Probabilistic and fuzzy choice theory are used to describe decision situations in which a certain degree of imprecision is involved. In this work we propose a correspondence between probabilistic and fuzzy choice functions, based on implication operators. Given a probabilistic choice function a fuzzy choice function can be constructed and, furthermore, a new set of rationality conditions is pro...

This paper presents a fuzzy optimization method based on the inclusion degrees of intuitionistic fuzzy sets to solve multi-criteria decision making problems under fuzzy environments. First, the inclusion degree of intuitionistic fuzzy sets is defined and a series of specific formulas of inclusion degree are presented by means of the normal implication operators. Some formulas of inclusion degre...

The concept of quasi-coincidence of interval valued fuzzy point with an interval valued fuzzy subset has considered. By using this idea, the notion of interval valued (α, β)-fuzzy hyperideal in a semihyperring introduced and consequently, a generalization of interval valued fuzzy hyperideals and interval valued fuzzy hyperideals have defined. In this paper, we study the related properties of th...

is obvious, and then what always hold in the Mamdani's case is the equivalence (p 2 q ! r) = (p ! r) ^ (q ! r): (14) Consequently, if I is a Mamdani–Larsen's implication (8) never holds, but (14) is always true. IV. CONCLUSION After remembering the four main types of implications used in Fuzzy Logic, the equality [p ^ q ! r] = [(p ! r) _ (q ! r)] (*) is analyzed bot in complemented lattices and...

Some open problems on fuzzy implications dealing with the so-called importation law are studied and totally or partially solved in this work. In particular, it is proved that such property (in fact a weaker version than the law of importation) is stronger than the exchange principle. Along this study, new characterizations of (S,N)-implications and R-implications involving the law of importatio...

This paper presents a study on inference in a Fuzzy Logic Controller (FLC). Inference is made up of interpretation, implication, combination and defuzzification. These last two steps can be performed in two sequences. An explanation, through approximate reasoning, on how to implement other than the welìknown Mamdani and Larsen implications is given. (Dis)advantages of several combinations of im...

1 Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320 Pakistan 2 The Foundation Department Sur University College P.O. Box 440 P.C 411, Sur, Muscat, Sultanate of Oman Abstract: The concept of quasi-coincidence of fuzzy point with a fuzzy subset has considered. By using this idea, the notion of (, )-fuzzy hyperideal in a semihyperring introduced and consequently, a generalizat...

This paper presents a study on inference in a Fuzzy Logic Controller (FLC). Inference is made up of interpretation, implication, combination and defuzzification. These last two steps can be performed in two sequences. An explanation, through approximate reasoning, on how to implement other than the welìknown Mamdani and Larsen implications is given. (Dis)advantages of several combinations of im...

Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed by Zadeh [1] in our ...

Yager introduced a fuzzy screening procedure to select, from a large class of alternatives, a small subset to be further investigated. In his methodology the Kleene-Dienes implication operator was employed to find the unit score of each alternative by each expert. Generalizing Yager’s principle we suggest the use of Sand R-implication operators to find the unit score.