Abstract — In this paper we propose a new algorithm for the initial fuzzy feasible solutionto a fully fuzzytransportationproblem. Then by using fuzzy version of modified distribution method, we obtain the fuzzyoptimalsolution for the fully fuzzytransportationproblem without converting to a classical transportationproblem. A numerical example is provided to illustrate the proposed algorithm. It can be seen that the proposed algorithm gives a better fuzzyoptimalsolutionto the given fuzzytransportationproblem.
using simple additions and subtractions only. There is no additional memory cost spent on searching and branching like what common search methods do, in order to determine the actual pouring sequence. Due to its novelty and simplicity, this approach is suitable for introduction to undergraduate students or researchers in the areas of artificial intelligence, discrete mathematics, computer sciences, engineering, number theory, problem-solving or cognitive psychology. Further development of this newapproach and the implemented Excel program to explore and formulate a criteria on how to obtain an optimalsolution of the general two water jugs problem, in the sense that the number of pouring steps involved is least possible, will be a meaningful and challenging research topic for pursue in the near future.
A first approach for solving IT2FS problems is by reducing its complexity into a simpler form in order to use well known algorithms. In this case, we propose the following three-step methodol- ogy: 1– compute a fuzzy set of optimal solutions namely ˜z; 2– apply a Type-reduction strategy to find a single fuzzy set Z ; and 3– apply the Zimmermann’s soft constraints method to find a crisp solution. This allows us to see the above problem as the problem of finding a vector of solutions x ∈ R m such that:
For an atypical year (i.e., when our rainfall model differs completely from reality) the results obtained by our model may not be the best. For example, we may face the situation where the quantity of water needed for irrigation may greatly exceed the computed optimalsolution of our prob- lem. In this case the culture can died and cause major economic and environmental damage. Be- cause of this, we develop a new model based on re- plan: first we calculate the optimalsolution based on the previous model and then at every time step we recalculate a new dynamic based on real data.
Recently, for a single product with demand related to unit price Cheng  has solved the EOQ model by geometric programming method. His treatments are fully analytical and much computational efforts were needed there to get the optimalsolution. But Roy et al. [1995, 1997] have considered the space constraint with the objective goal in fuzzy environment and attacked the fuzzy optimization problem directly using either fuzzy non-linear or fuzzy geometric programming technique similarly Lee et al.  and Vujosevic et al.  have applied fuzzy arithmetic approach in EOQ model without constraints. Tripathy et al. [2009, 2011, 2011a] also investigated fuzzy EOQ models where demand is deterministic and unit cost of production is a function of both process reliability and demand. Tripathy et al.  developed the fuzzy model by imposing entropy cost to modify the traditional EOQ model with stock dependent demand where pre- and post deterioration discounts are allowed.
Hosseinzadeh Lotfi et al. (2009) discussed FFLP problem where all parameters and variables were symmetric triangular fuzzy numbers. Kumar et al. (2010) proposed a method to find the fuzzyoptimalsolution of FFLP problem with equality constraints. Nasseri et al. (2013) proposed a new method for finding the fuzzysolution of FFLP problems with inequality constraints. Hatami and Kazemipoor (2014) proposed a new method for finding the fuzzysolution of the FFLP problem by converting it into LP problem. Khan et al. (2013) claimed there is no method in the literature to find the fuzzyoptimalsolution of a FFLP problem without converting it into crisp linear programming problem, and proposed a technique for the same. Bhardwaj and Kumar (2013) showed that according tofuzzy arithmetic operation used by Khan et al. (2013) for the fuzzy number the properties and could not be satisfied, there are errors in the proposed method by Khan et al. (2013), and there is no other option to solve the FFLP problems without converting them into crisp linear programming problems. Recently, Ezzati et al. (2014) defined a new operation on symmetric trapezoidal fuzzy numbers that the properties and are satisfied and based on newfuzzy arithmetic operations proposed, a new algorithm to find directly a lexicographic/preemptive fuzzyoptimalsolution of a fuzzy lexicographic multi-objective linear programming problem was proposed, but their model was not fully fuzzy optimization. In this paper, a new method by using Ezzati et al. (2014)’s fuzzy arithmetic operation and a fuzzy version of simplex algorithm is proposed for solving FFLP problem whose parameters all are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method the fuzzyoptimalsolution of FFLP problem can be easily obtained.
