Samina Ashraf

Numerical representation of product transitive complete fuzzy orderings

Let X be a space of alternatives with a preference relation in the form of product transitive complete fuzzy ordering R. We prove existence of continuous utility functions for R.

Group Decision Making by Using Incomplete Fuzzy Preference Relations Based on T-Consistency and the Order Consistency

The existing group decision making techniques may not satisfy the order consistency for aggregation in some cases. The algorithm proposed in this paper overcomes the weaknesses of the existing techniques. The method determines the unknown preferences for group decision making in such a manner that the resulting matrix is T‐consistent and order consistent simultaneously.

Fuzzy Similarity And Measure Of Similarity With Lukasiewicz Implicator

Given a universe of discourse X. A fuzzy similarity mapping ST,Inc : F(X) × F(X) → F(X) is defined, where F(X) denotes the set of all fuzzy subsets of X. Mapping ST,Inc maps two fuzzy sets A and B to a fuzzy set ST,Inc(A,B) in X called their fuzzy set of similarity. A measure of similarity between A and B is then obtained by applying the composite of fuzzy measure and fuzzy similarity mapping on the pair (A,B). Several properties of fuzzy set of similarity and the measure of fuzzy similarity are obtained within the framework of Lukasiewicz fuzzy implicator and its respective t-norm and t-conorm. Many examples of measure of similarity are also constructed.

Fuzzy dissimilarity and distance functions

Abstractε-fuzzy dissimilarity relation is defined by using the concept of ε- fuzzy equivalence relation and a strong negator. It is proved that the ε- fuzzy dissimilarity relation so defined satisfies inequalities resembling to generalized triangle inequality.

Fuzzy dissimilarity and generalization of Valverde's theorem on T-indistinguishability relations

Similarity and dissimilarity between fuzzy sets are popular notions in decision making problems. This paper studies the representations of ?-fuzzy dissimilarity relations as the counter part of ?-fuzzy equivalence relations. It is proved that these newly defined ?-fuzzy dissimilarity relations satisfy the axioms of self dissimilarity and symmetry along with certain inequalities which transform into Valverdes representation theorem in the particular case when the given relation is 1-fuzzy transitive.

Fuzzy Transitivity and Monotonicity of Cardinality-based Similarity Measures

The interrelationship of notions is presented in fuzzy transitivity and monotonicity of fuzzy similarity measures. It is observed that the axiom of fuzzy transitivity may replace that of monotonicity in the definition of fuzzy similarity measures.

Group Decision Making with Incomplete Reciprocal Preference Relations Based on Multiplicative Consistency

This paper comprises a new iterative method for multi-person decision making based on multiplicative consistency with incomplete reciprocal preference relations (IRPRs). Additionally, multiplicative transitivity property of reciprocal preference relation (RPR) is used at the first level to estimate the unknown preference values and get the complete preference relation, then it is confirmed to be multiplicative consistent by using transitive closure formula. Following this, experts weights are evaluated by merging consistency and trust weights. The consistency weights against the experts are evaluated through multiplicative consistency investigation of the preferences given by each expert, while trust weights play the role to measure the level of trust for an expert. The consensus process determines whether the selection procedure should start or not. If it results in negative, the feedback mechanism is used to enhance the consensus degree. At the end, a numerical example is given to demonstrate the efficiency and practicality of the proposed method.

FUZZY INCLUSION AND FUZZY SIMILARITY WITH GÖDEL FUZZY IMPLICATOR

Fuzzy inclusion and fuzzy similarity are introduced as mappings which produce fuzzy sets constructed with the help of Godel implicator. The properties of resulting fuzzy sets of inclusion and similarity are studied in detail. Some axiomatic characteristics for being fuzzy orders and fuzzy equivalence relations are also included.