Showing papers in "Journal of Intelligent and Fuzzy Systems in 2015"
TL;DR: This paper introduces a new generalized hierarchical FCM (GHFCM), which is more robust to image noise with the spatial constraints: the generalized mean, and introduces a more flexibility function which considers the distance function itself as a sub-FCM.
Abstract: Fuzzy c-means (FCM) has been considered as an effective algorithm for image segmentation. However, it still suffers from two problems: one is insufficient robustness to image noise, and the other is the Euclidean distance in FCM, which is sensitive to outliers. In this paper, we propose two new algorithms, generalized FCM (GFCM) and hierarchical FCM (HFCM), to solve these two problems. Traditional FCM can be considered as a linear combination of membership and distance from the expression of its mathematical formula. GFCM is generated by applying generalized mean on these two items. We impose generalized mean on membership to incorporate local spatial information and cluster information, and on distance function to incorporate local spatial information and image intensity value. Thus, our GFCM is more robust to image noise with the spatial constraints: the generalized mean. To solve the second problem caused by Euclidean distance (l2 norm), we introduce a more flexibility function which considers the distance function itself as a sub-FCM. Furthermore, the sub-FCM distance function in HFCM is general and flexible enough to deal with non-Euclidean data. Finally, we combine these two algorithms to introduce a new generalized hierarchical FCM (GHFCM). Experimental results demonstrate the improved robustness and effectiveness of the proposed algorithm.
434 citations
TL;DR: This paper presents a geometrical interpretation of picture fuzzy sets, and proposes correlation coefficients forPicture fuzzy sets which considers the degree of positive membership, degree of neutral membership,degree of negative membership and thedegree of refusal membership.
Abstract: Picture fuzzy sets are extension of Atanassov's intuitionistic fuzzy sets. Picture fuzzy set based models may be adequate in situations when we face human opinions involving more answers of types: yes, abstain, no, refusal. It can be considered as a powerful tool represent an uncertain information in the process of cluster analysis. In this paper, we present a geometrical interpretation of picture fuzzy sets. We propose correlation coefficients for picture fuzzy sets which considers the degree of positive membership, degree of neutral membership, degree of negative membership and the degree of refusal membership. Effectiveness of the proposed correlation coefficient has been established in a bidirectional approximate reasoning systems. We apply the correlation coefficient to clustering analysis under picture fuzzy environments. Advantages of proposed correlation coefficients and drawbacks of existing correlation coefficients have been discussed.
190 citations
TL;DR: The theory of fuzzy sets has delivered new tools for the analysis of such imprecise phenomena like consensus, which is a major aim of group decision making problems and has obtained a great attention in the literature.
Abstract: Group decision making is part of every organizational life. It is a type of participatory process in which multiple decision makers acting collectively, analyze problems, consider and evaluate several alternatives, and select from among the alternatives a solution. In such a situation, an important issue is the level of agreement or consensus achieved among the group of decision makers before obtaining the solution. In the beginning, consensus was meant as a full and unanimous agreement. Regrettably, this stringent concept of consensus in many cases is a utopia. As a result, and from a pragmatic point of view, it makes more sense to speak about a degree of consensus and, here, the theory of fuzzy sets has delivered new tools for the analysis of such imprecise phenomena like consensus. Given the significance of reaching an accepted solution by all the decision makers, consensus is a major aim of group decision making problems and, in such a way, it has obtained a great attention in the literature. However, there still exist several dares which have to be tackled by the researchers. The purpose of this paper is to bring out several issues that represent challenges that have to be faced.
180 citations
TL;DR: This paper demonstrates experimentally that samples with higher fuzziness outputted by the classifier mean a bigger risk of misclassification and proposes a fuzziness category based divide-and-conquer strategy which separates the high-fuzziness samples from the low fuzziness samples.
Abstract: This paper investigates a relationship between the fuzziness of a classifier and the misclassification rate of the classifier on a group of samples. For a given trained classifier that outputs a membership vector, we demonstrate experimentally that samples with higher fuzziness outputted by the classifier mean a bigger risk of misclassification. We then propose a fuzziness category based divide-and-conquer strategy which separates the high-fuzziness samples from the low fuzziness samples. A particular technique is used to handle the high-fuzziness samples for promoting the classifier performance. The reasonability of the approach is theoretically explained and its effectiveness is experimentally demonstrated.
