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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TL;DR: The centroid and generalized centroid of a type-2 fuzzy set are introduced, and how to compute them is explained, and examples are given that compare the exact computational results with the approximate results.
1,141 citations
15 Apr 1998
TL;DR: Part 1 Fundamentals of fuzzy sets: basic notions and concepts of fuzzy Set Theory, types of membership functions, characteristics of a fuzzy set, basic relationships between fuzzy sets, and problem solving with fuzzy sets.
Abstract: Part 1 Fundamentals of fuzzy sets: basic notions and concepts of fuzzy sets - set membership and fuzzy sets, basic definitions of a fuzzy set, types of membership functions, characteristics of a fuzzy set, basic relationships between fuzzy sets - equality and inclusion, fuzzy sets and sets - the representation theorem, the extension principles, membership function determination, generalizations of fuzzy sets, chapter summary, problems, references fuzzy set operations - set theory operations and their properties, triangular norms, aggregation operations on fuzzy sets, sensitivity of fuzzy sets operators, negations, comparison operations on fuzzy sets, chapter summary, problems, references information-based characterization of fuzzy sets -entropy measures of fuzziness, energy measures of fuzziness, specificity of a fuzzy set, frames of cognition, information encoding and decoding using linguistic landmarks, decoding mechanisms for pointwise data, decoding using membership functions of the linguistic terms of the codebook, general possibility-necessity decoding, distance between fuzzy sets based on their internal, linguistic representation, chapter summary, problems, references fuzzy relations and their calculus -relations and fuzzy relations, operations on fuzzy relations, compositions of fuzzy relations, projections and cylindric extensions of fuzzy relations, binary fuzzy relations, some classes of fuzzy relations, fuzzy-relational equations, estimation and inverse problem in fuzzy relational equations, solving fuzzy-relational equations with the sup-t composition, solutions to dual fuzzy-relational equations, adjoint fuzzy-relational equations, generaliations of fuzzy relational equations, approximate solutions to fuzzy-relational equations, chapter summary, problems, references fuzzy numbers - defining fuzzy numbers, interval analysis and fuzzy numbers, computing with fuzzy numbers, triangular fuzzy numbers and basic operations, general formulas for LR fuzzy numbers, accumulation of fuzziness in computing with fuzzy numbers, inverse problem in computation with fuzzy numbers, fuzzy numbers and approximate operations, chapter summary, problems, references fuzzy modelling - fuzzy models - beyond numerical computations, main phases of system modelling, fundamental design objectives in system modelling, general topology of fuzzy models, compatibility of encoding and decoding modules, classes of fuzzy models, verification and validation of fuzzy models, chapter summary, problems, references. Part 3 Problem solving with fuzzy sets: methodology -analysis and design, fuzzy controllers and fuzzy control, mathematical programming and fuzzy optimization, chapter summary, problems, references case studies - traffic intersection control, distributed traffic control, elevator group control, induction motor control, communication network planning, neurocomputation in fault diagnosis of dynamic systems, multicommodity transportation planning in railways.
1,120 citations
TL;DR: A method of ranking fuzzy numbers with integral value is proposed, which is independent of the type of membership functions used and the normality of the functions, and can rank more than two fuzzy numbers simultaneously.
1,098 citations
TL;DR: New techniques for handling multicriteria fuzzy decision-making problems based on vague set theory can provide a useful way to efficiently help the decision-maker to make his decisions.
1,091 citations
TL;DR: Some novel operational laws of PFSs are defined and an extended technique for order preference by similarity to ideal solution method is proposed to deal effectively with them for the multicriteria decision‐making problems with PFS.
Abstract: Recently, a new model based on Pythagorean fuzzy set PFS has been presented to manage the uncertainty in real-world decision-making problems. PFS has much stronger ability than intuitionistic fuzzy set to model such uncertainty. In this paper, we define some novel operational laws of PFSs and discuss their desirable properties. For the multicriteria decision-making problems with PFSs, we propose an extended technique for order preference by similarity to ideal solution method to deal effectively with them. In this approach, we first propose a score function based comparison method to identify the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution. Then, we define a distance measure to calculate the distances between each alternative and the Pythagorean fuzzy positive ideal solution as well as the Pythagorean fuzzy negative ideal solution, respectively. Afterward, a revised closeness is introduced to identify the optimal alternative. At length, a practical example is given to illustrate the developed method and to make a comparative analysis.
1,084 citations