A definition of the concept 'intuitionistic fuzzy set' (IFS) is given, the latter being a generalization of the concept 'fuzzy set' and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators...
Background knowledge is often expressed in linguistic forms; for example, “probability θ is low.” This information can be demonstrated in the form of fuzzy probability with fuzzy sets on the universe of the likelihood representing linguistic terms such as “low”. We can consider this knowledge...
In this case, the topology is compatible with the linear space structure of E and we obtain a topological vector space. If d is complete, we obtain an F-space (see [12], 1.8). Definition 2. ([2]). A fuzzy set F in 𝐸×ℝ is called a fuzzy pseudo-norm (shortened to FP-...
For example, the quantifier defined as “if 23 is in the universe of discourse, many, otherwise some” returns the same value as the quantifier “many” for universes that contain the number 23, and the same value as the quantifier “some” for other universes. This is PI (because any ...
In the paper a definition of the optimal solution of the transportation problem with fuzzy cost coefficients as well as an algorithm determining this solut... S Chanas,D Kuchta - 《Fuzzy Sets & Systems》 被引量: 366发表: 1996年 The fuzzy set theory approach to the vehicle routing problem ...
The following examples are presented for Definition 3. Example 1. A student achievement sheet is shown in Table 1, where 𝑈={𝑥1,𝑥2,𝑥3,𝑥4} is the set of four students, the value range of “Mathematics” is from (0,100], the value range of “English” is from {1,2,3...
Before applying the implication method, you must determine the rule weight. Every rule has aweight(a number from 0 through 1), which is applied to the number given by the antecedent. Generally, this weight is 1 (as it is for this example) and thus has no effect on the implication proce...
To understand what a fuzzy set is, first consider the definition of aclassical set. A classical set is a container that wholly includes or wholly excludes any given element. For example, the set of days of the week unquestionably includes Monday, Thursday, and Saturday. It just as unquestiona...
set theoretic operations for crisp and type-1 fuzzy sets, crisp and fuzzy relations and compositions on the same or different product spaces , compositions of a type-1 fuzzy set with a type-1 fuzzy relation , hedges, the Extension Principle (which is about functions of fuzzy sets), α-cuts...
To illustrate the proposed method an example is provided and the obtained results are discussed.M. ShanmugasundariK. GanesanArtificial Intelligent Systems & Machine LearningChen, M. S. 1985. On a fuzzy assignment problem. Tamkang J., ... M Shanmugasundari,K Ganesan - 《Artificial Intelligent Sys...