156 citations
TL;DR: In this article, a neurosophic subsethood measure for single valued neutrosophic sets is introduced and an application is presented in multicriteria decision making problem and results obtained are discussed.
Abstract: The main aim of this paper is to introduce a neurosophic subsethood measure for single valued neutrosophic sets. For this purpose, we rst introduce a system of axioms for subsethood measure of single valued neutrosophic sets. Then we give a simple subsethood mea- sure based to distance measure. Finally, to show eectiveness of intended subsethood measure, an application is presented in multicriteria decision making problem and results obtained are discussed. Though having a simple measure for calculation, the subsethood measure presents a new approach to deal with neutrosophic information.
140 citations
TL;DR: An extended TOPSIS method for a multiple attribute group decision making problem based on the SVNLNs under single valued neutrosophic linguistic environment is developed and an illustrative example of investment alternatives is given.
Abstract: The paper proposes the concepts of a single valued neutrosophic linguistic set (SVNLS) and a single valued neutrosophic linguistic number (SVNLN) as a further generalization of the concepts of a linguistic variable, an intuitionistic linguistic set and an intuitionistic linguistic number (ILN). Then, we introduce the basic operational rules of SVNLNs and define a generalized distance measure between SVNLNs. Furthermore, we develop an extended TOPSIS method for a multiple attribute group decision making problem based on the SVNLNs under single valued neutrosophic linguistic environment. Finally, an illustrative example of investment alternatives and the comparative analysis are given to demonstrate the application and effectiveness of the developed approach.
125 citations
TL;DR: This paper defines three new operations on bipolar fuzzy graph, viz. direct product, semi strong product and strong product, and it is proved that any of the products of strong bipolar fuzzy graphs are strongipolar fuzzy graphs.
Abstract: Recently, bipolar fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. In this paper, at first we define three new operations on bipolar fuzzy graphs, viz. direct product, semi strong product and strong product. Likewise, sufficient conditions for each one of them to be complete are given. Also, it is proved that any of the products of strong bipolar fuzzy graphs are strong bipolar fuzzy graphs.
122 citations
TL;DR: The aim of this paper is to introduce the notion of a rough soft hemiring, which is an extended notion ofa rough hemiring and a soft hemires, and to study roughness in soft hemirings with respect to Pawlak approximation spaces.
Abstract: The aim of this paper is to introduce the notion of a rough soft hemiring, which is an extended notion of a rough hemiring and a soft hemiring. We study roughness in soft hemirings with respect to Pawlak approximation spaces. Some new rough soft operations are explored. In particular, lower and upper rough soft hemirings and k-idealistic, h-idealistic, strong h-idealistic idealistic soft hemirings are investigated. Finally, an important result on an upper strong h-idealistic rough soft hemiring via Bourne's congruence relations are obtained.
110 citations
TL;DR: This editorial presents a background of the special issue and a brief introduction to the 5 papers in this special issue on learning from big data with uncertainty.
Abstract: Focusing on learning from big data with uncertainty, this special issue includes 5 papers; this editorial presents a background of the special issue and a brief introduction to the 5 papers.
109 citations
TL;DR: In this article, a decision making method, called NSM-decision making, based on the neutrosophic soft sets is proposed. But it is not suitable for use in computer memory.
Abstract: In this paper, we have firstly redefined the notion of neutrosophic soft set and its operations in a new way to handle the indeterminate information and inconsistent information which exists commonly in belief systems. Then, we defined neutrosophic soft matrix and their operators which are more functional to make theoretical studies and application in the neutrosophic soft set theory. The matrix is useful for storing a neutrosophic soft set in computer memory which are very useful and applicable. We finally construct a decision making method, called NSM-decision making, based on the neutrosophic soft sets.
102 citations
TL;DR: A decision- making method using the weighted cosine similarity measures for choosing mechanical design schemes (alternatives) and the comparative analysis of various trigonometric similarity measures by several numerical examples to illustrate the effectiveness of the developed cosin similarity measures of IFSs are developed.
