Intuitionistic Fuzzy T-norm Research Articles

Intuitionistic fuzzy-valued neutrosophic multi-sets and numerical applications to classification

A single-valued neutrosophic multi-set is characterized by a sequence of truth membership degrees, a sequence of indeterminacy membership degrees and a sequence of falsity membership degrees. Nature of a single-valued neutrosophic multi-set allows us to consider multiple information in the truth, indeterminacy and falsity memberships which is pretty useful in multi-criteria group decision making. In this paper, we consider sequences of intuitionistic fuzzy values instead of numbers to define the concept of intuitionistic fuzzy-valued neutrosophic multi-set. In this manner, such a set gives more powerful information. We also present some set theoretic operations and a partial order for intuitionistic fuzzy-valued neutrosophic sets and provide some algebraic operations between intuitionistic fuzzy-valued neutrosophic values. Then, we develop two types of weighted aggregation operators with the help of intuitionistic fuzzy t-norms and t-conorms. By considering some well-known additive generators of ordinary t-norms, we give the Algebraic weighted arithmetic and geometric aggregation operators and the Einstein weighted arithmetic and geometric aggregation operators that are the particular cases of the weighted aggregation operators defined via general t-norms and t-conorms. We also define a simplified neutrosophic valued similarity measure and we use a score function for simplified neutrosophic values to rank similarities of intuitionistic fuzzy-valued neutrosophic multi-values. Finally, we give an algorithm to solve classification problems using intuitionistic fuzzy-valued neutrosophic multi-values and proposed aggregation operators and we apply the theoretical part of the paper to a real classification problem.

MORE ON INTUITIONISTIC FUZZY SUBLATTICES AND THEIR IDEALS

In this paper, we study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals with respect to an intuitionistic fuzzy t-norm on an adequate lattice. Some characterizations and properties of these intuitionistic fuzzy sublattices and ideals with respect to intuitionistic fuzzy t-norm are established.

INTUITIONISTIC FUZZY BI-IMPLICATOR AND PROPERTIES OF LUKASIEWICZ INTUITIONISTIC FUZZY BI-IMPLICATOR

This paper presents axiomatic as well as constructive definitions of intuitionistic fuzzy bi-implicators based on intuitionistic fuzzy t-norms and their intuitionistic fuzzy residual implicators. The inter-relationship among different proposed classes is presented along with a detailed study of the properties of one of these intuitionistic fuzzy bi-implicators called the intuitionistic fuzzy beta-bi-operator constructed using Lukasiewicz intuitionistic fuzzy t-norm and its R-implicator.

H-max distance measure of intuitionistic fuzzy sets in decision making

Intuitionistic fuzzy sets (IFSs) are successful to handle the uncertain situations of data. Distance measures of IFSs are important in the evaluation of IFSs relationships. In this paper, we analyzed the disadvantages of existing distance measures of IFSs and proposed a new distance measure called H-max of IFSs. We continued to point out some new results on intuitionistic t-norms and intuitionistic t-conorms and evaluated distance measure between two IFSs which are basically structured from these operations. Further, we combined the classification of t-representable intuitionistic fuzzy t-norms and t-conorms with the proposed distance measure to study some interesting properties. Moreover, we studied De Morgan triplets of IFSs based on the proposed distance measure. Finally, we applied the proposed distance measure to medical diagnosis problem examples and experimental validation on real-world datasets to check the applicability and effectiveness.

Variable precision intuitionistic fuzzy rough sets model and its application

Rough set theory is an important mathematical tool to deal with insufficient and incomplete information. The concepts of intuitionistic fuzzy rough sets and variable precision rough sets are very useful in the study of intelligent systems. The aim of this paper is to present a new extension of the rough set theory by means of integrating the variable precision rough set theory with the intuitionistic fuzzy rough set theory, i.e., the variable precision intuitionistic fuzzy rough set model is presented based on the intuitionistic fuzzy inclusion sets and intuitionistic fuzzy inclusion ratio which are defined in this paper, and by employing the intuitionistic fuzzy implicator and the intuitionistic fuzzy t-norm. Meanwhile, the approximation quality and attribute reduction of the variable precision intuitionistic fuzzy rough sets are defined. It shows that the results obtained in this paper extend the previous related conclusions. Finally, an example is given to illustrate our results.

