Iranian journal of fuzzy systems
Volume:13 Issue: 2, Apr-May 2016

The fuzzy structured element (FSE) theory is a very useful tool for dealing with fuzzy multi-criteria decision making (MCDM) problems by transforming the criterion value vectors of each alternative into the corresponding criterion function vectors. In this paper, some concepts related to function vectors are first defined, such as the inner product of two function vectors, the cosine of the included angle between two function vectors and the projection of a function vector on another. Then a method based on FSE is developed to solve fuzzy MCDM problems in which the criterion values take the form of general bounded closed fuzzy numbers and the criterion weight information is incomplete certain. In this method, the projections of criterion function vectors on the fuzzy ideal function point (FIFP) are used to rank all the alternatives and then select the most desirable one, and an optimization model is constructed to determine the weights of criteria according to the incomplete weight information. Finally, an example is given to illustrate the feasibility and effectiveness of the developed method.

In recent years, many studies have been done on forecasting fuzzy time series. First order fuzzy time series forecasting methods with first-order lagged variables and high order fuzzy time series forecasting methods with consecutive lagged variables constitute the considerable part of these studies. However, these methods are not effective in forecasting fuzzy time series which contain seasonal structures. In this respect, it would be more appropriate to use methods that consider the seasonal relations in seasonal fuzzy time series forecasting. Although seasonal fuzzy time series forecasting methods exist in literature, these methods use equal interval lengths in partition of the universe of discourse. This situation incapacitates the performance of the method in forecasting time series including seasonality and trend. In this study, a new fuzzy time series forecasting method in which intervals constituting partition of the universe of discourse increase in time at a rate that obtained based on optimization was proposed. The proposed method was applied to two real time series and obtained results were compared with other methods and the superior performance of the proposed method was proved.

Because of the complexity of decision-making environment, the uncertainty of fuzziness and the uncertainty of grey maybe coexist in the problems of multi-attribute group decision making. In this paper, we study the problems of multi-attribute group decision making with hybrid grey attribute data (the precise values, interval numbers and linguistic fuzzy variables coexist, and each attribute value has a certain grey degree), and present a new grey hybrid multi-attribute group decision making method based on grey linguistic -tuple. Concretely, the concept of grey linguistic 2-tuple is defined based on the traditional linguistic 2-tuple, and the transformation methods of transforming the precise values, interval numbers and linguistic fuzzy variables into the grey linguistic 2-tuples are presented respectively. Further, a new grey linguistic 2-tuple weighted averaging (emp {GLTWA}) operator is presented to aggregate multiple decision maker's individual decision information into comprehensive decision information, and then a ranking method based on grey 2-tuple correlation degree is presented to rank all alternatives and to select the winners. An application decision making example of supplier selection is also given to validate the method developed and to highlight the implementation, practicality and effectiveness of the presented method.

Induction motors (IMs) are widely used in many industrial applications due to their robustness, low cost, simplicity and relative good efficiency. One of the major considerations for IMs is their speed control. PI (proportional-integrator) controllers are usually used as speed controller. Adjusting the gain of PI controller is time-consuming which needs thorough considerations. Hence, fuzzy controllers are proposed to overcome such problems. In this paper, firstly drive of a three-phase induction motor is designed based on PI controller and then fuzzy logic controller is implemented. This paper presents a novel speed control technique based on fuzzy logic with two inputs and one output for drive of an IM. The inputs are speed error and derivation of speed error and the output is speed. Finally comparison is done between the PI and fuzzy controllers which shows superiority of the fuzzy controller over PI controller.

In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued) regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is taken over to prove a main theorem: the class of languages generated by an {L}valued alternating regular tree grammar {LAG}) is equal to the class of languages accepted by an {L}valued alternating top-down tree automaton {LAA}). The second way is taken over to define a new type of automaton by combining the {L}valued alternating top-down tree automaton with stack, called {L}-valued alternating stack tree automaton {LASA} and the generative power of it is compared to some well-known language classes, especially to {LAA} and to {LAG}Also, we have derived a characterization of the state alternating regular tree grammar {LSAG}) in terms of {LASA}.

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the same. Also some special subsets of $tilde{L}$ such as regular elements $Rg(tilde{L})$, dense elements $D(tilde{L})$, infinitesimal elements $Inf(tilde{L})$, boolean elements $B(tilde{L})$ and $Rad_{BL}(tilde{L})$ are characterized. The relations between these and corresponding sets in $L$ will be investigated.

In this paper, we consider the width invariant trapezoidal and triangular approximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserve the expected value too.

The aim of this paper is the study of a covering of a max-min general fuzzy automaton by another, admissible relations, admissible partitions of a max-min general fuzzy automaton, $tilde{delta}$-orthogonality of admissible partitions, irreducible max-min general fuzzy automata. Then we obtain the relationships between them.

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm, we present a method to construct a metric on a fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space. Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some problems for fuzzy metric spaces in the literature, which are shown by examples in this paper.