Recently, Pramanik and Dey  studied priority based FGP approachto multi-objective quadratic programming problem. In this study, we extend the concept of Pramanik and Dey  for solving QBLPP. We first construct quadratic membership function by determining individual best solution of the objective function of the level DMs. The quadratic membership functions are then transformed into linear membership functions by first order Taylor series approximation. Since the objectives of the level DMs are generally conflicting in nature, possible relaxations of decision of upper and lower level DMs are simultaneously considered for avoiding decision deadlock in the decision-making situation by providing preference bounds on the decision variables under their control. Then FGP models are formulated for achieving highest degree of each of the membership goals by minimizing negative deviational variables. To demonstrate the efficiency of the proposed FGP approach, three numerical examples are solved and distance function is used to select compromise optimalsolution.
Applications of optimal control problems involve the control of dynamic systems that evolve over time either continuous-time systems or discrete-time systems. In order to deal with such systems, stochastic optimal control theory has been investigated and widely applied to physical, biological, ﬁnance, economics, production and inventory, marketing, maintenance and replacement, and the consumption of natural resources. Whenever the system is characterized with white noise and is represented by a controlled stochastic process then it is called stochastic control system which are described by Ito’s stochastic diﬀerential equations. A traditional approachto solving optimal control problems consists of formulation of optimality conditions directly, use of the calculus of variations and Pontryagin’s maximum principle (Bellman ), and then solving the resulting equations to obtain the solutionto the problems.
One of the basic references in the area of FLP is due to Bellman and Zadeh . The type of FLP that has been considered for this research is the possibilistic programming, that recognizes uncer- tainties in the objective function coefficients, as well as in constraint coefficients. The member- ship function is used to represent the degree of satisfaction of constraints, the decision-maker’s expectations about the objective function level, and the range of uncertainty of coefficients . Based in the great success of the FLP, the approach is applied to a voltage divider model. In fact, an electrical circuit has components characterized by diverse parameters, each one associated to a tolerance, given by the product manufacturer. For example, a resistance of 48 ohms can have ± 10% tolerance, due to temperature, time of use, among other reasons . This gradualness motivated this study to use the fuzzy linear programming approach for a problem of a voltage divider. The value given by the electric appliance manufacturer is called the centered value. The tolerances and the centered values allow better control over the limits under which the circuit keeps operating and, thereby, optimize its performance. The model use for this research was built by Salazar in . The objective of this research is to study three cases for the components of the LP. The first case is for real numbers components we proposed of validating the other two results. The second case refers to trapezoidal fuzzy number of type-1 as a components of LP system. The optimalsolution is obtained through a total linear order defuzzification function, defined in the trapezoidal fuzzy numbers subspace of fuzzy numbers vector space. The third case extends the second case for type-2 independent LP components. The α−levels representation theorem is the method to obtain the optimalsolution of type-2. For the numerical simulation for all cases it is use the classical interior point method , using the linear programming algorithm linprog of the software Matlab R , and an algorithm that reproduces the representation theorem.
