Penalty method for fuzzy linear programming with trapezoidal numbers

In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. Furthermore, the obtained deterministic problem will have only unavoidable inequalities between trapezoidal fuzzy numbers parameters as constraints

Approximate Membership Function Shapes of Solutions to Intuitionistic Fuzzy Transportation Problems

In this paper, proposing a mathematical model with disjunctive constraint system, and providing approximate membership function shapes to the optimal values of the decision variables, we improve the solution approach to transportation problems with trapezoidal fuzzy parameters. We further extend the approach to solving transportation problems with intuitionistic fuzzy parameters; and compare the membership function shapes of the fuzzy solutions obtained by our approach to the fuzzy solutions to full fuzzy transportation problems yielded by approaches found in the literature

A bicriterion Steiner tree problem on graph

This paper presents a formulation of bicriterion Steiner tree problem which is stated as a task of finding a Steiner tree with maximal capacity and minimal length. It is considered as a lexicographic multicriteria problem. This means that the bottleneck Steiner tree problem is solved first. After that, the next optimization problem is stated as a classical minimums Steiner tree problem under the constraint on capacity of the tree. The paper also presents some computational experiments with the multicriteria problem

Solving Method for Linear Fractional Optimization Problem with Fuzzy Coefficients in the Objective Function

The importance of linear fractional programming comes from the fact that many real life problems are based on the ratio of physical or economic values (for example cost/-time, cost/volume, profit/cost or any other quantities that measure the efficiency of a system) expressed by linear functions. Usually, the coefficients used in mathematical models are subject to errors of measurement or vary with market conditions. Dealing with inaccuracy or uncertainty of the input data is made possible by means of the fuzzy set theory.Our purpose is to introduce a method of solving a linear fractional programming problem with uncertain coefficients in the objective function. We have applied recent concepts of fuzzy solution based on α-cuts and Pareto optimal solutions of a biobjective optimization problem.As far as solving methods are concerned, the linear fractional programming, as an extension of linear programming, is easy enough to be handled by means of linear programming but complicated enough to elude a simple analogy. We follow the construction of the fuzzy solution for the linear case introduced by Dempe and Ruziyeva (2012), avoid the inconvenience of the classic weighted sum method for determining Pareto optimal solutions and generate the set of solutions for a linear fractional program with fuzzy coefficients in the objective function

Combining different types of data in studying attitudes to English as a Lingua Franca

This paper deals with the attitudes of Croatian speakers to ELF, in particular to its pronunciation. Four methods were combined to reach conclusions about the status of ELF in Croatia: diary study, teacher interviews, a preliminary focus group interview and a survey. Whilst the first three methods revealed that the subjects regularly disfavour ‘bad pronunciation’, the survey showed that when it actually comes to talking to either native or non-native speakers, the subjects turned out to be tolerant to a slight accent. This clearly suggests a case of what is known as linguistic schizophrenia (B.B. Kachru 1977; Seidlhofer 2001). However, there are notable differences among groups of participants depending on variables such as professional profile, gender, degree of ease and success in learning pronunciation, and national pride. In any case, the combination of these methods proved to be a very good way to deal with the topic. The diary study is a valuable method to look into everyday practices and can feed nicely into survey questions. The preliminary survey highlighted the importance of different groups of participants and the need for groups of questions focusing around different factors. The preliminary focus group interview showed that it is crucial to have a single homogenous group of participants, as well as a trained facilitator. Finally, teacher interviews pointed to the possibility of similar attitudes being held by university teachers and the students they teach, which suggests that attitudes may be perpetuated. Overall, triangulation across methods and participants in the way proposed in the present paper provided a wealth of data, allowing a bottom-up view and a top-down view on the state of ELF in Croatia

Topološko strateško konstruiranje značenja: frazni glagoli s up i down u jeziku slijepih

The aim of this paper is to investigate the role of the particles upand downin the strategic meaning construal of particle verbs (PVs) in blind and sighted users of English as L2. The paper is situated within the cognitive linguistic framework. Based on the results of a speaker–judgment study with 20 blind and 20 sighted users of English, we show that PVs with downare more informative to all the participants, and that blind users rely on the particles (particularly the particle up) more than sighted users. We claim that the difference in informativeness is related to the experiential status of upand down. Downis more informative because it is at human scale, which limits its metaphorization potential. Upis more open–ended, making it more schematic and allowing greater departure from its original topology. Blind users rely on the particles more because they are more inclined to analyzing linguistic cues, since they often serve as additional experiential input. Moreover, the blind rely more on egocentric topology, which produces similar results for down, and different for up.Cilj je ovoga rada istražiti ulogu up \u27gore\u27 i down\u27dolje\u27 u strateškome konstruiranju fraznih glagola kod slijepih i videćih govornika engleskoga kao drugoga jezika. Rad se oslanja na teorijske postavke kognitivne lingvistike u kojoj su jezik i naše svakodnevno iskustvo neodvojivo povezani. U istraživanju je sudjelovalo 20 slijepih i 20 videćih govornika engleskoga kao drugoga jezika kojima je materinski jezik hrvatski. Ispitanici su rješavali upitnik u kojemu su trebali odrediti na koji način sastavnice zajedno pridonose značenju fraznoga glagola (primjerice, jedan ispitanik kaže da glagol go down \u27biti poslan u zatvor\u27 ima smisla jer se down \u27dolje\u27 odnosi na dno društva). Rezultati pokazuju da je down\u27dolje\u27 informativniji svim ispitanicima. Nadalje, slijepi ispitanici značenje objašnjavaju više se oslanjajući na sastavnice up i down, osobito na up \u27gore\u27, a manje na glagol kao sastavnicu konstrukcije. Dva su temeljna zaključka rada: prvo, smatramo da je down\u27dolje\u27 općenito informativniji jer je bliži tzv. »ljudskoj mjeri« (Turner 2014), što ograničava koliko ga je moguće metaforizirati, dok je up\u27gore\u27 shematičniji pa ima i veći metaforički potencijal, te drugo, da slijepi ispitanici u procesu konstruiranja značenja daju prioritet prostornim sastavnicama (u ovome slučaju up i down) jer su skloniji analiziranju jezika. Navedena sklonost analizi proizlazi velikim dijelom iz činjenice da im jezik služi kao dodatan način stvaranja iskustvenih veza i značajan izvor informacija o svijetu. Ipak, razlika između videćih i slijepih ispitanika nije značajna za down, što tumačimo kao rezultat veće uloge iskustva vlastite smještenosti u prostoru

Standardni pravopis za nestandardni engleski?

In an etymological spelling such as English, in order to show dialectal features of a character\u27s speech writers use non-standard spelling (eye dialect) which has a long tradition in English literature. Dealing with eye dialect diachronically and synchronically, it is shown that dialect is not represented in a maximally accurate way, but approximated in varying degrees. Although variant spellings for different features can be observed throughout (inconsistencies occur inside one work and in the whole corpus), standardizing tendencies can be observed, which, together with the semantic and syntactic context, make eye dialect more intelligible for the average reader