Abstract: Based on cosine function and the information carried by the membership degrees, nonmembership degree and hesitancy degree in intuitionistic fuzzy sets (IFSs), this paper proposes two new cosine similarity measures and weighted cosine similarity measures between IFSs. Then, we give the comparative analysis of various trigonometric similarity measures by several numerical examples to illustrate the effectiveness of the developed cosine similarity measures of IFSs. Furthermore, we develop a decision- making method using the weighted cosine similarity measures for choosing mechanical design schemes (alternatives). Finally, a decision-making example on choosing mechanical design schemes is given to demonstrate the applications and efficiency of the proposed decision-making method.
TL;DR: An improved fuzzy ranking method is proposed, which considers the areas of the positive side, the area of the negative side and the spreads of generalized fuzzy numbers as the ranking factors for ranking fuzzy numbers.
Abstract: Ranking fuzzy numbers is a very important issue in fuzzy sets theory and applications. The methods for ranking fuzzy numbers have been extensively researched and used to solve many problems. Recently, Chen et al. [11] proposed a fuzzy ranking method to calculate the areas on the negative side, the areas on the positive side and the centroid of the generalized fuzzy numbers to evaluate the ranking scores of generalized fuzzy numbers with different left heights and right heights. The method can provide us with a useful way for fuzzy risk analysis based on generalized fuzzy numbers with different left heights and right heights. However, in several situations, the ranking results of Chen et al.’s method are unreasonable. In this paper, we propose an improved method, which considers the areas of the positive side, the areas of the negative side and the spreads of generalized fuzzy numbers as the ranking factors for ranking fuzzy numbers. The proposed method not only can rank generalized fuzzy numbers with different left heights and right heights, but also overcome the drawbacks of the existing fuzzy ranking methods.
TL;DR: This work does not aim to be exhaustive since it is not possible to recall all known results about all classes of uninorms in a reduced space, but it will state the general research lines of these classes in the two main frameworks whereuninorms have been studied: the unit interval (0, 1) and the discrete setting.
Abstract: This paper wants to be a compilation of the different existing classes of uninorms. From their introduction, uninorms have been extensively studied not only as aggregation operators but also as logical connectives. The study of both aspects has produced many results on this kind of operators and many different classes have appeared. This work does not aim to be exhaustive since it is not possible to recall all known results about all classes of uninorms in a reduced space. Thus, we only want to state the general research lines of these classes in the two main frameworks where uninorms have been studied: the unit interval (0, 1) and the discrete setting. However, we will also compile the references where more details about all the existing classes of uninorms can be found, for the convenience of the interested reader. Uninorms in other frameworks are also recalled and finally, a section devoted to applications of uninorms is included.
TL;DR: Improved aggregation operation rules for IVNSs are proposed, and the generalized weighted aggregation (GWA) operator is extended to work congruently with IVNS data.
Abstract: Neutrosophic sets are powerful logics designed to facilitate understanding of indeterminate and inconsistent information; many types of incomplete or complete information can be expressed as interval valued neutrosophic sets (IVNSs). This paper proposes improved aggregation operation rules for IVNSs, and extends the generalized weighted aggregation (GWA) operator to work congruently with IVNS data. The aggregated results are also expressed as IVNSs, which are characterized by truthmembership degree, indeterminacy-membership degree, and falsity-membership degree. The proposed method is proved to be the maximum approximation to the original data, and maintains most of the information during data processing. Then, a method is proposed to determine the ranking orders for all alternatives according to their comparative advantage matrices based on their general score, degree of accuracy and degree of certainty expressed by the aggregated IVNSs. Finally, a numerical example is provided to illustrate the applicability and efficiency of the proposed approach.
TL;DR: With respect to multiple attribute group decision making (MAGDM) problems in which attribute values take the form of the intuitionistic fuzzy numbers, two group decisionMaking methods based on IFFPWA and IFFFOWA operators are developed.
