فهرست مطالب
Transactions on Fuzzy Sets and Systems
Volume:2 Issue: 2, Fall  Winter 2023
 تاریخ انتشار: 1402/08/10
 تعداد عناوین: 12

Pages 114The United Nation's Sustainable Development Goals encourage countries to solve many social problems. One of these problems is homelessness. We consider those goals which are most pertinent to homelessness according to \cite{13}. We rank countries with respect to the achievement of these goals. We use fuzzy similarity measures to determine the degree of similarity between these rankings. We use three methods to rank the counties, namely, the Analytic Hierarchy Process, the Guiasu method, and the Yen method. Overall scores of categories in some basic research papers pertaining to Sustainable Development Goals were obtained by using multiplication of the scores of the category's targets. Multiplication was used to agree with the philosophy that in order for a high score to be obtained, all targets must have a high score. To support this philosophy in the decision process, we use the $t$norms bounded difference, algebraic product, and standard intersection as experts. We also suggest a way the techniques used here can be extended to nonstandard analysis.Keywords: Homelessness, Sustainable development goals, Analytic hierarchy process, Fuzzy similarity measures, Country rankings

Pages 1538Here we research the univariate fuzzy ordinary and fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasiinterpolation general sigmoid activation function relied on fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the function, or of the right and left Caputo fuzzy fractional derivatives of the involved function. The approximations are fuzzy pointwise and fuzzy uniform. The related feedforward fuzzy neural networks are with one hidden layer. We study in particular the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional approximation result using higher order fuzzy differentiation converges better than in the fuzzy just continuous case.Keywords: General sigmoid activation function, Neural network fuzzy fractional approximation, Fuzzy quasiinterpolation operator, Fuzzy modulus of continuity, Fuzzy derivative, fuzzy fractional derivative

Pages 3962In real life, structural problems can be described in linear and nonlinear forms. This nonlinear structural problem is very challenging to solve when its all parameters are imprecise in nature. Intuitionistic fuzzy sets were proposed to manage circumstances in which experts have some membership and nonmembership value to judge an option. Hesitant fuzzy sets were used to manage scenarios in which experts pause between many possible membership values while evaluating an alternative. A new growing area of a generalized fuzzy set theory called intuitionistic hesitant fuzzy set (IHFS) provides useful tools for dealing with uncertainty in structural design problem that is observed in the actual world. In this article, we have developed a procedure to solve nonlinear structural problem in an intuitionistic hesitant fuzzy (IHF) environment. The concept of an intuitionistic hesitant fuzzy set is introduced to provide a computational basis to manage the situations in which experts assess an alternative in possible membership values and nonmembership values. This important feature is not available in the intuitionistic fuzzy optimization technique. Here we have discussed the solution procedure of intuitionistic hesitant fuzzy optimization technique dedicatedly for linear, exponential, and hyperbolic types of membership and nonmembership functions. Some theoretical development based on these functions has been discussed. A numerical illustration is given to justify the effectiveness and efficiency of the proposed method in comparison with fuzzy multiobjective nonlinear programming method and intuitionistic fuzzy multiobjective nonlinear programming method. Finally, based on the proposed work, conclusions and future research directions are addressed.Keywords: Multi objective structural problem, Hesitant fuzzy set, Intuitionistic fuzzy optimization, Intuitionistichesitant fuzzy optimization, Pareto optimal solution

Pages 6376This paper has a twofold goal: The first is to study how the inferential zigzag can be activated, even computationally, trying to analyse what kind of reasoning consists of, where its 'mechanism' is rooted, how it can be activated since without all this it can just seem a metaphysical idea. The second, not so deeply different  as it can be presumed at a first view  but complementary, is to explore the subject's link with the old thought on conjectures of the 15th Century Theologist and Philosopher Nicolaus Cusanus who was the first thinker consciously and extensively using conjectures.Keywords: Commonsense reasoning, Language at work, Inferential zigzag, 'Out of logic'