This paper presents an alternate technique based on fuzzy goal programming (FGP) approachto solve multi-objective programming problem with fuzzy relational equations (FREs) as constraints. The proposed technique is more efficient and requires less computational work than that of algorithm suggested by Jain and Lachhwani (2009) [Jain, & Lachhwani (2009). Multiobjective programming problem with fuzzy relational equations. International Journal of Operations Research, 6(2), 55−63.]. In FGP formulation, objectives are transformed into the fuzzy goals using maximum and minimal solutions elements of FREs feasible solution set. A pseudo code computer algorithm is developed for computation of maximum solution of FREs. Suitable linear membership function is defined for each objective function. Then achievement of the highest membership value of each of the fuzzy goals is formulated by minimizing the sum of negative deviational variables. The aim of this paper is to present a simple and efficient solution procedure to obtain compromise optimalsolution of multiobjective optimization problem with FREs as constraints. A comparative analysis is also carried out between two methodologies based on numerical examples.
As a consequence of this slight modification of such neutral element axiom of triangular (co)norms, it leads to a more general definition of sub(co)implications by relaxing the bound- ary condition I (1, 0) = 0. Thus, the fuzzy (S,N)-subimplication class, explicitly represented by negations and fuzzy t-subconorms is considered in this paper, including their dual constructions. In particular, generalizations of well-known operators product t-norm and probabilistic sum are taken into account and provide interesting examples based on the median aggregation operator. Since this study considers n-ary aggregations, generalized associativity, exchange principle and distributivity properties also need to be considered.
Nowadays, switched reluctance motors (SRM) attract more and more attention. The SRM is simple to construct. It has not only a salient pole stator with concentrated coils, but also a salient pole rotor without any conductors or magnets. Simplicity makes the SRM inexpensive and reliable, and together with its high speed capacity and high torque to inertia rotor ratio make it a superior choice in different applications. References [1-2] show the implementations of the control of the SRM is not an easy task. The motor’s double salient structure makes its magnetic characteristic highly nonlinear. Therefore, its mathematical model is too complex to be analytically developed. Since the 1960’s, with the advent of power electronics and high power semiconductor switches, control of the SRM become much easier and there has been a renewed interest in SRM drives .
Human resource management plays an essential role on development of any business organization. Selection of employee normally depends on various criteria such as employee commitment, necessary skills, etc. Therefore, a good strategy to hire appropriate employee is a multi-criteria decision making (MCDM) specially the ones, which could handle uncertainty, properly. In this paper, we present a method to use MCDM techniques for hiring employees. In fact, the present work proposes a Fuzzy Analytic Hierarchy Process (FAHP) as one of the most popular multi-criteria decision making techniques. A computer application is developed where it receives the configuration of the employee selection problem, evaluates the candidates and ranks them using the appropriate voting system.
Este estudio tuvo como objetivo realizar una revisión integradora investigando como la lógica fuzzy ha sido utilizada en investigaciones con participación de enfermeros. La búsqueda de los artículos fue realizada en las bases de datos CINAHL, Embase, SCOPUS, Medline y PubMed, sin especiicar un intervalo de años determinado. Fueron incluidos artículos en los idiomas: portugués, inglés y castellano; con una temática relacionada a la enfermería y a la lógica fuzzy; y con autoría o participación de enfermeros. La muestra inal fue de 21 artículos, de ocho países. Para el análisis, los artículos fueron distribuidos en las categorías: teoría, método y modelo. En la enfermería, la lógica fuzzy ha contribuido signiicativamente para la comprensión de temas relativos a la imprecisión o a la necesidad del especialista, como método de investigación y en el desarrollo de modelos o sistemas de apoyo a la decisión y de tecnologías duras. El uso de la lógica fuzzy en la enfermería ha demostrado gran potencial y representa un vasto campo para investigaciones.
Most literature on optimal control deals with problems with only real-valued controls , both the analytical methods based on variational analysis (see e.g. , ) and also nu- merical schemes (, ). There are, however, some works that are able to address optimal control problems (OCP) with discrete control sets (see e.g. , ), although dealing directly with the discrete-valued controls is computationally heavy. The transformation of a mixed-integer optimal control problem into a problem with only real-valued controls is not new, nor is new the general idea of a variable time transformation method. See the classical reference  and also , , , , . See also the recent work  for a discussion of several variable time transformation methods.