ARROW-TYPE RESULTS UNDER INTUITIONISTIC FUZZY PREFERENCES

Fono et al.11 characterized, for an intuitionistic fuzzy t-norm [Formula: see text], two properties of a given regular intuitionistic fuzzy strict component of a (T,S)-transitive intuitionistic fuzzy preference. In this paper, we examine these characterizations in the particular case where [Formula: see text]. We then use these (general and particular) results to obtain some intuitionistic fuzzy versions of Arrow's impossibility theorem. Therefore, by weakening a requirement to social preferences, we deduce a positive result, that is, we display an example of a non-dictatorial Intuitionistic Fuzzy Agregation Rule (IFAR) and, we establish an intuitionistic fuzzy version of Gibbard's oligarchy theorem.

A general frame for intuitionistic fuzzy rough sets

Intuitionistic fuzzy rough sets are investigated in a general framework which includes generalizations of many related results in early literatures. A new definition of intuitionistic fuzzy rough sets is given with the analysis of its basic properties based on the notion of two universes, general binary relations, and a pair (T, I) of intuitionistic fuzzy t-norm T and intuitionistic fuzzy implicator I. For t-representable intuitionistic fuzzy t-norms and its residual implicators, intuitionistic fuzzy rough approximation operators are defined by axioms, and its connections with special intuitionistic fuzzy relations are investigated.

A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components

We establish, by means of a large class of continuous t-representable intuitionistic fuzzy t-conorms, a factorization of an intuitionistic fuzzy relation (IFR) into a unique indifference component and a family of regular strict components. This result generalizes a previous factorization obtained by Dimitrov (2002) with the intuitionistic fuzzy t-conorm. We provide, for a continuous t-representable intuitionistic fuzzy t-norm , a characterization of the -transitivity of an IFR. This enables us to determine necessary and sufficient conditions on a -transitive IFR under which a strict component of satisfies pos-transitivity and negative transitivity.

Intuitionistic fuzzy rough sets based on residuation implication of T-norms

This paper researched and constructed residuation implication operator of intuitionistic fuzzy T-norms.Based on this,the paper deducted the intuitionistic fuzzy rough sets model,and proved that the Pawlak rough sets,intuitionistic fuzzy sets,fuzzy rough sets,rough fuzzy sets and fuzzy T-norms rough sets were special cases of intuitionistic fuzzy rough sets.At last,some properties of intuitionistic fuzzy sets were presented and proved.

On the Representation of Intuitionistic Fuzzy>tex<$t$>/tex<-Norms and>tex<$t$>/tex<-Conorms

Intuitionistic fuzzy sets form an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a nonmembership degree. The only constraint on those two degrees is that their sum must be smaller than or equal to 1. In fuzzy set theory, an important class of triangular norms and conorms is the class of continuous Archimedean nilpotent triangular norms and conorms. It has been shown that for such t-norms T there exists a permutation /spl phi/ of [0,1] such that T is the /spl phi/-transform of the Lukasiewicz t-norm. In this paper we introduce the notion of intuitionistic fuzzy t-norm and t-conorm, and investigate under which conditions a similar representation theorem can be obtained.

CLASSES OF INTUITIONISTIC FUZZY T-NORMS SATISFYING THE RESIDUATION PRINCIPLE

Intuitionistic fuzzy sets constitute an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a non-membership degree. The only constraint on those two degrees is that the sum must be smaller than or equal to 1. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In the fuzzy case a t-norm satisfies the residuation principle if and only if it is left-continuous. Deschrijver, Cornelis and Kerre proved that for intuitionistic fuzzy t-norms the equivalence between the residuation principle and intuitionistic fuzzy left-continuity only holds for t-representable t-norms.1 In this paper we construct particular subclasses of intuitionistic fuzzy t-norms that satisfy the residuation principle but that are not t-representable and we show that a continuous intuitionistic fuzzy t-norm [Formula: see text] satisfying the residuation principle is t-representable if and only if [Formula: see text].