Pages 77112Recently, Gautama algebras were defined and investigated as a common generalization of the variety $\mathbb{RDBLS}\rm t$ of regular double Stone algebras and the variety $\mathbb{RKLS}\rm t$ of regular Kleene Stone algebras, both of which are, in turn, generalizations of Boolean algebras. Those algebras were named in honor and memory of the two founders of Indian Logic{\bf Akshapada Gautama} and {\bf Medhatithi Gautama}. The purpose of this paper is to define and investigate a generalization of Gautama algebras, called ``Almost Gautama algebras ($\mathbb{AG}$, for short).'' More precisely, we give an explicit description of subdirectly irreducible Almost Gautama algebras. As consequences, explicit description of the lattice of subvarieties of $\mathbb{AG}$ and the equational bases for all its subvarieties are given. It is also shown that the variety $\mathbb{AG}$ is a discriminator variety. Next, we consider logicizing $\mathbb{AG}$; but the variety $\mathbb{AG}$ lacks an implication operation. We, therefore, introduce another variety of algebras called ``Almost Gautama Heyting algebras'' ($\mathbb{AGH}$, for short) and show that the variety $\mathbb{AGH}$ %of Almost Heyting algebras is termequivalent to that of $\mathbb{AG}$. Next, a propositional logic, called $\mathcal{AG}$ (or $\mathcal{AGH}$), is defined and shown to be algebraizable (in the sense of Blok and Pigozzi) with the variety $\mathbb{AG}$, via $\mathbb{AGH},$ as its equivalent algebraic semantics (up to term equivalence). All axiomatic extensions of the logic $\mathcal{AG}$, corresponding to all the subvarieties of $\mathbb{AG}$ are given. They include the axiomatic extensions $\mathcal{RDBLS}t$, $\mathcal{RKLS}t$ and $\mathcal{G}$ of the logic $\mathcal{AG}$ corresponding to the varieties $\mathbb{RDBLS}\rm t$, $\mathbb{RKLS}\rm t$, and $\mathbb{G}$ (of Gautama algebras), respectively. It is also deduced that none of the axiomatic extensions of $\mathcal{AG}$ has the Disjunction Property. Finally, We revisit the classical logic with strong negation $\mathcal{CN}$ and classical Nelson algebras $\mathbb{CN}$ introduced by Vakarelov in 1977 and improve his results by showing that $\mathcal{CN}$ is algebraizable with $\mathbb{CN}$ as its algebraic semantics and that the logics $\mathcal{RKLS}\rm t$, $\mathcal{RKLS}\rm t\mathcal{H}$, 3valued \L ukasivicz logic and the classical logic with strong negation are all equivalent.Keywords: Regular double Stone algebra, regular Kleene Stone algebra, Gautama algebra, Almost Gautama algebra, Almost Gautama Heyting algebra, subdirectly irreducible algebra, simple algebra, logic $, mathcal{AG}$, logic $, mathcal{G}$, logic $, mathcal{RDBLS}t$, logic $, mathcal{RKLS}t$

Pages 113126After the introduction of the concept of fuzzy sets by Zadeh, several researches were conducted on the generalizations of the notion of fuzzy sets. There are many viewpoints on the notion of metric space in fuzzy topology. One of the most important problems in fuzzy topology is obtaining an appropriate concept of fuzzy metric space. This problem has been investigated by many authors from different points of view. Atanassov gives the concept of the intuitionistic fuzzy set as a generalization of the fuzzy set. Park introduced the notion of intuitionistic fuzzy metric space as a natural generalization of fuzzy metric spaces due to George and Veeramani. This paper introduces the concept of intuitionistic fuzzy modular space. Afterward, a Hausdorff topology induced by a $\delta$homogeneous intuitionistic fuzzy modular is defined and some related topological properties are also examined. After giving the fundamental definitions and the necessary examples, we introduce the definitions of intuitionistic fuzzy boundedness, intuitionistic fuzzy compactness, and intuitionistic fuzzy convergence, and obtain several preservation properties and some characterizations concerning them. Also, we investigate the relationship between an intuitionistic fuzzy modular and an intuitionistic fuzzy metric. Finally, we prove some known results of metric spaces including Baire’s theorem and the Uniform limit theorem for intuitionistic fuzzy modular spaces.Keywords: fuzzy set, modular space, Fuzzy modular space, Intuitionistic fuzzy modular space

