Earticle

Material selection is a complex problem in the design and development of products for diverse engineering applications. This paper is aimed to present a fuzzy decision‐making approach to deal with the material selection in engineering design problems. A fuzzy multi criteria decision‐making model is proposed for solving the material selection problem. The proposed model makes use of fuzzy TOPSIS (Technique for Order reference by Similarity to Ideal Solution) with trapezoidal numbers for evaluating the criteria and ranking the alternatives. And result is compared with fuzzy VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian, means Multi criteria Optimisation and Compromise Solution) which is proposed by Jeya Girubha and Vinodh [2012]. The present paper is aimed to also improve literature of fuzzy decision making for material selection problem.

The technology based self service banking (TBSSB) refers to automated banking services that customer avail in self service mode using various electronic banking channels, without any interaction with bank employees. Researchers have used numerous methods to evaluate automated banking service quality. In this paper, a methodology to quantify the overall effect of key TBSSB service quality attributes is discussed. The TBSSB service quality index is calculated by using fuzzy along with graph theory and matrix methods. Broad attributes affecting TBSSB service quality are identified. The fuzzy numbers are used to convert intangible attributes to crisp scores and then graph theoretic approach has been applied to calculate the single numerical index. This study may help bank management to take various decisions pertaining to TBSSB service quality using TBSSB index. It will also assist academicians in better understanding of TBSSB services.

Similarity measures of fuzzy numbers have been widely applied in various areas. In the last decade, many similarity measures of generalized fuzzy numbers were proposed. However, there are two main limitations in existing similarity measures: 1) they cannot correctly calculate the degree of similarity between two generalized trapezoidal fuzzy numbers in some cases; and 2) the definitions of recently developed similarity measures are complicated and difficult to interpret. In this paper, a novel approach to similarity measurement between generalized trapezoidal fuzzy numbers is proposed. The proposed similarity measure has a simple definition and is easier to understand intuitively. Furthermore, we analyze its properties and compare it with existing similarity measures. The results show that the proposed measure outperforms existing similarity measures. Finally, we apply the proposed similarity measure to develop a fuzzy-logic-based approach for new product go/nogo decision-making at the front end. The proposed fuzzy software quality evaluation method is more flexible and more intelligent than existing methods due to the fact that it considers the degrees of confidence of evaluators’ opinions.

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy quantities based on the extension principle suggested by Mare (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous t-norm which holds the distributivity under t-norm based fuzzy arithmetic operations.

This paper shows that fuzzy set theory can be useful in modeling and solving job scheduling problems with uncertain processing times. The processing times are considered as fuzzy numbers(fuzzy intervals or time intervals) and the fuzzy Delphi method is used to estimate a reliable time interval of each processing time. Based on these time estimates, we then propose an efficient methodology for calculating the optimal sequence and the fuzzy makespan.

It is generally difficult to compute the level cut sets of type-2 fuzzy sets, so type-2 fuzzy sets that are more naturally represented and whose level cut sets can be computed relatively easily are desired. Then, we introduce a new type-2 fuzzy number called Triangular Shaped Type-2 Fuzzy Number in this paper. Moreover, we study calculus for type-2 fuzzy-number-valued functions and solve the problem of a fuzzy differential equation whose initial value is this type-2 fuzzy number.

The objective of this paper is to devise a new technique to combine generalized interval valued fuzzy numbers (GIVFNs)based on average width of fuzzy set concept. The effectiveness and applicability of the proposed technique are illustrated with an example.

This paper aims to develop new theoretical foundations for solving convex multi-objective fuzzy optimization problems in a quotient space of fuzzy numbers. The primary objective is to extend the Karush-Kuhn-Tucker optimality conditions, originally designed for single-objective fuzzy optimization, to the multi-objective setting under convexity and differentiability assumptions. The methodology relies on defuzzification using midpoint functions, derived from $\alpha$-cuts and Mare? cores, which transform fuzzy problems into classical equivalents. The proposed framework allows for the definition of Pareto, weak Pareto, and strong Pareto solutions in a fuzzy context. Key results include the necessary and sufficient Karush-Kuhn-Tucker optimality conditions. This approach bridges the gap between fuzzy mathematical theory and practical optimization techniques in uncertain environments.