Abstract: On the basis of Frank operators, the operational rules of intuitionistic fuzzy numbers are redefined, then the intuition- istic fuzzy Frank power average operator (IFFPA), intuitionistic fuzzy Frank power weighted average operator (IFFPWA) and intuitionistic fuzzy Frank power ordered weighted average operator (IFFPOWA) are proposed by combining Frank operations and power aggregation operators. At the same time, some desirable properties of these operators, such as idempotency, commutativity and boundedness, are studied, and some special cases are analyzed. Furthermore, with respect to multiple attribute group decision making (MAGDM) problems in which attribute values take the form of the intuitionistic fuzzy numbers, two group decision making methods based on IFFPWA and IFFPOWA operators are developed. Finally, an illustrative example is given to verify the proposed methods and to demonstrate their practicality and effectiveness.
TL;DR: A decision-making method is established based on the possibility degree ranking method and the INNOWA and INNOWG operators to handle multiple attribute decision- making problems with interval neutrosophic information.
Abstract: The paper proposes the possibility degree ranking method for interval neutrosophic numbers INNs from the probability viewpoint since the ranking of INNs is very important for the interval neutrosophic decision-making problems. Then, we develop an interval neutrosophic number ordered weighted averaging INNOWA operator and an interval neutrosophic number ordered weighted geometric INNOWG operator and investigate their properties, and then establish a decision-making method based on the possibility degree ranking method and the INNOWA and INNOWG operators to handle multiple attribute decision-making problems with interval neutrosophic information. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.
TL;DR: Some distance and similarity measures for DHFSs based on Hamming distance, Euclidean distance and Hausdorff distance are introduced and their applications in pattern recognition are illustrated.
Abstract: Dual hesitant fuzzy set (DHFS) is a very comprehensive set which includes fuzzy set, intuition fuzzy set and hesitant fuzzy set as its special cases. Distance and similarity measures play great roles in many areas, such as decision making, pattern recognition, etc. In this paper, we introduce some distance and similarity measures for DHFSs based on Hamming distance, Euclidean distance and Hausdorff distance. Two examples are used to illustrate these distance and similarity measures and their applications in pattern recognition. Finally, the comparisons among DHFSs and the corresponding IVIFSs and HFSs are made in detail by utilizing the developed distance measures.
TL;DR: A novel framework for sentiment detection in Arabic tweets is introduced by translating the SentiStrength English sentiment lexicon into Arabic and afterwards the lexicon was expanded using Arabic thesauri.
Abstract: Sentiment analysis aims at extracting sentiment embedded mainly in text reviews. The prevalence of semantic web technologies has encouraged users of the web to become authors as well as readers. People write on a wide range of topics. These writings embed valuable information for organizations and industries. This paper introduces a novel framework for sentiment detection in Arabic tweets. The heart of this framework is a sentiment lexicon. This lexicon was built by translating the SentiStrength English sentiment lexicon into Arabic and afterwards the lexicon was expanded using Arabic thesauri. To assess the viability of the suggested framework, the authors have collected and manually annotated a set of 4400 Arabic tweets. These tweets were classified according to their sentiment into positive or negative tweets using the proposed framework. The results reveal that lexicons are helpful for sentiment detection. The overall results are encouraging and open venues for future research.
TL;DR: In this paper, the notion of M-fuzzifying restricted hull operators is introduced and several equivalent characterizations are given and it is shown that there is a one-to-one correspondence between M- fuzzifyingrestricted hull operators and M-Fuzzifying convex structures.
Abstract: In this paper, the notion of M-fuzzifying restricted hull operators is introduced and several equivalent characterizations are given. It is shown that there is a one-to-one correspondence between M-fuzzifying restricted hull operators and M-fuzzifying convex structures. As applications, some properties of the cut convex structures of an M-fuzzifying convex structure and of M-fuzzifying convexity preserving functions and of M-fuzzifying convex-to-convex functions are derived. In addition, using M-fuzzifying restricted hull operators, some M-fuzzifying convexities are naturally constructed from M-fuzzy quasi-orders.
TL;DR: The dual Maclaurin symmetric mean (DMSM) operator is proposed and extend the DMSM operator to accommodate uncertain linguistic environment and two approaches to multiple attribute decision making with uncertain linguistic information are developed.