Pages 127136We define and study two completeness notions for saturated $\mathsf{L}$quasiuniform limit spaces. The one, that we term Lawvere completeness, is defined using the concept of promodule and lends a lax algebraic interpretation of completeness also for saturated $\mathsf{L}$quasiuniform limit spaces. The other, termed Cauchy completeness, is defined using saturated Cauchy pair prefilters. We show that both concepts coincide with related notions in the case of saturated $\mathsf{L}$quasiuniform spaces and that also for saturated $\mathsf{L}$quasiuniform limit spaces, both completeness notions are equivalent.Keywords: Saturated prefilter, Saturated Lquasiuniform limit space, Completeness

Pages 137154This paper develops the notion of fuzzy ideal and generalized fuzzy ideal on double Boolean algebra (dBa). According to Rudolf Wille, a double Boolean algebra $\underline{D}:=(D, \sqcap, \sqcup, \neg, \lrcorner, \bot, \top)$ is an algebra of type $(2, 2, 1, 1, 0, 0),$ which satisfies a set of properties. This algebraic structure aimed to capture the equational theory of the algebra of protoconcepts. We show that collections of fuzzy ideals and generalized fuzzy ideals are endowed with lattice structures. We further prove that (by isomorphism) lattice structures obtained from fuzzy ideals and generalized fuzzy ideals of a double Boolean algebra D can entirely be determined by sets of fuzzy ideals and generalized fuzzy ideals of the Boolean algebra $D_{\sqcup}.$Keywords: Double Boolean algebras, Fuzzy ideals, Fuzzy primary ideal

Pages 155183Cloudbased machine learning tools for enhanced Big Data applications}, where the main idea is that of predicting the ``\emph{next}'' \emph{workload} occurring against the target Cloud infrastructure via an innovative \emph{ensemblebased approach} that combines the effectiveness of different wellknown \emph{classifiers} in order to enhance the whole accuracy of the final classification, which is very relevant at now in the specific context of \emph{Big Data}. The socalled \emph{workload categorization problem} plays a critical role in improving the efficiency and reliability of Cloudbased big data applications. Implementationwise, our method proposes deploying Cloud entities that participate in the distributed classification approach on top of \emph{virtual machines}, which represent classical ``commodity'' settings for Cloudbased big data applications. Given a number of known reference workloads, and an unknown workload, in this paper we deal with the problem of finding the reference workload which is most similar to the unknown one. The depicted scenario turns out to be useful in a plethora of modern information system applications. We name this problem as \emph{coarsegrained workload classification}, because, instead of characterizing the unknown workload in terms of finer behaviors, such as CPU, memory, disk, or network intensive patterns, we classify the whole unknown workload as one of the (possible) reference workloads. Reference workloads represent a category of workloads that are relevant in a given applicative environment. In particular, we focus our attention on the classification problem described above in the special case represented by \emph{virtualized environments}. Today, \emph{Virtual Machines} (VMs) have become very popular because they offer important advantages to modern computing environments such as cloud computing or server farms. In virtualization frameworks, workload classification is very useful for accounting, security reasons, or user profiling. Hence, our research makes more sense in such environments, and it turns out to be very useful in a special context like Cloud Computing, which is emerging now. In this respect, our approach consists of running several machine learningbased classifiers of different workload models, and then deriving the best classifier produced by the \emph{DempsterShafer Fusion}, in order to magnify the accuracy of the final classification. Experimental assessment and analysis clearly confirm the benefits derived from our classification framework. The running programs which produce unknown workloads to be classified are treated in a similar way. A fundamental aspect of this paper concerns the successful use of data fusion in workload classification. Different types of metrics are in fact fused together using the DempsterShafer theory of evidence combination, giving a classification accuracy of slightly less than $80\%$. The acquisition of data from the running process, the preprocessing algorithms, and the workload classification are described in detail. Various classical algorithms have been used for classification to classify the workloads, and the results are compared.Keywords: Virtual machines, Workload, DempsterShafer theory, Classification

