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A logical reasoning based decision making method for handling qualitative knowledge Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201113
Shuwei Chen; Jun Liu; Yang XuSuccessful decisionmaking analysis needs to take both advantages of human analysts and computers, and human knowledge is usually expressed in a qualitative way. Computer based approaches are good at handling quantitative data, while it is still challenging on how to well structure qualitative knowledge and incorporate them as part of decision analytics. This paper develops a logical reasoning based

Credal sets representable by reachable probability intervals and belief functions Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201119
Serafín MoralGarcía; Joaquín AbellánBelief functions and reachable probability intervals are theories based on imprecise probabilities that generalize classical probability theory. On the one hand, belief functions have been commonly used to deal with uncertainty and in the combination of information provided by different sources. On the other hand, reachable probability intervals have high expressive power, are easy to manage, and can

An evolutionary strategic weight manipulation approach for multiattribute decision making: TOPSIS method Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201119
Bapi Dutta; Son Duy Dao; Luis Martínez; Mark GohWeight information of the attributes plays a pivotal role in multiattribute decision making (MADM) problems. Oftentimes, a decision maker may try to manipulate this weight information to persuade a particular rank order of the alternatives of his/her interest. In the literature, this type of manipulation is known as strategic manipulation of the weight information. In this study, we consider the manipulation

Note on topologies induced by coverings of approximation spaces Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201104
Michiro KondoWe consider topological properties of an approximation space U with a covering C of U. A topology τ is defined by use of covering C. We show that τ forms an Alexandrov topology and any member K of C is a closed subset with respect to τ. Moreover, we prove some fundamental properties of the topological space (U,τ). In particular, if the topological space (U,τ) satisfies one of the separation axioms

Two clustering methods based on the Ward method and dendrograms with intervalvalued dissimilarities for intervalvalued data Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201117
Yu Ogasawara; Masamichi KonNumerous studies have focused on clustering methods for intervalvalued data, which is a type of symbolic data. However, limited attention has been awarded to a clustering method employing intervalvalued dissimilarity measures. To address this issue, herein, we propose two clustering approaches based on the Ward method using intervalvalued dissimilarity for the intervalvalued data. Each clustering

Fuzzy extensions of the dominancebased rough set approach Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201112
Marko Palangetić; Chris Cornelis; Salvatore Greco; Roman SłowińskiIn this paper, we first review existing fuzzy extensions of the dominancebased rough set approach (DRSA), and advance the theory considering additional properties. Moreover, we examine the application of Ordered Weighted Average (OWA) operators to fuzzy DRSA. OWA operators have shown a lot of potential in handling outliers and noisy data in decision tables, when they are combined with the indiscernibilitybased

Nondeterministic finite automata based on quantum logic: Language equivalence relation and robustness Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201109
Haihui Wang; Luyao Zhao; Ping LiAutomata theory based on quantum logic has been established by Ying. Nondeterministic fuzzy finite automata theory has been proposed by Cao, and further generalized by Pan et al. In this paper, we propose the notion of nondeterministic finite automaton based on quantum logic whose underlying structure is a complete orthomodular lattice l, called nondeterministic lvalued finite automaton (NlFA, for

On interval RO and (G,O,N)implications derived from interval overlap and grouping functions Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201021
Meng Cao; Bao Qing HuThis paper deals with two sorts of interval fuzzy implications derived from interval overlap and grouping functions, viz., interval RO and (G,O,N)implications. Firstly, interval ROimplications, preserving the residuation property, are the interval generalization of ROimplications induced by overlap functions. We investigate their properties and their correlations with interval automorphisms. Secondly

Local regression smoothers with setvalued outcome data Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201017
Qiyu Li; Ilya Molchanov; Francesca Molinari; Sida PengThis paper proposes a method to conduct local linear regression smoothing in the presence of setvalued outcome data. The proposed estimator is shown to be consistent, and its mean squared error and asymptotic distribution are derived. A method to build error tubes around the estimator is provided, and a small Monte Carlo exercise is conducted to confirm the good finite sample properties of the estimator

On a distribution form of subcopulas Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201021
Santi TasenaIn this work, we study the problem of (sub)copula estimation via continuity of the Sklar's correspondence. One benefit of this approach is that the estimator can be obtained from that of the corresponding (joint) distribution function via plugin method. Additional proof is not required. Our approach is to naturally embed the space of subcopulas into the space of distribution functions. This allows

