Many applications e.g. in approximate reasoning, data summarisation, information retrieval etc. can profit from the use of fuzzy quantifiers like “almost all” or “many”, which provide flexible means of information aggregation, and are capable of extracting meaningful linguistic summaries from large amounts of raw data. However, as will be shown by a number of counterexamples, existing approache...

We introduce a new choice rule that is based on the evidence that decision makers do not pay attention to all items in a menu. Nevertheless they have an underlying rational preference. The Fuzzy Attention Model (FAM) is characterized by an axiom based on revealed stochastic choice akin to the Strong Axiom of Revealed Preference (SARP). The model helps to introduce novel notions of substitutabil...

The way poverty is measured is important for an understanding of what has happened to poverty as well as for anti-poverty policy evaluation. Sen’s (1976) pathfinding work has motivated many researchers to focus on the way poverty should be measured. A poverty measure, argued by Sen, should satisfy certain properties or axioms and the desirability of a poverty measure should be evaluated by thes...

The purpose of this paper is to extend a new balancing and ranking method to handle uncertainty for a multiple attribute analysis under a hesitant fuzzy environment. The presented hesitant fuzzy balancing and ranking (HF-BR) method does not require attributes’ weights through the process of multiple attribute decision making (MADM) under hesitant conditions. For the rating of possible alternati...

Although there have been quite a number of theoretical and practical studies where axiomatic design (AD) principles have been used in the last few years, there is a lack of a comprehensive literature survey which evaluates and classifies these papers. This study provides a recognizable overview of literature on AD principles from the past 20 years and introduces a novel classification scheme co...

When the first operation’s inverse axiom is deleted from ring, an algebraic structure, semiring, generated. Subsemiring one of subjects covered in semiring. The concepts fuzzy subsemiring, anti subsemiring and complement are introduced this paper. In addition, anti-subsemiring a wedge, or combination two more associated with non-empty subset semiring whose membership criteria defined by value z...

Debates about poverty relief and foreign aid often hinge on claims about how many poor people there are in the world and what constitutes poverty. Good measures of poverty are essential for addressing the world poverty problem. Measures of poverty require a basis for determining who is poor and a method of aggregation. Historically, the methods of aggregation were quite simple. The headcount in...

Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example Intuitionistic Logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the Basic Logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models...

We formalize reasoning about fuzzy belief and fuzzy common belief, especially incomparable beliefs, in multi-agent systems by using a logical system based on Fitting’s many-valued modal logic, where incomparable beliefs mean beliefs whose degrees are not totally ordered. Completeness and decidability results for the logic of fuzzy belief and common belief are established while implicitly exploi...

Goguen categories were introduced as a suitable categorical description of L-fuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. In this paper we want to study the algebraic structures derived from Goguen categories by replacing its second-order axiom by some weaker versions.