This work introduces an innovative approach from modeling to simulations, integrating quantum fuzzy interpretations, focusing on the expression of membership degrees in quantum circuits, interpreted as a unitary quantum transformation. Our research contrasts Quantum Fuzzy Computing with Classical Computing, particularly in the context of the prisoner's dilemma and parent-child relationships. Through the Qiskit framework, we conduct simulations, demonstrating the differences in results obtained by both approaches. Well-known fuzzy connectives, such as “exclusive or” and “arithmetic means”, provide an algebraic description for the corresponding composition of quantum operators and circuit representations. Thus, such algorithms can easily extend to model multiple agents' relationships, described by multidimensional quantum registers. The Qiskit simulations provide the structure for the algorithms' computation on the actual quantum platforms, indicating a promising direction for future research in this hybrid research area.

This study introduces an innovative quantum fuzzy approach for modeling and simulating complex decision-making processes, utilizing quantum circuits to express membership degrees as unitary transformations. We contrast Quantum Fuzzy Computing with Classical Computing, highlighting advancements in modeling the prisoner's dilemma. Using the Qiskit framework, we demonstrate how quantum fuzzy algorithms featuring connectives such as ‘exclusive or’ and ‘arithmetic mean’ enable detailed modeling of multi-agent relationships via multidimensional quantum registers, showcasing potential advancements in this hybrid research area.

This study is given at the intersection of three important areas: Modal Logic (ML), Fuzzy Logic (FL), and Quantum Computing (QC), leveraging from their main features. On the one hand, we have the QC ability to handle complex data more efficiently, taking advantage of the quantum mechanics concepts. On the other hand, ML and FL allow us to express uncertainties by mathematically modeling the imprecision of the natural language. Therefore, we first provide an algebraic model to interpret modal operators on fuzzy logic, and then we represent them in a quantum computing environment. Besides, we present some case studies simulating the fuzzy modal connectives in the Qiskit platform, aiming to better understand the evolution of quantum circuits.

Firstly, this work discusses the main conditions guarantying that general overlap (grouping) functions can be obtained from n-dimensional overlap (grouping) functions. Focusing on QL-implications, which are usually generated by strong negations together with t-norms and t-conorms, we consider a non-restrictive construction, by relaxing not only the associativity and the corresponding neutral elements (NE) but also the reverse construction of other properties. Thus, the main properties of the QL-implication class are studied, considering a tuple (G,N,O) generated from grouping and overlap functions together with the greatest fuzzy negation. In addition, in order to provide more flexibility, we define a subclass of QL-implications generated from general overlap and general grouping functions. Some examples are introduced, illustrating the constructive methods to generate such operators.

Grouping functions and their dual counterpart, overlap functions, have drawn the attention of many authors, mainly because they constitute a richer class of operators compared to other types of aggregation functions. Grouping functions are a useful theoretical tool to be applied in various problems, like decision making based on fuzzy preference relations. In pairwise comparisons, for instance, those functions allow one to convey the measure of the amount of evidence in favor of either of two given alternatives. Recently, some generalizations of grouping functions were proposed, such as (i) the n-dimensional grouping functions and the more flexible general grouping functions, which allowed their application in n-dimensional problems, and (ii) n-dimensional and general interval-valued grouping functions, in order to handle uncertainty on the definition of the membership functions in real-life problems. Taking into account the importance of interval-valued fuzzy implication functions in several application problems under uncertainty, such as fuzzy inference mechanisms, this paper aims at introducing a new class of interval-valued fuzzy material implication functions. We study their properties, characterizations, construction methods and provide examples.

This paper contributes to classifying video streaming traffic by exploring concepts of Interval-Valued Fuzzy Logic. This approach extends related works by considering the uncertainties generated by variations in network conditions and the parameter imprecision affecting the behavior of network flow, which increases the complexity to reach high accuracy in identifying the network traffic. Some evaluations using the interval-valued logic approach for video streaming traffic classification are presented using application tools and datasets to validate the proposal.

