Pseudo-uninorms and Atanassov’s intuitionistic pseudo-uninorms

IEEE Trans. Fuzzy Syst.

Arrastia

et al. 2022

Throughout this paper, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first we introduce the concept of a general mean on an abstract set. This new concept conciliates the Social Choice -where well-known impossibility results as the Arrovian ones are encountered-and the Decision-Making approaches -where the necessity of fusing rankings is unavoidable-. Moreover it gives rise to a reasonable definition of the concept of a ranking fusion function that does indeed satisfy the axioms of a general mean. Then we will introduce some methods to build ranking fusion functions, paying a special attention to the use of score functions, and pointing out the equivalence between ranking and scoring. To conclude, we prove that any ranking fusion function introduces a partial order on rankings implemented on a finite set of alternatives. Therefore, this allows us to compare rankings and different methods of aggregation, so that in practice one should look for the maximal elements with respect to such orders defined on rankings.

Section: Illustrative Examplesmentioning

confidence: 79%

Section: Manuscriptmentioning

confidence: 80%

See 1 more Smart Citation

Aggregation of Individual Rankings Through Fusion Functions: Criticism and Optimality Analysis

Bustince

IEEE Trans. Fuzzy Syst.

Arrastia

et al. 2022

“…We will consider the illustrative example used in [9,21] to show how to use our method. Suppose that an investor intends to invest part of his capital in a company.…”

Section: Illustrative Examplementioning

confidence: 99%

“…On the other hand, the Table 9 adds this two ranking and the ranking obtained in [9] to the Table 10 of [21] which contains the result of twelve methods for this same MAGDMP. Analysing this table, we can see that the fifteen methods return fifteen different rankings.…”

Section: Ranking Maximummentioning

confidence: 99%

Weighted Average Operators Generated by n-dimensional Overlaps and an Application in Decision

Silva

Advances in Intelligent Systems Research

Bustince

2015

Self Cite

In this paper we provide a way to generate a class of weighted average operator from n-dimensional overlap functions and aggregation functions. These weighted average operators are used in an algorithm of a multiattribute group decision making problem based on decision matrix. An illustrative example is considered with the application of our method for two specific weighted average operators of this class. This result is compared with the ranking of other methods.

Relating Kleene Algebras with Pseudo Uninorms

Lecture Notes in Computer Science

Santiago

Madeira

et al. 2023

This paper explores a strict relation between two core notions of the semantics of programs and of fuzzy logics: Kleene Algebras and (pseudo) uninorms. It shows that every Kleene algebra induces a pseudo uninorm, and that some pseudo uninorms induce Kleene algebras. This connection establishes a new perspective on the theory of Kleene algebras and provides a way to build (new) Kleene algebras. The latter aspect is potentially useful as a source of formalism to capture and model programs acting with fuzzy behaviours and domains.