Lukasiewicz Fuzzy Implication Operator on Pythagorean Fuzzy Tautological Matrices

In this paper, introduced Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices and some properties of Lukasiwicz implication operator over Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices are discussed. Also discussed the relation between implication with Lukasiewicz disjunction and conjunction operations of PFCMs and PFCTMs.

Pythagorean fuzzy full implication multiple I method and corresponding applications

The overwhelming majority of existing decision-making methods combined with the Pythagorean fuzzy set (PFS) are based on aggregation operators, and their logical foundation is imperfect. Therefore, we attempt to establish two decision-making methods based on the Pythagorean fuzzy multiple I method. This paper is devoted to the discussion of the full implication multiple I method based on the PFS. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO), Pythagorean fuzzy biresiduum, and the degree of similarity between PFSs based on the Pythagorean fuzzy biresiduum. In addition, the full implication multiple I method for Pythagorean fuzzy modus ponens (PFMP) is established, and the reversibility and continuity properties of the full implication multiple I method of PFMP are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in a decision-making problem. The advantages of the new method over existing methods are also explained. Overall, the proposed methods are based on logical reasoning, so they can more accurately and completely express decision information.

Measurement of Countable Compactness and Lindelöf Property in RL -Fuzzy Topological Spaces

Based on the concepts of pseudocomplement of L -subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL -fuzzy compactness degree and the Lindelöf property degree of an L -subset in RL -fuzzy topology are introduced and characterized. Since L -fuzzy topology in the sense of Kubiak and Šostak is a special case of RL -fuzzy topology, the degrees of RL -fuzzy compactness and the Lindelöf property are generalizations of the corresponding degrees in L -fuzzy topology.

Willmott Fuzzy Implication in Fuzzy Databases

The object of the research are fuzzy functional dependencies on given relation scheme, and the question of their obtaining using the classical and innovated techniques. The attributes of the universal set are associated to the elements of the unit interval, and are turned into fuzzy formulas in this way. We prove that the dependency (which is treated as a fuzzy formula with respect to appropriately chosen valuation) is valid whenever it agrees with the attached two-elements fuzzy relation instance. The opposite direction of the claim is proven to be incorrect in this setting. Generalizing things to sets of attributes, we prove that particular fuzzy functional dependency follows form a set of fuzzy dependencies (in both, the world of two-element and the world of arbitrary fuzzy relation instances) if and only if the dependency is valid with respect to valuation anytime the set of fuzzy formulas agrees with the valuation. The results derived in paper show that the classical techniques in the procedure for generating new fuzzy dependencies may be replaced by the resolution ones, and hence automated. The research is conducted with respect to Willmott fuzzy implication operator

The logic of orthomodular posets of finite height

Orthomodular posets form an algebraic formalization of the logic of quantum mechanics. A central question is how to introduce implication in such a logic. We give a positive answer whenever the orthomodular poset in question is of finite height. The crucial advantage of our solution is that the corresponding algebra, called implication orthomodular poset, i.e. a poset equipped with a binary operator of implication, corresponds to the original orthomodular poset and that its implication operator is everywhere defined. We present here a complete list of axioms for implication orthomodular posets. This enables us to derive an axiomatization in Gentzen style for the algebraizable logic of orthomodular posets of finite height.

Prediction of Visibility Under Radiation Fog by DNA Computing

In this paper, we propose a wet lab algorithm for prediction of visibility under radiation fog by DNA computing. The model is based on a concept of similarity based fuzzy reasoning suitable for wet lab implementation. The concept of similarity based fuzzy reasoning using DNA sequences is different from conventional approach to fuzzy reasoning. It replaces the logical aspect of classical fuzzy reasoning by DNA chemistry. By the proposed algorithm the tedious job to choose suitable implication operator, which is absolutely necessary for classical fuzzy reasoning, can be avoided. If the fuzzified forms of five observed parameters, i.e. dew point, dew point spread, the rate of change of dew point spread per day, wind speed and sky condition are given, the newly proposed algorithm efficiently predicts the possibility of visibility under radiation fog. The final result of the wet lab algorithm, which is in form of fuzzy DNA, produces multi valued status which can be linguistically interpreted to match the perception of an expert.

Lukaswize Triple-Valued Intuitionistic Fuzzy BCK/BCI-Subalgebras

The authors studied the notion of (α,β)-intuitionistic fuzzy BCK/BCI-subalgebras by applying the Lukasiewicz 3-valued implication operator, where α,β∈{∈,q,∈∧q,∈∨q} for α≠∈∧q. In this chapter, an intuitionistic fuzzy set A is an (∈,∈) (or (∈∧q,∈) or (∈,∈∨q))-intuitionistic fuzzy subalgebras if and only if for any p∈(0,1] (or p∈(0,0.5] or p∈(0.5,1]), then Ap is a fuzzy subalgebras of X respectively. Next, the authors defined intuitionistic fuzzy subalgebras with thresholds (s,t) and then provided intuitionistic fuzzy subalgebras with thresholds (0,1) (or (0,0.5) or (0.5,1)) by the concept of quasi-coincidence of fuzzy point respectively. Also, A is an intuitionistic fuzzy subalgebras with thresholds (s,t) if and only if for any p∈(s,t], then cut set A_p is a fuzzy subalgebras.

The Measure of Fuzzy Filters on BL-Algebras

The new concept of the fuzzy filter degree was given by means of the implication operator, which enables to measure a degree to which a fuzzy subset of a BL-algebra is a fuzzy filter. In this paper, we put forward several equivalent characterizations of the fuzzy filter degree by studying its properties and the relationship with level cut sets. Furthermore, we study the fuzzy filter degrees of the intersection and fuzzy direct products of fuzzy subsets and investigate the fuzzy filter degrees of the image and the preimage of a fuzzy subset under a homomorphism.

A degree approach to relationship among fuzzy convex structures, fuzzy closure systems and fuzzy Alexandrov topologies

In this paper, by means of the implication operator → on a completely distributive lattice M, we define the approximate degrees of M-fuzzifying convex structures, M-fuzzifying closure systems and M-fuzzifying Alexandrov topologies to interpret the approximate degrees to which a mapping is an M-fuzzifying convex structure, an M-fuzzifying closure system and an M-fuzzifying Alexandrov topology from a logical aspect. Moreover, we represent some properties of M-fuzzifying convex structures as well as its relations with M-fuzzifying closure systems and M-fuzzifying Alexandrov topologies by inequalities.