Observability in locally vague environments Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201021
Mustafa DemirciIn this paper, we introduce observable Lfuzzy subsets of an Lfuzzy set in a locally vague environment, and give their axiomatization. In addition to this, lower and upper observability operators that enable us to approximate nonobservable Lfuzzy sets within some observable bounds are studied. In particular, we deal with their topological characterization, and expose that they can be identified

Label distribution feature selection for multilabel classification with rough set Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201015
Wenbin Qian; Jintao Huang; Yinglong Wang; Yonghong XieMultilabel learning deals with cases where every instance corresponds to multiple labels. The objective is to learn mapping from an instance to a relevant label set. Existing multilabel learning approaches assume that the significance for all related labels is same for every instance. Several problems of label ambiguity can be dealt with using multilabel learning, but some practical applications

Asymmetric dependence in the stochastic frontier model using skew normal copula Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201027
Zheng Wei; Erin M. Conlon; Tonghui WangIn this paper, a new skew normal copulabased stochastic frontier model (SFM) is proposed to investigate the asymmetric dependence among the disturbances U (representing technical inefficiency) and V (representing noise). By employing the skewnormal copula in SFM, the asymmetric joint behavior of U and V can be parameterized, thereby allowing the data to have the opportunity to determine the adequacy

Scalinginvariant maximum margin preference learning Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201019
Mojtaba Montazery; Nic WilsonOne natural way to express preferences over items is to represent them in the form of pairwise comparisons, from which a model is learned in order to predict further preferences. In this setting, if an item a is preferred to the item b, then it is natural to consider that the preference still holds after multiplying both vectors by a positive scalar (e.g., 2a≻2b). Such invariance to scaling is satisfied

Modus tollens with respect to uninorms: UModus Tollens Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201019
Isabel Aguiló; Juan Vicente Riera; Jaume Suñer; Joan TorrensIn fuzzy logic and approximate reasoning the inference rule given by the Modus Tollens usually derives into an inequality involving three logical operators: a conjunction, an implication function and a negation. Until now, in this scenario the conjunction has been commonly modeled by a tnorm, but recently the possibility of using a more general conjunction has been pointed out. In this work, we want

On subjective expected value under ambiguity Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201015
Radim Jiroušek; Václav KratochvílThe paper describes decisionmaking models based on a newly introduced notion of personal expected value. Such models exhibit the ambiguity aversion, which is controlled by a subjective parameter with the semantics of “the higher the aversion, the higher the coefficient”. For negative values of this parameter the models thus manifest a positive attitude to ambiguity. If this parameter equals zero,

A practical reliability design method considering the compound weight and loadsharing Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201001
Yao Li; Frank P.A. Coolen; Caichao ZhuReliability design is an important work in the early design stage of offshore wind turbines. Due to the incomplete considerations and poor feasibility of the drawbacks for existing methods, a set of the practical reliability design method is proposed in this paper. The time characteristics and many influential factors of units are considered in the design process. The influential factors of the system's

A novel quantum grasshopper optimization algorithm for feature selection Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200903
Dong Wang; Hongmei Chen; Tianrui Li; Jihong Wan; Yanyong HuangFeature selection is an indispensable work to make the data mining more effective. It reduces the computational complexity and effectively improves the performance of learning models. The exhaustive algorithm and the greedy algorithm cannot adapt to the current increasing number of features when finding the potential optimal feature subset. Therefore, the feasible way for feature selection called swarm

Relationships between relationbased rough sets and belief structures Int. J. Approx. Reason. (IF 2.678) Pub Date : 20201014
YanLan Zhang; ChangQing LiAs two important methods used to deal with uncertainty, the rough set theory and the evidence theory have close connections with each other. The purpose of this paper is to examine relationships between the relationbased rough set theory and the evidence theory, and to present interpretations of belief structures in relationbased rough set algebras. The probabilities of relation lower and upper approximations

From equivalence queries to PAC learning: The case of implication theories Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200922
Ramil Yarullin; Sergei ObiedkovIn Angluin's exactlearning framework, equivalence queries can be simulated by stochastic equivalence testing to achieve a probably approximately correct identification of an unknown concept. We present an analysis of the number of samples that need to be generated in the process leading to a theoretical improvement on an earlier approach. We apply this modification to a previously known probably approximately

