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We propose a new method for ranking alternatives represented by Atanassov's intuitionistic fuzzy sets (A-IFSs) which takes into account the amount of information related to an alternative (expressed by a distance from the ideal positive alternative) and the reliability of information (how sure the information is).

This paper presents an extended Branch-and-Bound algorithm for solving fuzzy linear bilevel programming problems. In a fuzzy bilevel programming model, the leader attempts to optimize his/her fuzzy objective with a consideration of overall satisfaction, and the follower tries to find an optimized strategy, under himself fuzzy objective, according to each of possible decisions made by the leader. This paper first proposes a new solution concept for fuzzy linear bilevel programming. It then presents a fuzzy number based extended Branch-and-bound algorithm for solving fuzzy linear bilevel programming problems.

This study focuses on the fundamental issues of granular information and information granulation, and discusses their role in pattern recognition. We demonstrate how to characterize information granules in terms of their size (dimension) and variability. We also show that these two essential aspects of information granules are closely linked: the increasing size of the granule implies increased variability. Two detailed models of the variability of information granules are included; the first exploits the notion of entropy, while the second expresses a mix between patterns from different classes. Finally, we elaborate on the development of granular neural classifiers, and outline the main advantages stemming from the usage of granular rather than numeric patterns.

This paper determines the risk for cardiovascular diseases (CVDs), and nutrition level in infants aged 0–6 months using Fuzzy Cognitive Maps (FCMs). The aim of this study is to facilitates the medical experts to early detects these diseases with accuracy, so that overall death ratio can be reduced. Firstly, we have introduced the concepts of FCMs and briefly refer to the applications of these methods in medical. After that, two intelligent decision support systems for cardiovascular and malnutrition are developed using FCMs. The proposed cardiovascular risk assessment system takes six inputs: chest pain, cholesterol, heart rate, blood pressure, blood sugar, and old peak and determines CVDs risk. The second decision support system of malnutrition diagnosis takes twelve inputs: breastfeeding, daily income, maternal education, colostrum intake, energy intake, protein intake, vitamin A intake, iron intake, family size, height, weight, head circumference, and skin fold thickness and diagnoses the nutrition level in infants. We have explained the working of both decision support systems using case studies.

In this paper we deal with the entropy of fuzzy sets. We first review several defined entropies of fuzzy sets and then propose a new one. Some comparisons are made with some existing entropies to show the effectiveness of the proposed one.

Nowadays, the capital cost of open-pit mining equipment is very high so any mistake in the selection of quantity, type and capacity of equipment may cause irreparable impact on the net present value of mining project. Mine planning engineers generally use their intuition and experience in decision making even though equipment selection is a complex multi criteria decision problem. Considering the tangible along with intangible factors in the mine equipment selection problem, this paper proposes a new method of multi criteria decision making (MCDM) that makes it possible to select the optimal equipment that satisfies the decision maker. In a real-world situation, because of incomplete or non-obtainable information, the data (attributes) are often not deterministic but they are usually fuzzy-imprecise. Our proposed model considers objective, critical, and subjective factors as the three main common factors in equipment selection analysis. The last two factors, critical and subjective factors, are defined by decision maker's judgments for more adoption with real world problems. A case study is presented to illustrate the use of the proposed model and to demonstrate the capability of the model. The result of this study shows significant reduction of time consumption of calculation and good precision compared to customary methods such as Chang's fuzzy AHP method.

Although image retrieval for e-commerce field has a huge commercial potential, e-commerce oriented content-based image retrieval is still very raw. Modern online shopping systems have certain limitations. In particular, they use conventional tag-based retrieval and lack making use of visual content. The paper presents a methodology to retrieve images of shopping items based on fuzzy dominant colors. People regard color as an aesthetic issue, especially when it comes to choosing the colors of their clothing, apartment design and other objects around. No doubt, color inuences purchasing behavior — to a certain extent, it is a reection of human's likes and dislikes. The fuzzy color model that we are proposing represents the collection of fuzzy sets, providing the conceptual quantization of crisp HSI space having soft boundaries. The proposed method has two parts: assigning a fuzzy colorimetric profile to the image and processing the user query. We also use underlying mechanisms of attention from a theory of visual attention, like perceptual categorization. Subjectivity and sensitivity of humans in color perception and bridging the semantic gap between low-level color visual features and high-level concepts are major issues that we plan to tackle in this research.

