Diyar Akay

A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain. On the other hand, it is a hard problem since supplier selection is typically a multi criteria group decision-making problem involving several conflicting criteria on which decision makers knowledge is usually vague and imprecise. In this study, TOPSIS method combined with intuitionistic fuzzy set is proposed to select appropriate supplier in group decision making environment. Intuitionistic fuzzy weighted averaging (IFWA) operator is utilized to aggregate individual opinions of decision makers for rating the importance of criteria and alternatives. Finally, a numerical example for supplier selection is given to illustrate application of intuitionistic fuzzy TOPSIS method.

Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations

In this paper, the concept of multiplicative transitivity of a fuzzy preference relation, as defined by Tanino T. Tanino, Fuzzy preference orderings in group decision-making, Fuzzy Sets and Systems 12 (1984) 117-131, is extended to discover whether an interval fuzzy preference relation is consistent or not, and to derive the priority vector of a consistent interval fuzzy preference relation. We achieve this by introducing the concept of interval multiplicative transitivity of an interval fuzzy preference relation and show that, by solving numerical examples, the test of consistency and the weights derived by the simple formulas based on the interval multiplicative transitivity produce the same results as those of linear programming models proposed by Xu and Chen Z.S. Xu, J. Chen, Some models for deriving the priority weights from interval fuzzy preference relations, European Journal of Operational Research 184 (2008) 266-280. In addition, by taking advantage of interval multiplicative transitivity of an interval fuzzy preference relation, we put forward two approaches to estimate missing value(s) of an incomplete interval fuzzy preference relation, and present numerical examples to illustrate these two approaches.

Comparison of direct and iterative artificial neural network forecast approaches in multi-periodic time series forecasting

Artificial neural network is a valuable tool for time series forecasting. In the case of performing multi-periodic forecasting with artificial neural networks, two methods, namely iterative and direct, can be used. In iterative method, first subsequent period information is predicted through past observations. Afterwards, the estimated value is used as an input; thereby the next period is predicted. The process is carried on until the end of the forecast horizon. In the direct forecast method, successive periods can be predicted all at once. Hence, this method is thought to yield better results as only observed data is utilized in order to predict future periods. In this study, forecasting was performed using direct and iterative methods, and results of the methods are compared using grey relational analysis to find the method which gives a better result.

A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition

Unlike an ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a non-membership degree, is a more flexible way to capture the uncertainty. One of the important topics in IFS is the measure of the similarity between IFSs for which several studies have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity, and provide counter-intuitive cases. In this paper, a new general type of similarity measure for IFS with two parameters is proposed along with its proofs. A comparison between the existing similarity measures and the proposed similarity measure is also performed in terms of counter-intuitive cases. The findings indicate that the proposed similarity measure does not provide any counter-intuitive cases.

Conceptual design evaluation using interval type-2 fuzzy information axiom

Concept selection is the most critical part of the design process as it determines the direction of subsequent design stages. In addition, it is a difficult task because available information for decision-making at this stage is imprecise and subjective. This necessitates the need for fuzzy decision models for selecting the best conceptual design among a set of alternatives. Although ordinary fuzzy sets cover uncertainties of linguistic words to some extent, it is recommended to use interval type-2 fuzzy sets (IT2FS) to capture potential uncertainties of words. This paper presents a new concept selection methodology that extends the fuzzy information axiom (FIA) approach to incorporate IT2FSs. The proposed methodology is called interval-type-2 fuzzy information axiom (IT2-FIA). IT2-FIA method is also enriched by using ordered weighted geometric aggregation operator to include the decision makers attitude during the aggregation process. A case study is given to demonstrate the potential of the methodology.

Collaborative tool for solving human factors problems in the manufacturing environment : the Theory of Inventive Problem Solving Technique (TRIZ) method

In this study an analysis is made regarding the Theory of Inventive Problem Solving Technique (TRIZ), which emerged in Russia in 1946 and has been commonly used in the USA and Europe in the past few last decades. TRIZ is a method that is used successfully to solve the problems arising during the process of product development. Within this study this method is evaluated from the human factors point of view for the first time. In addition, two applications of the adaptation of TRIZ into human factors problems and works on this goal are presented. The benefits of TRIZ when solving such kind problems are also revealed.