Partialoverall dominance threeway decision models in intervalvalued decision systems Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200909
Dandan Yang; Tingquan Deng; Hamido FujitaThreeway decisions are a generalization of classical decision theory and receive increasing attentions from various fields to handle decisionmaking problems, especially when involving in incomplete information. An interval is a typical notion of information representation with incompleteness and uncertainty. To measure the dominance degree of one interval dominating or being dominated by another

A latticebased representation of independence relations for efficient closure computation Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200828
Linda C. van der Gaag; Marco Baioletti; Janneke H. BoltIndependence relations in general include exponentially many statements of independence, that is, exponential in the number of variables involved. These relations are typically characterised however, by a small set of such statements and an associated set of derivation rules. While various computational problems on independence relations can be solved by manipulating these smaller sets without the

Extended belief rulebased model for environmental investment prediction with indicator ensemble selection Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200827
FeiFei Ye; Suhui Wang; Peter Nicholl; LongHao Yang; YingMing WangEnvironmental investment prediction is an effective solution to reduce the wasteful investments of environmental management. Since environmental management involves diverse environmental indicators, investment prediction modeling usually causes the curse of dimensionality and uses irrelevant indicators. A common solution to solve these problems is the use of indicator selection methods to select representative

A probabilistic deontic argumentation framework Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200831
Régis Riveret; Nir Oren; Giovanni SartorWhat does it mean that something is probably obligatory? And how does it relate to the probability that it is permitted or prohibited? In this paper, we provide a possible answer by merging deontic argumentation and probabilistic argumentation into a probabilistic deontic argumentation framework. This framework allows us to specify a semantics for the probability of deontic statuses. The deontic argumentation

Efficient approaches for maintaining dominancebased multigranulation approximations with incremental granular structures Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200820
Chengxiang Hu; Li ZhangIn practical decision making applications, it is computationally timeconsuming to maintain multigranulation approximations from scratch in dynamic ordered decision information systems (ODISs) with incremental granular structures consisting of the changing of granular structures by adding granular structures, or by adding an attribute set into each granular structure. The time consumed in the process

Semiring programming: A semantic framework for generalized sum product problems Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200826
Vaishak Belle; Luc De RaedtTo solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving realworld problems requires an integration amongst these, contemporary representation methodologies offer little support for this. In an attempt to alleviate this situation, we position and motivate a new declarative

Thirty years of credal networks: Specification, algorithms and complexity Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200821
Denis Deratani Mauá; Fabio Gagliardi CozmanCredal networks generalize Bayesian networks to allow for imprecision in probability values. This paper reviews the main results on credal networks under strong independence, as there has been significant progress in the literature during the last decade or so. We focus on computational aspects, summarizing the main algorithms and complexity results for inference and decision making. We address the

Efficient algorithms for robustness analysis of maximum a posteriori inference in selective sumproduct networks Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200812
Julissa Villanueva Llerena; Denis Deratani MauáSumProduct Networks (SPN) are deep probabilistic models with demonstrated excellent performance in several machine learning tasks. As with many other probabilistic models, performing MaximumAPosteriori inference in SPNs is NPhard. Selective SPNs are a subclass of SPNs that allow for efficient MaximumAPosteriori inference and closedform parameter learning. Due to the high number of parameters

Dynamic reliability analysis of nonlinear structures using a Duffingsystembased equivalent nonlinear system method Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200820
Zhenhao Zhang; Minhan Liu; Mingliao Zhou; Jigong ChenTo improve the analysis accuracy of dynamic reliability of a nonlinear system, an equivalent nonlinear system method is presented. In this method, general nonlinear systems are converted to equivalent Duffing nonlinear systems according to the minimum mean square error criterion, whose exact analytical solution of the random steadystate responses can be determined by a FokkerPlanckKolmogorov equation

Algebraic aspects and coherence conditions for conjoined and disjoined conditionals Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200819
Angelo Gilio; Giuseppe SanfilippoWe deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known properties, valid in the case of unconditional events, still hold in our approach to logical operations among conditional events. In particular we prove a decomposition

Notes on the lattice of fuzzy rough sets with crisp reference sets Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200820
Dávid Gégény; László Kovács; Sándor RadeleczkiSince the theory of rough sets was introduced by Zdzislaw Pawlak, several approaches have been proposed to combine rough set theory with fuzzy set theory. In this paper, we examine one of these approaches, namely fuzzy rough sets with crisp reference sets, from a latticetheoretic point of view. We connect the lower and upper approximations of a fuzzy relation R to the approximations of the core and

