Iranian journal of fuzzy systems
Volume:16 Issue: 5, Sep-Oct 2019

The main aim of this paper is to present a novel method for ranking hesitant fuzzy sets (HFSs) based on transforming HFSs into fuzzy sets (FSs). The idea behind the method is an interesting HFS decomposition which is referred here to as the horizontal representation in the current study. To show the validity of the proposed ranking method, we apply it to solve a multi-attribute decision-making problem under hesitant fuzzy environment.Interestingly, the results show that the proposedmethod gives the most accepted precedence of alternatives in comparison with the other existingmethods.

Due to the complexities of objects and the vagueness of the human mind, it has attracted considerable attention from researchers studying fuzzy classification algorithms. In this paper, we propose a concept of fuzzy relative entropy to measure the divergence between two fuzzy sets. Applying fuzzy relative entropy, we prove the conclusion that patterns with high fuzziness are close to the classification boundary. Thus, it plays a great role in classification problems that patterns  with high fuzziness are classified correctly. Meanwhile, we draw a conclusion that the fuzziness of a pattern and the uncertainty of its class label are equivalent. As is well known, entropy not only measures the uncertainty of random variable, but also represents the amount of information carried by the variable. Hence, a fuzzy classifier with high fuzziness would  carry much information about training set. Therefore, in addition to some assessment criteria such as classification accuracy, we could study the classification performance from the perspective of the fuzziness of classifier. In order to try to ensure the objectivity in dealing with unseen patterns, we should make full use of information of the known pattern set and do not make too much subjective assumptions in the process of learning. Consequently,  for problems with rather complex decision boundaries especially, under the condition that a certain training accuracy threshold is maintained, we demonstrate that a fuzzy classifier with high fuzziness would have a well generalization performance.

Srivastava and Maheshwari (Iranian Journal of Fuzzy Systems 13(1)(2016) 25-44) introduced a new divergence measure for intuitionisticfuzzy sets (IFSs). The properties of the proposed divergence measurewere studied and the efficiency of the proposed divergence measurein the context of medical diagnosis was also demonstrated. In thisnote, we point out some errors in the proving process of twoproperties of the proposed divergence measure. Then we give amodification of the proving process.

In this paper, the fuzzy matrix equation $Awidetilde{X}B=widetilde{C}$ in which $A,B$ are $n times n$crisp matrices respectively and $widetilde{C}$ is an $n times n$ arbitrary LR fuzzy numbers matrix, is investigated. A new numerical procedure for calculating the fuzzy solution is designed and a sufficient condition for the existence of strong fuzzy solution is derived. Some examples are given to illustrate the proposed method.

Information Overloadrq  is not a new term but with the massive development in technology which enables anytime, anywhere, easy and unlimited access; participation & publishing of information has consequently escalated its impact. Assisting userslq    informational searches with reduced reading surfing time by extracting and evaluating accurate, authentic & relevant information are the primary concerns in the present milieu.  Automatic text summarization is the process of condensing an original document into shorter form to create smaller, compact version from the abundant information that is available, preserving the content & meaning such that it meets the needs of the user. Though many summarization techniques have been proposed but there are no lq silver bulletsrq   to achieve the superlative results as of human generated summaries. Thus, the domain of text summarization is an active and dynamic field of study, practice & research with the continuous need to expound novel techniques for achieving comparable & effectual results. Fuzzy logic has appeared as a powerful theoretical framework for studying human reasoning and its application has been explored within the domain of text summarization in the past few years. This paper is a systematic literature review to gather, analyze, and report the trends, gaps and prospects of using fuzzy logic for automatic text summarization on the basis of the findings in original studies.

This article introduces a general framework of multi-granulation fuzzy probabilistic roughsets (MG-FPRSs) models in multi-granulation fuzzy probabilistic approximation space over twouniverses. Four types of MG-FPRSs are established, by the four different conditional probabilitiesof fuzzy event. For different constraints on parameters, we obtain four kinds of each type MG-FPRSsover two universes. To find a suitable way of explaining and determining these parameters in eachkind of each type MG-FPRS, three-way decisions (3WDs) are studied based on Bayesian minimum-riskprocedure, i.e., the decision-theoretic rough set (DTRS) approach. The main contribution of this paperis twofold. One is to extend the fuzzy probabilistic rough set (FPRS) to MG-FPRS model over two universes.Another is to present an approach to select parameters in MG-FPRS modeling by using the process ofdecision-making under conditions of risk.