An overview of methods for linguistic summarization with fuzzy sets

We review the evaluating methods on linguistic summarization.We propose a taxonomy for the methods.We present the differences between methods.We illustrate that fuzzy cardinality based methods provides consistent results. While the rapid development of information technology has made easy to store and access the huge amount of data, it also brings another problem, that of how to extract potentially useful knowledge not only in an efficient way but also in a way that could be easily understandable by humans. One of the solutions to this problem is linguistic summarization, aim of which is to generate explicit and concise summaries from data that is more compatible with human cognitive mechanism. The most crucial step in linguistic summarization is certainly the evaluation of linguistic summaries since they are the most important element of fuzzy rule based systems commonly used in expert systems and intelligent systems. Therefore, the selection of appropriate method for evaluating linguistic summaries in sense of different views such as quality, quantity, relevance and simplicity becomes vital. The aim of this paper is to review the state of art on linguistic summarization in the framework of fuzzy sets, focusing on the methods for evaluating linguistic summaries and the current applications. A taxonomy is proposed to identify the existing methods depending on the type of fuzzy sets (i.e., type-1 fuzzy set and type-2 fuzzy set) and the type of cardinalities (i.e., scalar cardinality and fuzzy cardinality). The recent studies on linguistic summarization are also presented to give a comprehensive framework for the future directions. The paper ends with conclusions, addressing some important issues and open questions which can be subject for future research.

A generic method for the evaluation of interval type-2 fuzzy linguistic summaries.

Linguistic summarization has turned out to be an important knowledge discovery technique by providing the most relevant natural language-based sentences in a human consistent manner. While many studies on linguistic summarization have handled ordinary fuzzy sets [type-1 fuzzy set (T1FS)] for modeling words, only few of them have dealt with interval type-2 fuzzy sets (IT2FS) even though IT2FS is better capable of handling uncertainties associated with words. Furthermore, the existent studies work with the scalar cardinality based degree of truth which might lead to inconsistency in the evaluation of interval type-2 fuzzy (IT2F) linguistic summaries. In this paper, to overcome this shortcoming, we propose a novel probabilistic degree of truth for evaluating IT2F linguistic summaries in the forms of type-I and type-II quantified sentences. We also extend the properties that should be fulfilled by any degree of truth on linguistic summarization with T1FS to IT2F environment. We not only prove that our probabilistic degree of truth satisfies the given properties, but also illustrate by examples that it provides more consistent results when compared to the existing degree of truth in the literature. Furthermore, we carry out an application on linguistic summarization of time series data of Europe Brent Spot Price, along with a comparison of the results achieved with our approach and that of the existing degree of truth in the literature.

Usability ranking of intercity bus passenger seats using fuzzy axiomatic design theory

Usability, considering user satisfaction along with the user performance, is one of the key factors in determining the success of a product in today’s competitive market. Designing usable intercity bus seats is important for passengers during the long hours of traveling. Comfort, aesthetic, safety, convenience to the body posture, durability, harmoniousness with the seat accessories and operability are expected usability dimensions of seats for both user and the designers. Aim of this study is to identify and rank ten alternative seats of an intercity bus manufacturing company according to these usability attributes. The products are evaluated by five subjects and assessed for each usability attributes by using linguistic variables. Then Fuzzy Axiomatic Design Theory (FADT), which is the combination of second axiom, is used as a multi attribute decision making tool to determine most usable seat design solution. Design range is defined by design engineers and system ranges for seats are obtained from linguistic assessment of five subjects for applying conformance testing in cooperative engineering.

Evaluation of product design concepts using grey-fuzzy information axiom

Evaluation of product design concepts is an important and critical problem, considering incomplete and imprecise information in the early stages of product design process. In order to solve this problem, grey theory, fuzzy sets and information axiom are combined in this study under the name of grey-fuzzy information axiom for solving product concept evaluation problem for the first time. The information axiom has the capability to solve multi-attribute evaluation problems. Grey and fuzzy set theories are complementary methods for quantification uncertainty. Applicability of the proposed method is demonstrated on the evaluation of dishwasher design concepts. It has been shown that grey-fuzzy information axiom is an appropriate tool to be used for the concept evaluation problem in case of having different types of uncertainties.