Deterministic and stochastic damage detection via dynamic response analysis Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200820
Michael Oberguggenberger; Martin SchwarzThe paper proposes a method of damage detection in elastic materials, which is based on analyzing the timedependent (dynamic) response of the material excited by an acoustic signal. A case study is presented consisting of experimental measurements and their mathematical analysis. The decisive parameters (wave speed and damping coefficient) of a mathematical model of the acoustic wave are calibrated

Couple fuzzy covering rough set models and their generalizations to CCD lattices Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200819
Liwen MaWe make gradual generalizations in this paper, from the concepts of twin approximation operators in covering rough set theory to the concepts of couple fuzzy covering rough set models in fuzzy rough set theory, and further to the concepts of couple Lfuzzy covering rough set models in Lfuzzy rough set theory. Given a fuzzy covering approximation space (U,C˜) and β∈(0,1], for each x∈U, we divide C˜

nDimensional (S,N)implications. Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200812
Rosana Zanotelli,Renata Reiser,Benjamin BedregalThe ndimensional fuzzy logic (nDFL) has been contributed to overcome the insufficiency of traditional fuzzy logic in modeling imperfect and imprecise information, coming from different opinions of many experts by considering the possibility to model not only ordered but also repeated membership degrees. Thus, nDFL provides a consolidated logical strategy for applied technologies since the ordered

Fuzzy βcovering approximation spaces Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200817
Xiaohong Zhang; Jingqian WangAll fuzzy coveringbased rough set models are constructed under a corresponding fuzzy covering approximation space (FCAS). The fuzzy βcovering approximation space (βFCAS) is a generalization of the FCAS through replacing the value 1 with a parameter β. In other words, the βFCAS is the basis of studying fuzzy coveringbased rough sets and their applications. Therefore, it is necessary to study some

On generating random Gaussian graphical models Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200812
Irene Córdoba; Gherardo Varando; Concha Bielza; Pedro LarrañagaStructure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In order to ensure positive definiteness in (ii), a dominant diagonal is usually imposed. In this work we investigate different methods to generate random symmetric

The joy of Probabilistic Answer Set Programming: Semantics, complexity, expressivity, inference Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200731
Fabio Gagliardi Cozman; Denis Deratani MauáProbabilistic Answer Set Programming (PASP) combines rules, facts, and independent probabilistic facts. We argue that a very useful modeling paradigm is obtained by adopting a particular semantics for PASP, where one associates a credal set with each consistent program. We examine the basic properties of PASP under this credal semantics, in particular presenting novel results on its complexity and

Heuristicbased feature selection for rough set approach Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200804
U. Stańczyk; B. ZieloskoThe paper presents the proposed research methodology, dedicated to the application of greedy heuristics as a way of gathering information about available features. Discovered knowledge, represented in the form of generated decision rules, was employed to support feature selection and reduction process for induction of decision rules with classical rough set approach. Observations were executed over

Constructions of overlap functions on bounded lattices Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200806
Haiwei WangIn this paper, we present two methods for constructing new overlap functions on bounded lattices from given ones. At first, we introduce the notion of overlap functions on bounded lattices, which is a generalization of overlap functions on the real unit interval. Then we provide the ∧extension of an overlap function on a subinterval and give the necessary and sufficient conditions for the ∧extension

BWM and MULTIMOORAbased multigranulation sequential threeway decision model for multiattribute group decisionmaking problem Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200731
Ying Wang; Bingzhen Sun; Xinrui Zhang; Qian WangThis paper proposes a sequential threeway decisionmaking approach based on BWM (bestworst method) and MULTIMOORA for multiple levels of granularity to deal with the multiattribute group decisionmaking problems under uncertainty. First, using BWM to preprocess the attribute indicators of the decision problem, the relationship between the criteria important for decision problem is determined. Then

The Fuzzy Logic Programming language FASILL: Design and implementation Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200725
Pascual JuliánIranzo; Ginés Moreno; José Antonio RiazaThe FASILL programming language (acronym of “Fuzzy Aggregators and Similarity Into a Logic Language”) combines a weak unification algorithm, based on similarity relations, along with a rich repertoire of fuzzy connectives and aggregators, whose truth functions can be defined on a complete lattice. In this work, we want to provide a unified view of the fundamental concepts and ideas that inspired its

