Narrow Results

In this paper, we introduce fuzzy stochastic differential equations (FSDEs) driven by sub-fractional Brownian motion (SFBM) which are applied to describe phenomena subjected to randomness and fuzziness simultaneously. The SFBM is an extension of the Brownian motion that retains many properties of fractional Brownian motion (FBM), but not the stationary increments. This property makes SFBM a possible candidate for models that include long-range dependence, self-similarity, and non-stationary increments which is suitable for the construction of stochastic models in finance and non-stationary queueing systems. We apply an approximation method to stochastic integrals, and a decomposition of the SFBM to find the existence and uniqueness of the solutions.

A fundamental issue about installation of photovoltaic solar power stations is the optimization of the energy generation and the fault detection, for which different techniques and methodologies have already been developed considering meteorological conditions. This fact implies the use of unstable and difficult predictable variables which may give rise to a possible problem for the plausibility of the proposed techniques and methodologies in particular conditions. In this line, our goal is to provide a decision support system for photovoltaic fault detection avoiding meteorological conditions. This paper has developed a mathematical mechanism based on fuzzy sets in order to optimize the energy production in the photovoltaic facilities, detecting anomalous behaviors in the energy generated by the facilities over time. Specifically, the incorrect and correct behaviors of the photovoltaic facilities have been modeled through the use of different membership mappings. From these mappings, a decision support system based on ordered weighted averaging operators informs of the performances of the facilities per day, by using natural language. Moreover, a state machine is also designed to determine the stage of each facility based on the stages and the performances from previous days. The main advantage of the designed system is that it solves the problem of “constant loss of energy production”, without the consideration of meteorological conditions and being able to be more profitable. Moreover, the system is also scalable and portable, and complements previous works in energy production optimization. Finally, the proposed mechanism has been tested with real data, provided by Grupo Energético de Puerto Real S.A. which is an enterprise in charge of the management of six photovoltaic facilities in Puerto Real, Cádiz, Spain, and good results have been obtained for faulting detection.

The application of additive manufacturing (AM) has increased exponentially in recent years. Industries are keen to explore this innovative technology but are apprehensive about the high processing cost of the process. Hence, it is crucial to carry out a cost analysis of the process. This paper presents an approach to compare the costs of an AM process (selective laser sintering (SLS)) and a traditional manufacturing process (injection molding (IM)) in the presence of uncertainties. Initially, the deterministic cost models comprising necessary cost variables for SLS and IM are described. The deterministic models are converted to fuzzy set-based models for tackling uncertainties. For this purpose, important uncertain variables are treated as fuzzy members and fuzzy arithmetic is employed. Only linear triangular fuzzy numbers are used in this work. Fuzzy cost estimates produce three values (low, most likely and high estimates) of cost corresponding to membership grades. A methodology to compare two fuzzy costs of the processes is proposed for a variable demand scenario. Concept of fuzzy reliability is suitably utilized and variability in demand is tackled from probability theory. Variable demand is assumed to follow uniform as well as normal probability distributions. The methodology is illustrated with the help of two examples.

This paper introduces a brand new algebraic methodology, Fermatean fuzzy soft matrices. A new hybrid tool called the Fermatean fuzzy soft set combines the strengths of the Fermatean fuzzy set and the parametric tool soft set to handle vague and ambiguous situations in various mathematical problems. Fundamental set operations of Fermatean fuzzy soft matrices are defined, and their properties are examined. Two algorithms using the score matrix and utility matrix have been proposed for medical diagnosis problems. Each of the applications has been successfully demonstrated using numerical examples. Finally, a brief comparison between the proposed model and several previous models is presented to ensure the feasibility of the proposed strategy.

Since transactions may contain quantitative values, many approaches have been proposed to derive membership functions for mining fuzzy association rules using genetic algorithms (GAs), a process known as genetic-fuzzy data mining. However, existing approaches assume that the number of linguistic terms is predefined. Thus, this study proposes a genetic-fuzzy mining approach for extracting an appropriate number of linguistic terms and their membership functions used in fuzzy data mining for the given items. The proposed algorithm adjusts membership functions using GAs and then uses them to fuzzify the quantitative transactions. Each individual in the population represents a possible set of membership functions for the items and is divided into two parts, control genes (CGs) and parametric genes (PGs). CGs are encoded into binary strings and used to determine whether membership functions are active. Each set of membership functions for an item is encoded as PGs with real-number schema. In addition, seven fitness functions are proposed, each of which is used to evaluate the goodness of the obtained membership functions and used as the evolutionary criteria in GA. After the GA process terminates, a better set of association rules with a suitable set of membership functions is obtained. Experiments are made to show the effectiveness of the proposed approach.