This paper presents a fuzzy set-based approach to the evaluation of information technology (IT) projects. We assume a multi-criteria decision-making framework, where sets of general and domain-specific criteria are used to judge the relative performance of alternative technologies. The methodology was originally developed for DIAS.net, an EU project aiming at the development of the Information Society in insular and isolated regions of Europe. In this paper, we present many aspects of our evaluation framework, including the synthesis of evaluation teams, the assessment of the importance of criteria, the evaluation of the performance of the alternatives and the final ranking and selection of projects. The methodology presented has the innovative feature of embodying techniques of fuzzy sets theory into the classical multi-criteria decision analysis. This combination enables us to handle efficiently the subjectiveness that often characterizes expert judgements on a decision problem. Fuzzy linguistic terms, such as "poor," "fair," "very important," etc. are proposed for assessing the relative merit of alternatives and criteria. The paper concludes by exploring the potentiality of the above methodology in providing a flexible and robust IT evaluation framework.

The majority rule is frequently presented as a cornerstone of any democratic society, guiding many group decision-making processes where final decision requires the agreement of more than half the people involved. But sometimes, some key decisions require a higher level of agreement. In such cases, an added value would be to reach some consensus about the decision-making problem. Decision making under consensus drives to decisions which are better accepted and appreciated. But it also implies a greater complexity and time consuming process to reach a final decision, and it may even lead to a deadlock or unsuccessful results, whenever the searched agreement is not achieved. Meanwhile, these problems arise because the requirements to achieve the consensus are too strong, and different processes have softened their requirements. In particular, soft consensus is one of the most widespread consensus reaching processes that uses fuzzy logic to soften the consensus requirements. However, several problems still persist despite the softening of the requirements.

In this paper, we are going to make a brief revision of the different concepts about consensus and about different consensus reaching processes, both in the crisp and fuzzy environment. We shall then analyze how to overcome their lacks, indicating the challenges facing these processes in order to obtain successful results in those group decision problems in which they are required to make a decision under consensus.

Type-1 OWA operator provides us with a new technique for directly aggregating linguistic variables expressing human experts' opinions or preferences by fuzzy sets via OWA mechanism in soft decision making. However, the existing Direct Approach to performing type-1 OWA operation involves high computational overhead. In this paper, a fast approach, called α-level Approach, is suggested to implement the type-1 OWA operator. Experimental results have shown that the α-level Approach can achieve much higher computing efficiency in performing type-1 OWA operation than the Direct Approach.

We give the expression for the solution to some particular initial value problems in the space E¹ of fuzzy subsets of ℝ. We deduce some interesting properties of the diameter and the midpoint of the solution and compare the solutions with the corresponding ones in the crisp case.

Social networks have gained a lot attention. They are perceived as a vast source of information about their users. Variety of different methods and techniques has been proposed to analyze these networks in order to extract valuable information about the users – things they do and like/dislike. A lot of effort is put into improvement of analytical methods in order to grasp a more accurate and detailed image of users. Such information would have an impact on many aspects of everyday life of people – from politics, via professional life, to shopping and entertainment.

The theory of fuzzy sets and systems, introduced in 1965, has the ability to handle imprecise and ambiguous information, and to cope with linguistic terms. The theory has evolved into such areas like possibility theory and computing with words. It is very suitable for processing data in a human-like way, and providing the results in a human-oriented manner.

The paper presents a short survey of works that use fuzzy-based technologies for analysis of social networks. We pose an idea that fuzzy-based techniques allow for introduction of humancentric and human-like data analysis processes. We include here detailed descriptions of a few target areas of social network analysis that could benefit from applications of fuzzy sets and systems methods.

In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some mathematical morphology operators to fuzzy concept analysis. We also propose to use mathematical morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.

This paper considers the introduced relations between fuzzy property-oriented concept lattices and fuzzy relation equations, on the one hand, and mathematical morphology, on the other hand, in the retrieval processing of images and signals. In the first part, it studies how the original images and signals can be retrieved using fuzzy property-oriented concept lattices and fuzzy relation equations. In the second one we analyze two of the most important tools in fuzzy mathematical morphology from the point of view of the fuzzy property-oriented concepts and the aforementioned study. Both parts are illustrated with practical examples.

