Inequality averse criteria for evaluating infinite utility streams: The impossibility of Weak Pareto

This paper investigates ethical aggregation of infinite utility streams by representable social welfare relations. We prove that the Hammond Equity postulate and other variations of it like the Pigou-Dalton transfer principle are incompatible with positive responsiveness to welfare improvements by every generation. The case of Hammond Equity for the Future is investigated too.Social welfare function; Equity; Inequality aversion; Pareto axiom; Intergenerational justice

Liberal approaches to ranking infinite utility streams: When can we avoid interferences?

In this work we analyse social welfare relations on sets of infinite utility streams that verify various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that agree with axioms of that kind together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani prove that a fully liberal non-interfering view of a finite society leads to dictatorship if weak Pareto optimality is imposed. We first prove that extending the horizon to infinity produces a reversal of such impossibility result. Then we investigate a related problem: namely, the possibility of combining “standard” semicontinuity with efficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between continuity and non-interference principles, both under ordinal and cardinal views of the problem. Our analysis ends with some insights on the property of representability in the presence of non-interference assumptions. In particular we prove that all social welfare functions that verify a very mild efficiency property must exert some interference (penalising both adverse and favorable changes) on the affairs of particular generations.Pareto axiom; Intergenerational justice; Social welfare relation; Non-interference; Continuity

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

Ranked hesitant fuzzy sets for multi-criteria multi-agent decisions

This paper introduces and investigates ranked hesitant fuzzy sets, a novel extension of hesitant fuzzy sets that is less demanding than both probabilistic and proportional hesitant fuzzy sets. This new extension incorporates hierarchical knowledge about the various evaluations submitted for each alternative. These evaluations are ranked (for example by their plausibility, acceptability, or credibility), but their position does not necessarily derive from supplementary numerical information (as in probabilistic and proportional hesitant fuzzy sets). In particular, strictly ranked hesitant fuzzy sets arise when no ties exist, i.e., when for any fixed alternative, each submitted evaluation is either strictly more plausible or strictly less plausible than any other submitted evaluation. A detailed comparison with similar models from the literature is performed. Then in order to produce a natural strategy for multi-criteria multi-agent decisions with ranked hesitant fuzzy sets, canonical representations, scores and aggregation operators are designed in the framework of ranked hesitant fuzzy sets. In order to help implementation of this model, Mathematica code is provided for the computation of both scores and aggregators. The decision-making technique that is prescribed is tested with a comparative analysis with four methodologies based on probabilistic hesitant fuzzy information. A conclusion of this numerical exercise is that this methodology is reliable, applicable and robust. All these evidences show that ranked hesitant fuzzy sets are an intuitive extension of the hesitant fuzzy set model designed by V. Torra, that can be implemented in practice with the aid of computationally assisted algorithms.Junta de Castilla y León y European Regional Development Fun

The semantics of N-soft sets, their applications, and a coda about three-way decision

This paper presents the first detailed analysis of the semantics of N-soft sets. The two benchmark semantics associated with soft sets are perfect fits for N-soft sets. We argue that N-soft sets allow for an utterly new interpretation in logical terms, whereby N-soft sets can be interpreted as a generalized form of incomplete soft sets. Applications include aggregation strategies for these settings. Finally, three-way decision models are designed with both a qualitative and a quantitative character. The first is based on the concepts of V-kernel, V-core and V-support. The second uses an extended form of cardinality that is reminiscent of the idea of scalar sigma-count as a proxy of the cardinality of a fuzzy set

Computation of Choquet integral for finite sets: Notes on a ChatGPT-driven experience

The Choquet integral, credited to Gustave Choquet in 1954, initially found its roots in decision making under uncertainty following Schmeidler's pioneering work in this field. Surprisingly, it was not until the 1990s that this integral gained recognition in the realm of multi-criteria decision aid. Nowadays, the Choquet integral boasts numerous generalizations and serves as a focal point for intensive research and development across various domains. Here we share our journey of utilizing ChatGPT as a helpful assistant to delve into the computation of the discrete Choquet integral using Mathematica. Additionally, we have demonstrated our ChatGPT experience by crafting a Beamer presentation with its assistance. The ultimate aim of this exercise is to pave the way for the application of the discrete Choquet integral in the context of N-soft sets

Ordering infinite utility streams: set-theoretical and topological issues

[EN]Invited talk at the Eighth Italian-Spanish Conference on General Topology and its Applications

Liberal approaches to ranking infinite utility streams: When can we avoid interference?

[EN]In this work we analyse social welfare relations on sets of finite and infinite utility streams that satisfy various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that verify non-interference axioms together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani prove that a fully liberal non-interfering view of a finite society leads to dictatorship if the weak Pareto principle is imposed. We first prove that this impossibility result vanishes when we extend the horizon to infinity. Then we investigate a related problem: namely, the possibility of combining \standard" semicontinuity with eficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between relaxed forms of continuity and non- interference principles, both under ordinal and cardinal views of the problem

Complemental Fuzzy Sets: A Semantic Justification of q-Rung Orthopair Fuzzy Sets

This article introduces complemental fuzzy sets, explains their semantics, and presents a subclass of this model that generalizes intuitionistic fuzzy sets in a novel manner. It also provides practical results that will facilitate their implementation in real situations. At the theoretical level, we define a family of c-complemental fuzzy sets from each fuzzy negation c. We argue that this construction provides semantic justification for all subfamilies of complemental fuzzy sets, which include q-rung orthopair fuzzy sets (when c is a Yager’s fuzzy complement) and the new family of Sugeno intuitionistic fuzzy sets (when c belongs to the class of Sugeno’s fuzzy complements). We study fundamental operations and a general methodology for the aggregation of complemental fuzzy sets. Then, we give some specific examples of aggregation operators to illustrate their applicability. On a more practical level, constructive proofs demonstrate that all orthopair fuzzy sets on finite sets that satisfy a mild restriction are Sugeno intuitionistic fuzzy sets, and they are q-rung orthopair fuzzy sets for some q too. These contributions produce a new operational model that semantically justifies, and mathematically contains, “almost all” orthopair fuzzy sets on finite sets.Junta de Castilla y León y European Regional Development Fund (Fondo Europeo de Desarrollo Regional), CLU-2019-03, de apoyo a la unidad de investigación de excelencia “Economic Management for Sustainability” (GECOS)

Finite sets of data compatible with multidimensional inequality measures

[EN]By using a general solution to the problem of extending a preorder conditional on a list of ex-ante comparisons between pairs, we elucidate when a finite set of predetermined comparisons can be incorporated to a multidimensional inequality measure even if the population size is variable