This paper considers the consensual analysis in decision-making (CDM) processes based on fuzzy logic (FL) and interval-valued fuzzy logic (IVFL), providing a CDM-strategy, by exploring the axiomatic properties of fuzzy consensus measures (FCM) via penalty functions. Thus, two models are formalized, FS-FCM and IVFS-FCM. In the former, the fuzzy-valued lattice enables the analysis of fuzzy information for linguistic variables (LV), which is obtained by the aggregation of penalty functions. And, in the latter, the consensus measures of fuzzy sets are aggregated to build a new consensual analysis modeling. Thus, e.g., the cohesion of several terms related to the same LV can be analyzed, and also the coherence between fuzzy sets referring to the lowest and highest projections. Such models decide based on relevance criteria and qualitative assessments, via the selection of alternatives, supporting the corresponding algorithmic strategies: FS-FCM strategy, applied to fuzzy values, and IVFS-FCM strategy, covering fuzzy sets. The Intf-HybridMem approach explores the access patterns to volatile and non-volatile memories related to decision-making in two steps: (i) the FS-FCM strategy explores consensus measures of fuzzy values from membership functions; and (ii) the IVFS-FCM strategy, modeling inaccuracy inherent in input variables, as read/write frequency and access recency, also including the migration recommendation as output, which is validated by evaluations carried out in both proposed strategies.

In this paper, we discussconsensus measures for typical hesitant fuzzy elements (THFE), which are the finite and nonempty fuzzy membership degrees under the scope of typical hesitant fuzzy sets (THFS). In our approach, we present a model that formally constructs consensus measures by means of aggregations functions, fuzzy implication-like functions and fuzzy negations, using admissible orders to compare the THFE, and also providing an analysis of consistency on them. Our theoretical results are applied into a problem of decision making with multicriteria illustrating our methodology to achieve consensus in a group of experts working with THFS.

Multi Expert-Multi Criteria Decision Making (ME-MCDM) problems have been well explored on hesitant fuzzy environments dealing with membership degrees as subsets which do not necessarily have the same cardinality. Admissible (total) orders collaborate by reducing the collapse in the ranking of alternatives related to preference relations. In such context, three classes of admissible orders are presented in a non-restrictive way, integrating the concepts of linearity and cardinality and providing support to the comparison between two typical hesitant fuzzy elements. In the sense of hesitant fuzzy logic, the study of fuzzy operators and their main properties is extended considering the admissible linear orders. Namely, the typical hesitant fuzzy aggregation functions, negations and implication functions are discussed mainly related to their (iso/anti)tonicity properties w.r.t. these admissible orders. An algorithmic procedure is introduced illustrating our strategy to solve an ME-MCDM problem, by selecting a Computer Integrating Manufacturing software and making use of the achieved theoretical results.

Grouping functions are aggregation functions used in decision making based on fuzzy preference relations in order to express the measure of the amount of evidence in favor of either of the two alternatives when performing pairwise comparisons. They have been also used as a disjunction operator in some important problems, such as image thresholding and the construction of a class of implication functions for the generation of fuzzy subsethood and entropy measures. Some generalizations of this concept were recently proposed, such as n-dimensional and general grouping functions, which allowed their application in ndimensional problems, such as fuzzy community detection. Also the concept of interval-valued overlap functions was presented, in order to deal with the uncertainty when defining membership functions. The aim of this paper is to introduce the concepts of n-dimensional interval-valued grouping functions and general interval-valued grouping functions, studying representability, characterization and construction methods.

In Multi-Criteria Decision Making, one of the most used algorithm designed to deal with decision making is the Technical Order by Preference to Ideal Solution (TOPSIS), which is based on finding a solution that is close to the best possible solution and distant from the worst possible solution. The Group Modular Choquet Random TOPSIS (GMC-RTOPSIS) is a generalization of the TOPSIS method capable of dealing with multiple and heterogeneous data types and interaction among criteria by means of the discrete Choquet integral. On the other hand, CT-integrals are a generalization of the Choquet integral using t-norms, which are more flexible than the standard Choquet integral. CT-integrals are pre-aggregation functions, which means that we do not require them to be monotonic in the whole domain, just in some specific directions, that is, they are directionally monotonic. Due to the excellent performance of CT-integrals in classification and multimodal fuzzy fusion decision problems, the objective of this paper is to generalize the GMC-RTOPSIS by using CT-integrals and to analyze the results provided by the use of five different t-norms in an example of a decision making problem.

It is common sense the relevance of overlap and grouping functions, specially in applications in which associativity is not required. In this work, based on previous investigations concerning classes of implication functions derived from overlap functions O, grouping functions G and fuzzy negations N (namely, (G, N)-implications, RO-implications and QL-implications constructed from (O, G, N)), a deep study on D-implications constructed from grouping functions G is carried out. Such fuzzy implications, also known as Dishkant implications, are obtained from D-operations derived from (O, G, N), which are used for the generalization of the implication p → q ≡ q(¬p∧¬q) of orthomodular lattices. We investigate under which conditions such D-operations are fuzzy implication functions, presenting a general form for obtaining D-implications. We also provide a comparative study of D-implications derived from grouping functions and other classes of fuzzy implications constructed from N, O and G, analysing the intersections among such classes.

