Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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01 May 2017
TL;DR: Two interval-valued fuzzy soft approaches based on prospect theory and regret theory are proposed and two algorithms to solve stochastic multi-criteria decision making problem are proposed that take regret aversion and prospect preference of decision makers into consideration in the decision process.
Abstract: Graphical abstractDisplay Omitted HighlightsWe initiate a new axiomatic definition of interval-valued fuzzy distance measure.We propose the method of computing objective weights.We propose two algorithms to solve stochastic multi-criteria decision making problem.The effectiveness and feasibility of two algorithms are demonstrated by two numerical examples.Two interval-valued fuzzy soft approaches based on prospect theory and regret theory are proposed. This paper presents two novel interval-valued fuzzy soft set approaches. First, we initiate a new axiomatic definition of interval-valued fuzzy distance measure, which is expressed by interval-valued fuzzy number (IVFN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via normal distribution. Combining objective weights with subjective weights, we present the combined weights, which can reflect both the subjective considerations of the decision maker and the objective information. Later, we propose two algorithms to solve stochastic multi-criteria decision making problem, which take regret aversion and prospect preference of decision makers into consideration in the decision process. Finally, the effectiveness and feasibility of two approaches are demonstrated by two numerical examples.
174 citations
TL;DR: Some theoretical analyses of the Nie-Tan direct defuzzification method are provided and it is suggested that the NT method is a very good way to simplify an interval type-2 fuzzy set.
Abstract: Type reduction (TR) followed by defuzzification is commonly used in interval type-2 fuzzy logic systems (IT2 FLSs). Because of the iterative nature of TR, it may be a computational bottleneck for the real-time applications of an IT2 FLS. This has led to many direct approaches to defuzzification that bypass TR, the simplest of which is the Nie-Tan direct defuzzification method (NT method). This paper provides some theoretical analyses of the NT method that answer the question “Why is the NT method good to use?” This paper also provides a direct relationship between TR followed by defuzzification (using KM algorithms) and the NT method. It also provides an improved NT method. Numerical examples illustrate our theoretical results and suggest that the NT method is a very good way to simplify an interval type-2 fuzzy set.
174 citations
TL;DR: A revised method for ranking fuzzy numbers with index of optimism and an algorithm for technology transfer strategy selection based on the concepts of fuzzy set theory and the hierarchical structure analysis are proposed.
174 citations
TL;DR: This paper proposes a new fuzzy multiattribute group decision making method based on intuitionistic fuzzy sets and the evidential reasoning methodology that can overcome the drawbacks of the existing methods for fuzzy multi attribute group decisionMaking in intuitionistic fuzzier environments.
173 citations
Book•
04 Feb 2010
TL;DR: This monograph is suitable for researchers, graduate students and seminars of theoretical and applied mathematics, computer science, statistics and engineering, and it is the first one in Fuzzy Approximation Theory.
Abstract: This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy Approximation Theory. The chapters are self-contained with lots of applications to teach several advanced courses and the topics covered are very diverse. An extensive background of Fuzziness and Fuzzy Real Analysis is given. The author covers Fuzzy Differentiation and Integration Theory followed by Fuzzy Ostrowski inequalities. Then results on classical algebraic and trigonometric polynomial Fuzzy Approximation are presented. The author develops a complete theory of convergence with rates of Fuzzy Positive linear operators to Fuzzy unit operator, the so-called Fuzzy Korovkin Theory. The related Fuzzy Global Smoothness is included. Then follows the study of Fuzzy Wavelet type operators and their convergence with rates to Fuzzy unit operator. Similarly the Fuzzy Neural Network Operators are discussed followed by Fuzzy Random Korovkin approximation theory and Fuzzy Random Neural Network approximations. The author continues with Fuzzy Korovkin approximations in the sense of Summability. Finally fuzzy sense differences of Fuzzy Wavelet type operators are estimated. The monograph's approach is quantitative and the main results are given via Fuzzy inequalities, involving Fuzzy moduli of continuity, that is Fuzzy Jackson type inequalities. The exposed theory is destined and expected to find applications to all aspects of Fuzziness from theoretical to practical in almost all sciences, technology, finance and industry. Also it has its interest within Pure Mathematics. So this monograph is suitable for researchers, graduate students and seminars of theoretical and applied mathematics, computer science, statistics and engineering.
173 citations