The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alpha-$univex fuzzy mappings and get some properties. In the last, we derive necessary and sufficient Karush-Kuhn-Tucker conditions and its dual problems with generalized differentiable $alpha-$univex fuzzy mappings for fuzzy constrained programming problem.

This paper addresses the problem of adaptive fuzzy tracking control for aclass of nonlinearly parameterized systems with unknown control directions.In this paper, the nonlinearly parameterized functions are lumped into the unknown continuous functionswhich can be approximated by using the fuzzy logic systems (FLS) in Mamdani type. Then, the Nussbaum-type function is used to detect the unknown control direction and based on the backstepping technique, the adaptive fuzzycontroller is designed. The main advantages of this paper are that (1) in the existing results the separation principle is used to deal with the nonlinearly parameterized functions, unlike them in this paper, the FLS are applied to approximate the nonlinearly parameterized functions, (2) by using the minimal learning parameters (MLP) algorithm, onlyone parameter needs to be adjusted online in the controller design procedure, which reduces the onlinecomputation burden greatly, (3) the Nussbaum-gain technique is introduced to resolve the unknown control direction problems. It is proven that the proposed control scheme renders the closed-loopsystem stable in the sense of semiglobal uniformly ultimately bounded (UUB). Finally, simulation results are provided to show the effectiveness of the proposed approach.

This paper addresses a behavior-based fuzzy controller (BFC) for mobile robot wall-following control.The wall-following task is usually used to explore an unknown environment.The proposed BFC consists of three sub-fuzzy controllers, including Straight-based Fuzzy Controller (SFC),Left-based Fuzzy Controller (LFC), and Right-based Fuzzy Controller (RFC).The proposed wall-following controller has three characteristics: the mobile robot keeps a distance from the wall,the mobile robot has a high moving velocity, and the mobile robot has a good robustness ability of disturbance.The proposed BFC will be used to control the real mobile robot.The Pioneer 3-DX mobile robot has sonar sensors in front and sides, and it is used in this study.The inputs of BFC are sonar sensors data and the outputs of BFC are robot¡¦s left/right wheel speed.Experimental results show that the proposed BFC successfully performs the mobile robot wall-following taskin a real unknown environment.

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such as Modus Ponens(MP) rule, Hypothetical Syllogism(HS) rule and completeness, etc. Especially, we provide two ways to prove the completeness of this logic system. We also introduce two extensions of equality propositional logic. The first one is involutive equality propositional logic, which is equality propositional logic with double negation. The second one adds prelinearity which is rich enough to enjoy the strong completeness property. Finally, we introduce additional connective $Delta$(delta) in equality propositional logic and demonstrate that the resulting logic holds soundness and completeness.

In this paper, it is shown that the category of stratified $L$-generalized convergence spaces is monoidal closed if the underlying truth-value table $L$ is a complete residuated lattice. In particular, if the underlying truth-value table $L$ is a complete Heyting Algebra, the Cartesian closedness of the category is recaptured by our result.

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for each dimension, a fuzzy membership grade is assigned to each tree. We study MFFTA by extending some classical problems and properties of automata and regular languages such as determinization, reduction, duality and operations on languages. Furthermore, we provided the method of converting every complete fuzzy tree automata to an MFFTA as well as an example to show the efficiency of MFFTA in comparison to FFTA.}

This study has developed a production inventory model where the cycle timeis fuzzy, the existence of defective products is assumed in each batch andproduct screening is performed both in-production and after-production.Triangular fuzzy numbers serve to model uncertainties in the cycle time, anda fuzzified total inventory profit function is created by thedefuzzification method known as the signed distance method. The classicalapproach is used to determine the optimal policy, with the ideal cycle timematched to the total profit. Although assuming asymmetric triangular fuzzynumbers prevents the calculation of a clear analytical solution, the methodapproaches as closely as possible to an analytical solution. A numericalsolution to only one equation is needed to obtain the optimal configuration.Conversely, there is a positive trade-off, with an analytical solution tothe optimization problem if there is an assumption of symmetrical triangularfuzzy numbers. The proposed model is illustrated by a numerical example. Thepaper presents results and sensitivity analyses, in both tables and graphicillustrations. The effects on total profit are discussed in relation tovarious parameters. From the numerical studies, it is observed that thelevel of fuzziness influences the cycle time and an approximately linearrelationship, in the opposite direction, was found between the total profitand the level of fuzziness, when it was increased.

By using an efficient partial order and concept of gH-differentiability oninterval-valued functions, we investigate some new variants of Gronwall typeinequalities on time scales, which provide explicit bounds on unknownfunctions. Our results not only unify and extend some continuousinequalities, but also in discrete case, all are new.