Observational nonidentifiability, generalized likelihood and free energy Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200707
A.E. AllahverdyanWe study the parameter estimation problem in mixture distributions with observational nonidentifiability: the full distribution (also containing hidden variables) is identifiable, but the marginal (observed) distribution is not. Hence global maxima of the marginal likelihood are (infinitely) degenerate and predictions of the marginal likelihood are not unique. We show how to generalize the marginal

Toward a DempsterShafer theory of concepts Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200702
Sabine Frittella; Krishna Manoorkar; Alessandra Palmigiano; Apostolos Tzimoulis; Nachoem WijnbergIn this paper, we generalize the basic notions and results of DempsterShafer theory from predicates to formal concepts. Results include the representation of conceptual belief functions as inner measures of suitable probability functions, and a DempsterShafer rule of combination on belief functions on formal concepts.

Tractable inference in credal sentential decision diagrams Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200709
Lilith Mattei; Alessandro Antonucci; Denis Deratani Mauá; Alessandro Facchini; Julissa Villanueva LlerenaProbabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of Boolean variables, that are also consistent with the logical constraints defined by the circuit. The probabilities in such a model are usually “learned” from a set of

Modelling epistemic irrelevance with choice functions Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200708
Arthur Van Camp; Enrique MirandaWe consider coherent choice functions under the recent axiomatisation proposed by De Bock and de Cooman that guarantees a representation in terms of binary preferences, and we discuss how to define conditioning in this framework. In a multivariate context, we propose a notion of marginalisation, and its inverse operation called weak (cylindrical) extension. We combine this with our definition of conditioning

An axiomatic framework for influence diagram computation with partially ordered preferences Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200708
Nic Wilson; Radu MarinescuThis paper presents an axiomatic framework for influence diagram computation, which allows reasoning with partially ordered values of utility. We show how an algorithm based on sequential variable elimination can be used to compute the set of maximal values of expected utility (up to an equivalence relation). Formalisms subsumed by the framework include decision making under uncertainty based on multiobjective

Distributivity between extended nullnorms and uninorms on fuzzy truth values Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200709
Xueping Wang; Zhiqiang LiuThis paper mainly investigates the distributive laws between extended nullnorms and uninorms on fuzzy truth values under the condition that the nullnorm is conditionally distributive over the uninorm. It presents the distributive laws between the extended nullnorm and tconorm, and the left and right distributive laws between the extended generalized nullnorm and uninorm, where a generalized nullnorm

An intervalvalued utility theory for decision making with DempsterShafer belief functions Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200701
Thierry Denœux; Prakash P. ShenoyThe main goal of this paper is to describe an axiomatic utility theory for DempsterShafer belief function lotteries. The axiomatic framework used is analogous to von NeumannMorgenstern's utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to intervalvalued utilities, and therefore, to a partial (incomplete) preference

Threeway decision models based on multigranulation support intuitionistic fuzzy rough sets Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200630
Zhan'ao Xue; Liping Zhao; Lin Sun; Min Zhang; Tianyu XueTo capture the influence of various uncertain factors during delayed decisionmaking, support intuitionistic fuzzy sets (SIFSs) are introduced for threeway decisions (TWDs) to study this topic from the perspective of multigranulation. First, the concepts of support intuitionistic fuzzy rough sets are defined, and their related properties are discussed. Then, we combine support intuitionistic fuzzy

Type2 fuzzy multigranulation rough sets Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200702
Juan LuAiming at expanding the application range of the multigranulation rough set (MGRS) theory, a type2 fuzzy multigranulation rough set (T2FMGRS) model is proposed by combining type2 fuzzy sets with multigranulation rough sets (MGRSs) in this paper. At first, definitions and properties of optimistic and pessimistic type2 fuzzy multigranulation rough sets (T2FMGRSs) are introduced. Then, the rough measure

On the approximation of a membership function by empirical quantile functions Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200708
Maria Letizia Guerra; Laerte Sorini; Luciano StefaniniThe Average Cumulative representation of fuzzy intervals is connected with the possibility theory in the sense that the possibility and necessity functions are substituted by a pair of non decreasing functions defined as the positive and negative variations in the Jordan decomposition of a membership function. In this paper we motivate the crucial role of ACF in determining the membership function

Consistent projections and indicators in pairwise comparisons Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200625
Ryszard Smarzewski; Przemysław RutkaThis study examines several generic properties of weighted consistent projections and indicators of inconsistency in an arbitrary finite dimensional inner product space of square matrices. In the case of weighted Frobenius inner products we present explicit formulae for them in terms of the matrix entries and weights. It extends the recent results, due to Koczkodaj et al. [Fund. Inform. 172 (2020)