Fuzzy set was introduced in 1965 by Prof. A. Lotfi Zadeh to deal with uncertainty. Fuzzy set is an important tool for solving real life problems. Similarly, hesitant fuzzy set is the extended tool of fuzzy set which plays an important role to deal with uncertainty, imprecision and vagueness more clearly and accurately. In this paper, hesitant fuzzy base rule system is proposed which is the extension of fuzzy base rule system. A new dimension of hesitant fuzzy set i.e. hesitant fuzzy membership line (HFML) is defined and the HFML is classified into different classes (Good, Fair, Poor) according to Quality Index Parameter (QIP) which is calculated by the expert only with the best of their knowledge. Also this paper consists of two newly defined operations AND and OR operations on hesitant fuzzy sets. The effective criteria like Ecology, Hostility, Cost, Water Quality and Air Quality are considered so that decision makers make appropriate site selection of the power plant in more rational and easy evaluation method. Using all the newly proposed methods in this paper, the policy makers are able to select the best power plant most easily and effectively without any big calculation. Finally, the power plant sites are ranked according to the highest value given by a score function.

We discuss the OWA and Choquet integral aggregation operators and point out the central role the ordering operation plays in these operators. We extend the capabilities of the Choquet integral aggregation by allowing the ordering to be induced by some values other then those being aggregated. This allows us to consider an induced Choquet Choquet integral aggregation operator. We look at the properties of this operator. We then look at its applications. Among the applications considered are aggregations guided by linguistic and other ordinal structures. We look at the use of induced aggregation in nearest neighbor methods. We also consider the Choquet aggregation of complex objects such as matrices and vectors.

An interval-valued hesitant fuzzy set (IVHFS) is a best tool to address uncertainty and hesitation of a production planning problem (PPP) which appears in engineering, agriculture, and industrial sectors. Often, a PPP is formulated as a multiobjective linear programming problem (MOLPP) and therefore, it is very necessary to develop a suitable and realistic method to deal MOLPP with uncertainty and hesitation. In this paper, we define a set of possible interval-valued hesitant fuzzy degrees for all objectives, and using this, a MOLPP is converted into a interval-valued hesitant fuzzy linear programming (IVHFLPP). Further, we introduce a new optimization technique based on a new operation of IVHFS, and later it is implemented in a computational method to search a Pareto optimal solution of the considered problem. Further, a PPP is solved by using the proposed method and the result shows the superiority of the proposed computational method over the existing methods.

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.

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 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.

Diabetes mellitus is a common chronic disease in recent years. According to the World Health Organization, the estimated number of diabetic patients will increase 56% in Asia from the year 2010 to 2025, where the number of anti-diabetic drugs that doctors are able to utilize also increase as the development of pharmaceutical drugs. In this paper, we present a recommendation system for anti-diabetic drugs selection based on fuzzy reasoning and ontology techniques, where fuzzy rules are used to represent knowledge to infer the usability of the classes of anti-diabetic drugs based on fuzzy reasoning techniques. We adopt the "Medical Guidelines for Clinical Practice for the Management of Diabetes Mellitus" provided by the American Association of Clinical Endocrinologists to build the ontology knowledge base. The experimental results show that the proposed anti-diabetic drugs recommendation system gets the same accuracy rate as the one of Chen et al.'s method (R. C. Chen, Y. H. Huang, C. T. Bau and S. M. Chen, Expert Syst. Appl.39(4) (2012) 3995–4006.) and it is better than Chen et al.'s method (R. C. Chen, Y. H. Huang, C. T. Bau and S. M. Chen, Expert Syst. Appl.39(4) (2012) 3995–4006.) due to the fact that it can deal with the semantic degrees of patients' tests and can provide different recommend levels of anti-diabetic drugs. It provides us with a useful way for anti-diabetic drugs selection based on fuzzy reasoning and ontology techniques.

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.

In a bilevel decision problem, both the leader and the follower may have multiple objectives, and the coefficients involved in these objective functions or constraints may be described by some uncertain values. To express such a situation, a fuzzy multi-objective bilevel (FMOBL) programming model and related solution methods are introduced. This research develops a FMOBL decision support system through implementing the proposed FMOBL methods.

A generalized Bayesian inference nets model (GBINM) and a new approach for internal fault detection and diagnosis of three-phase induction motor is proposed. The input data set for designing and testing the fault diagnostic system are acquired through on-site experiment. The preprocessed input data and experts' rich diagnostic experience/knowledge are used to define the membership functions and fault fuzzy sets. With GBINM and the defined fault fuzzy sets, the hierarchical Bayesian fuzzy inference nets are constructed to carry out the complex motor fault diagnostic procedure. The propagation of probability is used to address the uncertainties involved in detecting and diagnosing the motor incipient faults. The immense difficulties of defining and assigning statistical parameters, required for calculating the propagation of probability are effectively solved. The validity and effectiveness of the proposed approach is witnessed clearly from the testing results obtained.

We analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We also consider the converse setting, namely, given binary relations that accomplish some typical properties, we study whether or not they come from solutions of some functional equation. Applications to the numerical representability theory of ordered structures are also furnished as a by-product. Further interpretations of this approach as well as possible generalizations to the fuzzy setting are also commented. In particular, we discuss how the values taken for bivariate functions that are bounded solutions of some classical functional equations define, in a natural way, fuzzy binary relations on a set.

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.

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.

In this study, we highlight some fundamental issues of knowledge management and cast them in the setting of Granular Computing (GrC). We show how its formal constructs — information granules are instrumental in knowledge representation and specification of its level of abstraction.

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.