In these notes, I will summarize the basic ideas in choice theory, which you must be familiar with from 14.121. I will describe three ways of modeling individual choice, namely choice function, preference, and utility maximization. I will present the conditions under which one can use each model. One can always use choice functions in modeling a decision maker’s choice at a given situation. In ...

In this work we present a construction method for interval-valued fuzzy preference relations from a fuzzy preference relation and the representation of the lack of knowledge or ignorance that experts suffer when they define the membership values of the elements of that fuzzy preference relation. We also prove that, with this construction method, we obtain membership intervals for an element whi...

An abstract framework for formalising persuasion dialogues has recently been proposed. The framework provides for a range of speech acts, and protocols of varying levels of flexibility. However, the framework assumes the availability of preference information relevant to determining whether arguments moved in a dialogue defeat each other. However, preference information may only become availabl...

Intuitionistic fuzzy preference relation has turned out to be a powerful structure in representing the decision makers’ preference information especially when the decision makers are not able to express their preferences accurately due to the unquantifiable information, incomplete information, unobtainable information, partial ignorance, and so forth. The aim of this paper is to develop some te...

In this work we present a method for constructing an Atanassov’s intuitionistic fuzzy preference relation from a fuzzy preference relation that takes into account the ignorance of the expert when evaluating the preferences in the latter. Moreover, we present two algorithms that make use of this method for extending the weighted voting method to the Atanassov’s intuitionistic fuzzy setting in de...

In this paper, we study the tensor commutativity degree of pair of finite groups. Erdos introduced the relative commutativity degree and studied its properties. Then, Mr. Niroomand introduced the tensor relative commutativity degree, calculated tensor relative degree for some groups, and studied its properties. Also, he explained its relation with relative commutativity degree. In this paper, w...

This study introduces a new multi-criteria group decision-making model in organ transplant transportation networks under uncertain situations. A combined weighting approach is presented to obtain expert weights with various kinds of opinions by integrating similarity measure and subjective judgments experts. Also, the CRITIC given criteria weights. Finally, novel integrated ranking proposed cal...

An interactive procedure for generating a user-tailored fuzzy preference relation on intervals is proposed. This procedure allows the decision maker to choose a preference relation which suits best his intuition. The procedure is easy to use (it makes use of graphical representation) and general enough to comprise, as special cases, the intervals proposed in the literature.

In this paper we consider a decision maker who shows his/her preferences for different alternatives through a finite set of ordinal values. We analyze the problem of consistency taking into account some transitivity properties within this framework. These properties are based on the very general class of conjunctors on the set of ordinal values. Each reciprocal preference relation on a finite o...