.Fuzzy model has been applied to economics, sociology, management studies, psychology, and linguistics for decision-making under vague situations and specification of vague objects, and setup of vague model or structure. New method of measuring perceived service quality based on triangular fuzzy numbers in proposed in this study. Hamming distance method and Dubois’s methodology were used for our study to establish the validity of decision-making in each lodging attribute. We replace perceptions by satisfaction degree as well as expectation by importance degree. To evaluate the discrepancy between tourist’s satisfaction and impotance degree. we infer general solutions to compute the intersection area between to triangular fuzzy numbers, then the weak and/or strong attributes of lodging houses are clarified. Therefore, this study introduces a general concept of fuzzy theory through literature review of linguistic expressions and possibility theory. In terms of methodology this study disclosed that fuzzy model approach is greatly useful to evaluate perceived service quality. Our method overcome linguistic problems and this study provides more objective information for lodging industry in Kyongju.

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We define the pentagonal fuzzy sets and generalize the results of addition, subtraction, multiplication, and division based on the Zadeh's extension principle for two pentagonal fuzzy sets. In addtion, we find the condition that the result of addition or subtraction for two pentagonal fuzzy sets becomes a triangular fuzzy number and give some example.

In this paper, we want to represent a method for ranking of two exponential trapezoidal fuzzy numbers. In this study a new Cardinality between exponential trapezoidal fuzzy numbers is proposed. Cardinality in this method is relatively simple and easier in computation and ranks various types of exponential fuzzy numbers. For the validation the results of the proposed approach are compared with different existing approaches.

When data is classified and each class has weight, the mean of data is a weighted average. When the class values and weights are trapezoidal fuzzy numbers, we can prove the weghted average is a fuzzy number though not trapezoidal. Its 4 corner points are obtained.

There are many results on the extended operations of two fuzzy numbers based on the Zadeh's extension principle. For the calculation, we have to use existing operations between two ${\alpha}$-cuts. In this paper, we define parametric operations between two ${\alpha}$-cuts which are different from the existing operations. But we have the same results as the extended operations of Zadeh's principle.

In this paper, we find some algebraic properties of intuitionistic fuzzy numbers.

The sum Of L - R fuzzy numbers With Unbounded Supports based on Archimedean continuous f-norm T is considered. Results are more simple than those of the case for bounded supports.

본 논문에서는 사용자의 관심도나 선호도를 반영하여, 퍼지숫자를 정렬하는 방법을 제안한다. 사용자는 자신의 관심도나 선호도를 퍼지집합으로 표현한다. 제안하는 방법은 사용자로부터 주어진 퍼지집합을 평가관점으로 이용하며, 평가함수로는 이전에 제안된 만족도 함수를 이용한다. 제안하는 방법이 관점에 따라 어떠한 결과를 주는지를 보기 위하여, 퍼지숫자 정렬에 적용한 예를 보인다.

We compute the extended four operations of the 2-dimensional quadratic fuzzy numbers. Then we calculate the intersection between a plane perpendicular to the x-axis, which passes through each vertex, and the resulting 2-dimensional quadratic fuzzy number. We confirm that the equations of the two intersections acquired in this way and the graphs are actually identical, respectively.

Comparison between two or more fuzzy numbers, along with their ranking, is an important subject discussed in scholarly articles. We endeavor in this paper to present a simple yet effective parametric method for comparing fuzzy numbers. This method offer significant advantages over similar methods, in comparing intersected fuzzy numbers, rendering the comparison between fuzzy numbers possible in different decision levels. In the process, each fuzzy number will be given a parametric value in terms of $\alpha$, which is dependent on the related $\alpha$-cuts. We have compared this method to Cheng's centroid point method [5] (The relation of calculating centroid point of a fuzzy number was corrected later on by Wang [12]). The proposed method can be utilized for all types of fuzzy numbers whether normal, abnormal or negative.