Pages 184193In this paper we consider MValgebras and their prime spectrum. We show that there is an uncountable MValgebra that has the same spectrum as the free MValgebra over one element, that is, the MValgebra $Free_1$ of McNaughton functions from $[0,1]$ to $[0,1]$, the continuous, piecewise linear functions with integer coefficients. The construction is heavily based on Mundici equivalence between MValgebras and lattice ordered abelian groups with the strong unit. Also, we heavily use the fact that two MValgebras have the same spectrum if and only if their lattice of principal ideals is isomorphic.As an intermediate step we consider the MValgebra $A_1$ of continuous, piecewise linear functions with rational coefficients. It is known that $A_1$ contains $Free_1$, and that $A_1$ and $Free_1$ are equispectral. However, $A_1$ is in some sense easy to work with than $Free_1$. Now, $A_1$ is still countable. To build an equispectral uncountable MValgebra $A_2$, we consider certain ``almost rational'' functions on $[0,1]$, which are rational in every initial segment of $[0,1]$, but which can have an irrational limit in $1$.We exploit heavily, via Mundici equivalence, the properties of divisible lattice ordered abelian groups, which have an additional structure of vector spaces over the rational field.Keywords: MValgebras, Prime spectrum, Lattice ordered abelian groups

Pages 194218As users in an online social network are overwhelmed by the abundant amount of information, it is very hard to retrieve the preferred or required content. In this context, an online recommender system helps to filter and recommend content such as people,items or services. But, in a real scenario, people rely more on recommendations from trusted sources than distrusting sources. Though, there are many trust based recommender systems that exist, it lag in prediction error. In order to improve the accuracy of the prediction, this paper proposes a TrustBoosted Recommender System (TBRS). Since, the provenance derives the trust in a better way than other approaches, TBRS is built from the provenance concept. The proposed recommender system takes the provenance based fuzzy rules which were derived from the Fuzzy Decision Tree. TBRS then computes the multiattribute vector similarity score and boosts the score with trust weight. This system is tested on the bookreview dataset to recommend the topk trustworthy reviewers.The performance of the proposed method is evaluated in terms of MAE and RMSE. The result shows that the error value of boosted similarity is lesser than without boost. The reduced error rates of the Jaccard, Dice and Cosine similarity measures are 18\%, 15\% and 7\% respectively. Also, when the model is subjected to failure analysis, it gives better performance for unskewed data than slewed data. The models fbest, average and worst case predictions are 90\%, 50\% and $<$23\% respectively.Keywords: Social network, Provenance, Trust, Fuzzy rule, Fuzzy vector space, Multiattribute

Pages 219228In fuzzy set theory, the concept of a nonmembership function and the hesitation margin were not considered while these two concepts have been included along with the membership function for intuitionistic fuzzy sets. It is also to be noted that the intuitionistic fuzzy set is reflected as an extension of the fuzzy set accommodating both membership and nonmembership functions together with a hesitation margin. In the intuitionistic fuzzy set theory, the sum of the membership function and the nonmembership function is a value between 0 and 1. In recent times, intuitionistic fuzzy rough set theory has emerged as a powerful tool for dealing with imprecision and uncertain information in relational database theory. Measures of similarity between fuzzy rough sets as well as intuitionistic fuzzy rough sets provide wide applications in reallife problems and that is why many researchers paid more attention to this concept. Intuitionistic fuzzy rough set theory behaves like an excellent tool to tackle impreciseness or uncertainties. In this paper, we propose a new approach of similarity measure on an intuitionistic fuzzy rough set based on a settheoretic approach. The proposed measure is able to give an exact result. In the application part, we consider a reallife problem for selecting a fair play awardwinning team in a cricket tournament and describe the algorithm.Keywords: Similarity measure, Intuitionistic fuzzy set, Rough set