Entropy and monotonicity in artificial intelligence Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200530
Bernadette BouchonMeunier; Christophe MarsalaEntropies and measures of information are extensively used in several domains and applications in Artificial Intelligence. Among the original quantities from Information theory and Probability theory, a lot of extensions have been introduced to take into account fuzzy sets, intuitionistic fuzzy sets and other representation models of uncertainty and imprecision. In this paper, we propose a study of

Dynamic Łukasiewicz Logic and Dynamic MValgebras Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200629
Antonio Di Nola; Revaz Grigolia; Gaetano VitaleFollowing K. Segerberg [22], D. Kozen [15] and V. Pratt [19], who have been introduced dynamic propositional logic and dynamic algebras, dynamic propositional Łukasiewicz logic DPŁ (dynamic nvalued propositional Łukasiewicz logic DPŁn) and dynamic MValgebras (dynamic MVnalgebras) are introduced and theories of the logic DPŁ (DPŁn) and dynamic MValgebras (MVnalgebras) are developed. Dynamic MValgebras

Discriminative training of feedforward and recurrent sumproduct networks by extended BaumWelch Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200618
Haonan Duan; Abdullah Rashwan; Pascal Poupart; Zhitang ChenWe present a discriminative learning algorithm for feedforward SumProduct Networks (SPNs) [42] and recurrent SPNs [31] based on the Extended BaumWelch (EBW) algorithm [4]. We formulate the conditional data likelihood in the SPN framework as a rational function, and we use EBW to monotonically maximize it. We derive the algorithm for SPNs and RSPNs with both discrete and continuous variables. The

New results of fuzzy implications satisfying I(x,I(y,z))=I(I(x,y),I(x,z)) Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200620
Zuming Peng; Cong PengCruz et al. (2018) [10] investigated the fuzzy generalization of Frege's Law: x→(y→z)≡(x→y)→(x→z), i.e., I(x,I(y,z))=I(I(x,y),I(x,z)), which is called generalized Frege's Law. They showed conditions such that the generalized Frege's Law holds for (S,N)implications (R, QL, D, (T,N), H, respectively). In this paper, firstly, a new necessary condition such that the generalized Frege's Law holds

On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200612
W.W. Koczkodaj; F. Liu; V.W. Marek; J. Mazurek; M. Mazurek; L. Mikhailov; C. Özel; W. Pedrycz; A. Przelaskowski; A. Schumann; R. Smarzewski; D. Strzalka; J. Szybowski; Y. YayliThis paper examines the constricted use of group theory in the study of pairwise comparisons. The presented approach is based on the application of the celebrated Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation for multiplicative (ratio) pairwise comparisons is provided. Counterexamples are provided to support the theory. In our opinion, the scientific community must

Granulation in Rough Set Theory: A novel perspective Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200602
José Luis VelázquezRodríguez; Yenny VilluendasRey; Cornelio YáñezMárquez; Itzamá LópezYáñez; Oscar CamachoNietoConsidering data from different perspectives (views or granulations) is very common in several applications nowadays. Unfortunately, Rough Sets lack of effective tools for handling multiple granulation in mixed and incomplete information systems. This paper introduces a novel approach for dealing with such information systems: The Parameterized Granulation. The demonstration of some of the properties

Doublequantitative variable consistency dominancebased rough set approach Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200601
Wentao Li; Xiaoping Xue; Weihua Xu; Tao Zhan; Bingjiao FanRough set model with double quantification satisfies the requirement of quantitative information in practical applications, it has better fault tolerance than probabilistic rough set model considering only relative quantification and graded rough set model considering only absolute quantification. In this paper, two kinds of consistency levels are introduced from the perspective of double quantification

New twosided confidence intervals for binomial inference derived using Walley's imprecise posterior likelihood as a test statistic Int. J. Approx. Reason. (IF 2.678) Pub Date : 20200529
Michael Scott BalchStarting with the Sterne's confidence regions, there have been a string of related attempts to improve on the twosided Clopper–Pearson bounds for binomial inference. That work is brought to fruition using Walley's imprecise posterior likelihood as the basis for a new test statistic. The results are expressed as a consonant confidence structure, from which a new set of exact confidence intervals for