Globalization process has imposed the ever-increasing competitive pressure on organizations in all over the world since 1990. Some organizations have tried to promote simultaneously the efficiency and quality of their companies manufacturing unit in reaction to this process. The use of evaluation model proportionate to organizational objectives is an inevitable and necessary task along realization of this circumstance. It is always important to apply accurate evaluation models to organizations to design future strategies of organizations, effectively. It is also a vital task to adjust the functional objectives of staffs for achieving terminal objectives of the whole organization (Wu et al., 2011). Efficient and effective measuring systems are also considered as useful instruments enabling managers to supervise and control the organizational processes to achieve higher efficiency and higher performance (Wang et al., 2010).
Para a busca dos artigos foram utilizadas as bases de dados CINAHL, Embase, Scopus, MEDLINE e o serviço de pesquisa da National Library of Medicine nas bases de dados PubMed. Além disso, foi realizada busca manual de artigos não identiicados nas bases, mas citados em outros estudos. Foram usados os descritores do Medical Subject Headings (MeSH) e operador booliano AND, resultando nas seguintes combinações: enfermagem and lógica fuzzy, enfermeiros and lógica fuzzy. Na busca, os descritores foram utilizados em português, inglês e espanhol.
ment the necessary measures to reduce the proba- bility of occurrence or the impact of a risk. This im- plies a reduction of the likelihood, and/or impact of an adverse risk, to limits considered acceptable. Tak- ing early actions to reduce the likelihood and / or impact of a risk is often more effective than attempt- ing to repair the damage after the risk has occurred. Adopting simpler processes, conducting more trials or choosing more reliable suppliers and partners are examples of mitigation actions. When it is not pos- sible to reduce the probability of occurrence, a mit- igation strategy can be to seek to reduce the impact of the risk, for example through the implementation of redundant processes, thus achieving a reduction of its severity.
In particular, problems of determining possible values of latest starting times and floats in networks with imprecise activity durations which are represented by fuzzy or interval numbers have attracted many researchers [13-17]. These methods compute the possible values of the earliest starting times by means of a forward recursion procedure comparable to the one used in the traditional CPM. The backward recursion takes the imprecion of some durations into account twice so the backward recusion does not work . Kaufmann and Gupta , Hapke et al.  , Hapke and Slowinski  and Rommelfanger  proposed a backward recursion that relies on the optimistic fuzzy subtraction and they provided good results for particular networks but these methods fail to compute the fuzzy latest starting times and floats in general networks. Nasution  resorts to symbolic computations on variable duration times. McCahon and Lee , Mon et al.  and Yao and Lin  proposed to go back to classical CPM via defuzzification of the fuzzy durations. McCahon  proposed to compute approximated fuzzy floats of activities from the fuzzy starting times obtained by the forward and backward recursions.
Tonnon at all  have used interactive procedure to solve multiple-objective optimization problems. A fuzzy set has been used to model the engineer’s judgment on each objective function. The properties of the obtained compromise solution were investigated along with the links between the present method and those based fuzzy logic. An uncertainty which has been affecting the parameters is modelled by means of fuzzy relations or fuzzy numbers, whose probabilistic meaning is clarified by random set and possibility theory. Constraint probability bounds that satisfy a solution can be calculated and procedures that consider the lower bound as a constraint or as an objective criterion are presented. Some theorems make the computational effort particularly limited on a vast class of practical problems. The relations with a recent formulation in the context of convex modelling are also pressured. In the paper of Wang at all  a fuzzy-decision-making procedure is applied to find the optimal feed policy of a fed-batch fermentation process for fuel ethanol production using a genetically engineered Saccharomyces yeast 1400 (pLNH33). The policy consider control variables such as - feed flow rate, feed concentration, and fermentation time. By using an assigned membership function for each of the objectives, the general multiple-objective optimization problem can be converted into a maximizing decision problem. In order to obtain a global solution, a hybrid search method of differential evolution is introduced.