consistency property to complete incomplete preference relations, the preference values found may lie outside the interval [0, 1] or the resultant relation may itself be inconsistent. This paper proposes a method that avoids inconsistency and completes an inc...

Many of the new fuzzy structures with complete MV-algebras as value sets, such hesitant, intuitionistic, neutrosophic, or soft can be transformed into one type set values in special algebras, called AMV-algebras. The category AMV-algebras is isomorphic to pairs (R,R∗) commutative semirings and corresponding sets are (R,R∗)-fuzzy sets. We use this theory define relations, lower upper approximati...

This paper proposes a new practical model for project portfolio selection focusing on two issues; the first issue relates to managing uncertainty provoked by hesitant situations and the second issue relates to the interaction effect of projects on final value of portfolio. Based on the above issues, the hesitant fuzzy weighted averaging (HFWA) operator is applied to aggregate the hesitant fuzzy...

Inspired by the idea of multiplicative intuitionistic preference relation (Xia MM et al. Preference relations based on intuitionistic multiplicative information, IEEE Transactions on Fuzzy Systems, 2013, 21(1): 113-133), in this paper, a new preference relation called the interval-valued multiplicative intuitionistic preference relation is developed. It is analyzed the basic operations for inte...

The purpose of this paper is to present a classiication method of alternatives for multiple preference ordering criteria based on the concept of fuzzy majority. The fuzzy majority is represented by a fuzzy quantiier, and applied in the aggregation by means of an OWA operator whose weights are calculated by the fuzzy quantiier. For every preference ordering criterion we derive a preference order...