Abstract: The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multi-input arguments. In this paper, we propose the dual Maclaurin symmetric mean (DMSM) operator and extend the DMSM operator to accommodate uncertain linguistic environment. Some new aggregation operators based on DMSM for aggregating uncertain linguistic information are developed, such as the uncertain linguistic dual Maclaurin symmetric mean (ULDMSM) operator, the uncertain linguistic weighted dual Maclaurin symmetric mean (ULWDMSM) operator and the uncertain linguistic Choquet dual Maclaurin symmetric mean (ULCDMSM) operator. Meanwhile, some desirable properties and special cases with respect to different parameter values of these operators are studied in detail. Furthermore, based on the ULWDMSM and ULCDMSM operators, two approaches to multiple attribute decision making with uncertain linguistic information are developed. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver a comparative analysis with uncertain linguistic Bonferroni mean (ULBM) operator is also presented.
TL;DR: The entropy and granularity of the binary mapping between two different universes are defined, and an approach to uncertainty measurement based on the granular of binary mapping for multigranulation rough set over two universes is given.
Abstract: Recently, a multigranulation rough set MGRS has become a new direction in rough set theory, which is based on multiple binary relations on the universe of discourse. The existing literature about multigranulation rough set is based on the assumption of the same universe. In reality, however, a good deal of practical decision making may relate to the possibility of two or more different universes. In this paper, we consider the rough approximation of a given concept over two different universes with respect to the multigranulation space formed by different mappings of the two universes, i.e., the multigranulation rough set model. We respectively define the optimistic multigranulation rough set, pessimistic multigranulation rough set and variable precision multigranulation rough set over two universes, each of which can be appropriate to a different real-world decision-making problem in management science. Then several important properties of these models are discussed in detail. Also, the relationship between the multigranulation rough set over two universes and the existing models in the literature is investigated. At last, the entropy and granularity of the binary mapping between two different universes are defined, and then we give an approach to uncertainty measurement based on the granularity of binary mapping for multigranulation rough set over two universes. The multigranulation rough set model over two universes provides a new, effective approach for practical decision problems in management science.
TL;DR: The concepts of cardinality, dominating set, independent set, total dominating number and independent dominating number of a vague graph are introduced and the application of domination in vague graphs is given.
Abstract: The concept of vague graph introduced by Ramakrishna in (8). The main purpose of this paper is to introduce the concepts of cardinality, dominating set, independent set, total dominating number and independent dominating number of a vague graph. The notion of irredundance number of a vague graph is discussed, too. Finally we give an application of domination in vague graphs.
TL;DR: A simple approach for automatic detection and classification of brain MRI as malignant or benign using Artificial Neural Network is presented.
Abstract: There are many approaches for accurate and automatic classification of brain MRI. In this paper, a simple approach for automatic detection and classification is presented. Artificial Neural Network has been utilized for brain MRI classification as malignant or benign. The approach consists of three stages namely pre processing, features' extraction and classification. In pre-processing stage, filters are applied for the removal of noise. In the features' extraction phase, color moments are extracted as mean features from the MRI images and the color moments extracted are presented to simple feed forward artificial neural network for classification. The method was applied using total 70 images with 25 normal images and 45 abnormal images. The classification accuracy was found to be 88.9% for training data, 94.9% for validation data and 94.2% for testing data whereas the overall accuracy of 91.8% was observed.
TL;DR: An intuitionistic fuzzy multi-criteria decision making method for supplier selection problem in which attribute values take the form of intuitionists fuzzy numbers and attribute weights are completely unknown in advance is proposed.