The aim of this paper is pricing the vulnerable options in a vague world. Due to the vulnerability of financial markets and the economy environment in the real world, investors cannot always have precise information about firm value and default recovery rate in vulnerable option pricing. Therefore, following the framework of Klein in 1996, a fuzzy binomial tree pricing model is derived by modelling the firm value and default recovery rate as fuzzy numbers. The numerical results show that the precise information assumption about the firm value and recovery rate in Klein model may lead to underestimate the credit risk on the values of vulnerable options. This study aims to provide insights for future research on defaultable options pricing under imprecise market information.

In this paper, we provide a definition of α-fuzzified lower and upper approximations for fuzzy sets based on the α-cut of fuzzy binary relations. We show that the definition is a proper generalization of the previous one for approximations of crisp sets and compare it with an existing definition in the context of fuzzy tolerance relation.

Open electronic communities may bring together people geographically and culturally unrelated to each other. In this context, taking costly decisions depends on the expectations created according to past behaviour of others. This kind of information is usually called reputation and it is one of the most significant factors to trust merchants and recommenders in electronic commerce interactions. When agents are acting on behalf of humans in such commercial scenarios, they should represent and reason about trust and reputation as humans do. In this paper a trust management mechanism tackles the vague, subjective and uncertain information about others using fuzzy sets. The operations defined over such fuzzy sets updates the reputation of merchants according to the general situation faced. This trust management mechanism is applied to a multiagent system of merchants, recommenders and buyers, where collaborative recommendations coexist with competitive intentions. The developed multi-agent system is used to compare the level of success of predictions obtained from the fuzzy computations with some of the most well known (crisp) reputation mechanisms: ebay, bizrate, sporas and regret when the behaviour of merchants change in different degrees. Finally, the potential benefits of using fuzzy sets to manage reputation in multi-agent systems are analyzed according to the excellent experimental results shown.

The novel concept of Spherical Fuzzy Sets provides a larger preference domain for decision makers to assign membership degrees since the squared sum of the spherical parameters is allowed to be at most 1.0. Spherical fuzzy sets are a generalization of Pythagorean Fuzzy Sets, picture fuzzy sets and neutrosophic sets. Spherical Fuzzy Sets are newly developed one of the extensions of ordinary fuzzy sets. In this paper, we proposed a MCDM method based on spherical fuzzy information. The method uses entropy theory to calculate the criteria weights, and calculates the similarity ratio of alternatives by using cosine similarity theory. Then alternatives are ranked according to their similarity ratio in descending order. To show the applicability of the proposed method, an illustrative example is given. We conclude that the proposed method is a useful tool for handling multi-period decision making problems in spherical fuzzy environment.

A crisp image segmentation can be characterized in terms of the set of edges that separates the adjacent regions of the segmentation. Based on these edges, an alternative way to define a fuzzy image segmentation is introduced in this paper. In this sense, the notion of fuzzy image segmentation is characterized by means of a fuzzy set over the set of edges, which could in this way be understood as the fuzzy boundary of the image. Also, an algorithm to construct this fuzzy boundary is provided based on the relations that exist between the fuzzy boundary set problem and the (crisp) hierarchical image segmentation problem. Finally, some computational experiences have been included in order to show the fuzzy boundaries of some digital images.

The possibility for more confidential predictions, leaning on scientific methods and accomplishments of information technology leaves more time for the realization of logistic needs. Longstanding ambitions to acquire desired levels of efficiency within the system with minimal costs of resources, materials, energy and money are the features of executive structures of logistic systems. A successful logistic process is based on validation of technological development, indicating the need for a faster and more confidential integration of logistic systems and "instilling confidence" with military units that provide critical support (supply, transport and maintenance) will be reliably realized according to relevance and priority. Conclusions like these impose the necessity that the decision-making process of logistic organs is accessed carefully and systematically, since any wrong decision leads to a reduced state of readiness for military units. To facilitate the day-to-day operation of the Army of Serbia and the completion of both scheduled and unscheduled tasks it is necessary to satisfy the wide range of transport requirements. In this paper, the Adaptive Neuro Fuzzy Inference System (ANFIS) is described, thus making possible a strategy of coordination of transport assets to formulate an automatic control strategy. This model successfully imitates the decision-making process of the chiefs of logistic support. As a result of the research, it is shown that the suggested ANFIS, which has the ability to learn, has a possibility to imitate the decision-making process of the transport support officers and show the level of competence that is comparable with the level of their competence.