-algebras of the monad -Fuzz
-equivalences generated by shape function on the real line
This paper is devoted to give a new method of generating T-equivalence using shape function and finding the exact calculation formulas of T-equivalence induced by shape function on the real line. Some illustrative examples are given.
-extension as a method of construction of a generalized aggregation operator
Generalized aggregation operators are the tool for aggregation of fuzzy sets. The apparatus was introduced by Takači in [11]. -extension is a construction method of a generalized aggregation operator and we study it in the paper. We observe the behavior of a -extension with respect to different order relations and we investigate properties of the construction.
-Fuzzy topological concepts
-law of large numbers for fuzzy numbers
The notions of a -norm and of a fuzzy number are recalled. The law of large numbers for fuzzy numbers is defined. The fuzzy numbers, for which the law of large numbers holds, are investigated. The case when the law of large numbers is violated is studied.
The cancellation law for pseudo-convolution
Cancellation law for pseudo-convolutions based on triangular norms is discussed. In more details, the cases of extremal t-norms and , of continuous Archimedean t-norms, and of general continuous t-norms are investigated. Several examples are included.
The distribution of mathematical expectations of a randomized fuzzy variable.
The Shaffer's definition of the upper and lower expectations of fuzzy variables is considered with respect to randomized fuzzy sets. The notion of randomized fuzzy sets is introduced in order to evaluate fuzzy statistical indices for an arbitrary chosen fuzzy variable. Provided the distribution of the mathematical expectation of a randomized fuzzy variable is known, it is possible to adopt the traditional methods of testing statistical hypotheses for fuzzy variables.We show that this distribution...
The embedding of the formal concept analysis into the L-Fuzzy concept theory.
In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the L-Fuzzy concept lattice ([2]) developed by us. To do it, we have defined an application g that associates to each concept of Wille an L-Fuzzy concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the L-Fuzzy concept lattice. At the end, we show a typical example in the formal...
The Formal Construction of Fuzzy Numbers
In this article, we continue the development of the theory of fuzzy sets [23], started with [14] with the future aim to provide the formalization of fuzzy numbers [8] in terms reflecting the current state of the Mizar Mathematical Library. Note that in order to have more usable approach in [14], we revised that article as well; some of the ideas were described in [12]. As we can actually understand fuzzy sets just as their membership functions (via the equality of membership function and their set-theoretic...
The fuzzy hyperbolic inequality index of fuzzy random variables in finite populations.
This paper presents an approach to the problem of quantifying the inequality of a finite population with respect to a (social, economical, etc.) fuzzy-valued attribute. For this purpose, the fuzzy hyperbolic inequality index is introduced, and some properties extending the basic ones for real-valued attributes are examined.
The internal rate of return of fuzzy cash flows.
An internal rate of return (IRR) of an investment or financing project with cash flow (a0,a1,a2,...,an) is usually defined as a rate of interest r such thata0 + a1(1 + r)-1 + ... + an(1 + r)-n = 0.If the cash flow has one sign change then the previous equation has a unique solution r > -1.Generally the IRR technique does not extend to fuzzy cash flows, as it can be seen with examples (see [2]). In this paper we show that under suitable hypothesis a unique fuzzy IRR exists for a fuzzy cash...
The similarity of two strings of fuzzy sets
Let be the strings of fuzzy sets over , where is a finite universe of discourse. We present the algorithms for operations on fuzzy sets and the polynomial time algorithms to find the string over which is a closest common subsequence of fuzzy sets of and using different operations to measure a similarity of fuzzy sets.
The stability of parameter estimation of fuzzy variables
Recently, the parameter estimations for normal fuzzy variables in the Nahmias’ sense was studied by Cai [4]. These estimates were also studied for general -related, but not necessarily normal fuzzy variables by Hong [10] In this paper, we report on some properties of estimators that would appear to be desirable, including unbiasedness. We also consider asymptotic or “large-sample” properties of a particular type of estimator.
The study of the L-fuzzy concept lattice.
The L-Fuzzy concept theory that we have developed sets up classifications from the objects and attributes of a context through L-Fuzzy relations. This theory generalizes the formal concept theory of R. Wille. In this paper we begin with the L-Fuzzy concept definition that generalizes the definitions of the formal concept theory, and we study the lattice structure of the L-Fuzzy concept set, giving a constructive method for calculating this lattice. At the end, we apply this constructive method to...
The study on semicopula based implications
Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula...
The variational principle of fixed point theorems in certain fuzzy topological spaces
The main purpose of this paper is to introduce the concept of -type fuzzy topological spaces. Further variational principle and Caristi’s fixed point theorem have been extended in the -type fuzzy topological spaces.
The σ-complete MV-algebras which have enough states
We characterize Łukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the Łukasiewicz t-norm with countably many arguments. As a tool, we introduce σ-McNaughton functions as the closure of McNaughton functions under countable MV-algebraic operations. We give a measure-theoretical characterization of σ-complete MV-algebras which are isomorphic to Łukasiewicz tribes.
Tietze extension theorem for pairwise ordered fuzzy extremally disconnected spaces
In this paper a new class of fuzzy topological spaces called pairwise ordered fuzzy extremally disconnected spaces is introduced. Tietze extension theorem for pairwise ordered fuzzy extremally disconnected spaces has been discussed as in the paper of Kubiak (1987) besides proving several other propositions and lemmas.
Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets
In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the...
Towards the properties of fuzzy multiplication for fuzzy numbers
In this paper, by using a new representation of fuzzy numbers, namely the ecart-representation, we investigate the possibility to consider such multiplication between fuzzy numbers that is fully distributive. The algebraic and topological properties of the obtained semiring are studied making a comparison with the properties of the existing fuzzy multiplication operations. The properties of the generated fuzzy power are investigated.