Abstract: This article proposes an intuitionistic fuzzy multi-criteria decision making method for supplier selection problem in which attribute values take the form of intuitionistic fuzzy numbers and attribute weights are completely unknown in advance. Firstly, the definition of intuitionistic fuzzy judgement matrix by conducting pair-wise comparisons for green supplier selection criteria is introduced. Then, a novel approach for making priority of the intuitionistic fuzzy judgement matrix is proposed to determine the subject weights of criteria. Secondly, an optimization model is established to determine the objective weights, which maximizes the distance of every alternative to negative-ideal solution. Furthermore, the subject and objective weights are integrated to general weights. Then, a Technique of ranking Preferences by Similarity to the Ideal Solution (TOPSIS) method combined with intuitionistic fuzzy set is set up to rank all the alternatives. The novelty of this method is that it conducts sensitivity analysis to determine the impact of criteria weights on ranking order of alternatives. Finally, a numerical example for green supplier selection is given to illustrate application of the proposed approach.
TL;DR: The main purpose of this paper is to review some decision making methods based on (fuzzy) soft sets in more details, and put forward some revised algorithms in decision making.
Abstract: Soft set theory is provided as a general mathematical tool for dealing with uncertainties. At present, it is very important to put forward some decision making methods based on (fuzzy) soft sets. The main purpose of this paper is to review some decision making methods based on (fuzzy) soft sets in more details. Furthermore, we put forward some revised algorithms in decision making, and provide some good examples. Finally, we construct a kind of new decision making method for rough
TL;DR: An operational law is proposed for fuzzy arithmetic, providing a novel approach to analytically and exactly calculating the inverse credibility distribution of some specific arithmetical operations based on the credibility measure.
Abstract: In practice, some special LR fuzzy numbers, like the triangular fuzzy number, the Gaussian fuzzy number and the Cauchy fuzzy number, are widely used in many areas to deal with various vague information. With regard to these special LR fuzzy numbers, called regular LR fuzzy numbers in this paper, an operational law is proposed for fuzzy arithmetic, providing a novel approach to analytically and exactly calculating the inverse credibility distribution of some specific arithmetical operations based on the credibility measure. As an application of the operational law, an equivalent form of the expected value operator as well as a theorem for computing the expected value of strictly monotone functions is suggested. Finally, we utilize the operational law to construct a solution framework of fuzzy programming with parameters of regular LR fuzzy numbers, and such type of fuzzy programming problems can be handled by the operational law as the classic deterministic programming without any particular solving techniques.
TL;DR: The Choquet integral and the interval neutrosophic set theory are combined to make multi-criteria decision for problems under neutrosophile fuzzy environment and a ranking index is proposed according to its geometrical structure.
Abstract: In this paper, the Choquet integral and the interval neutrosophic set theory are combined to make multi-criteria decision for problems under neutrosophic fuzzy environment. Firstly, a ranking index is proposed according to its geometrical structure, and an approach for comparing two interval neutrosophic numbers is given. Then, a ≤L implied operation-invariant total order which satisfies order-preserving condition is proposed. Secondly, an interval neutrosophic number Choquet integral (INNCI) operator is established and a detailed discussion on its aggregation properties is presented. In addition, the procedure of multi-criteria decision making based on INNCI operator is given. Finally, a practical example for selecting the third party logistics providers is provided to illustrate the feasibility of the developed approach.
TL;DR: A novel concept of Hesitancy index of hesitant fuzzy set is proposed to measure the hesitancy degree among the possible values in each hesitant fuzzy element of the hesitant fuzzySet to show that existing distance and similarity measures are not reasonable in some situations.
Abstract: Distance and similarity measures are fundamentally important in a variety of scientific fields such as clustering analysis, pattern recognition and decision making, etc. In this paper, by analyzing the existing distance and similarity measures between hesitant fuzzy sets, we show that they are not reasonable in some situations. To this end, we propose a novel concept of hesitancy index of hesitant fuzzy set to measure the hesitancy degree among the possible values in each hesitant fuzzy element of the hesitant fuzzy set. By taking their hesitancy indices into account, new methods for measuring the distances between hesitant fuzzy sets are proposed and their properties are discussed. According to the relationship between the distance measure and the similarity measure, two novel similarity measures for hesitant fuzzy sets are further developed. Afterwards, we propound a novel hesitant fuzzy clustering algorithm on the basis of the novel similarity measures for classifying objects with hesitant fuzzy sets. At length, a real-life example is given to illustrate the detailed implementation process of the proposed clustering approach, and a comparative study on the same example is conducted.