Fuzzy Rule Based Classification Systems are an useful tool to deal with classification problems. In these systems, one fundamental point is the manner of how the available information about the problem is aggregated. The mechanism responsible to perform the aggregation is the Fuzzy Reasoning Method (FRM). Recently, some FRMs using generalizations of the Choquet integral to perform the aggregation were proposed in the literature. Since these generalizations are defined considering a specific fuzzy measure, in this paper we apply different fuzzy measures in the generalizations that presented the best performance in each study in the literature. We analyze how the performance is affected according to each fuzzy measure.

In this work we propose a new axiomatic definition of distance between interval-valued fuzzy sets which takes into account the width of the membership intervals and linear orders. We discuss some construction methods using aggregation functions which are defined in terms of admissible orders.

In this study, we discuss a new class of fuzzy subsethood measures between fuzzy sets. We propose a new definition of fuzzy subsethood measure as an intersection of other axiomatizations and provide two construction methods to obtain them. The advantage of this new approach is that we can construct fuzzy subsethood measures by aggregating fuzzy implication operators which may satisfy some properties widely studied in literature. We also obtain some of the classical measures such as the one defined by Goguen. The relationships with fuzzy distances, penalty functions, and similarity measures are also investigated. Finally, we provide an illustrative example which makes use of a fuzzy entropy defined by means of our fuzzy subsethood measures for choosing the best fuzzy technique for a specific problem.

The use of fuzzy implications is widespread as easily found in the literature. The study of fuzzy implications attracts the attention of many authors probably because of their theoretical features and also the diversity of applications where they can be applied. In the present work we continue the study of a type of fuzzy implication, called (T, N)-implication, constructed by joining a fuzzy negation and a t-norm. However, we generalize those (T, N)-implications by presenting a new operator, named (N', T, N)-implication, which can be derived from two negations. We also study the properties of (N', T, N)-implications and compare the new results with the previous ones.

The aim of this work is to study a certain fuzzy implication, called (T, N)-implication, obtained by composition of a fuzzy negation and a t-norm. Thus, it discusses under which conditions such functions preserve the main properties of fuzzy implications, in which some are related to the laws of contraposition. Finally, we prove a result that ensure the necessary and sufficient conditions for a function I : [0,1]2→ [0,1] to be a (T, N)-implication.

Penalty functions are widely used to measure disagreement or consensus. On the other hand, subsethood measures have been applied in several areas. In this paper, we introduce a method for constructing penalty functions by means of QL fuzzy subsethood measures, introduced by Dimuro et al., which are built from QL-operations derived from tuples (O, G, N), for overlap functions O, grouping functions G and fuzzy negations N.

The final goal of this study is to adapt the concept of fuzzy entropy of De Luca and Termini to deal with type-2 fuzzy sets. We denote this concept type-2 fuzzy entropy set. However, the construction of the notion of entropy measure on an infinite set, such us [0,1], is not effortless. For this reason, we first introduce the concept of quasi-entropy of a fuzzy set on the universe [0,1]. Furthermore, whenever the membership function of the considered fuzzy set in the universe [0,1] is continuous, we prove that the quasi-entropy of that set is a fuzzy entropy in the sense of De Luca and Termini. Finally, we present an illustrative example, where we use type-2 fuzzy entropy sets instead of fuzzy entropies in a classical fuzzy algorithm.

Triangular norms or t-norms, in short, and automorphisms are very useful to fuzzy logics in the narrow sense. However, these notions are usually limited to the set [0,1]. In this paper we will consider a generalization of the t-norm notion for arbitrary bounded lattices as a category, where these generalized t-norms are the objects, and a generalization of automorphism notion as the morphism of the category. We will prove that, this category is Cartesian and a subcategory of it is Cartesian closed. We show that the usual interval t-norms can be seen as a covariant functor for that category.

Triangular norms or t-norm, in short, and automorphisms are very useful to fuzzy logics in the narrow sense. Moreover, these notions are usually limited to the set [0,1]. In this paper we will consider a well known generalization of the t-norm for arbitrary bounded lattices and provide a generalization of automorphism notion for this same structure. We consider several typical lattice constructors and introduce versions of them for t-norms and morphisms. We also analyze some properties of these constructions.