The fuzzy logic deals incomplete information with belief rather than probability. The fuzzy propositions deal with incomplete information. In this paper, a new representation of fizzy set typ-2, fuzzy set α-cut and fuzzy temporal set occurs in fuzzy propositions. These fuzzy quantifiers set, fizzy set typ-2, fuzzy set α-cut ,fuzzy temporal sets, fuzzy granular sets and fuzzy rough sets are studied. These are generalized and quantified under single category. This work is only trying to overcome difficulties in computations.
Zadeh defined fuzzy sets for incomplete information with single fuzzy membership. REN Ping has defined Generalized fuzzy set with two fold membership functions "True" and "False". In this paper Zadeh fuzzy logic is extended to REN Ping generalize fuzzy logic for incomplete information. Generalized fuzzy logic, fuzzy inference and fuzzy reasoning are discussed using Feneralized fuzzy sets. Generalized Fuzzy Certainty Factor(GFCF) is studied as the difference of "True " and "False" fuzzy membership functions to eliminate the conflict of evidence in Incomplete Information. The fuzzy truth variables are also discussed for Generalised fuzzy sets.
Computer programs are now acceptable in Medicine. Artificial Intelligence in Medicine will perform better medical diagnosis and better surgery. Surgery intelligence is supporting system for the surgeon to take decision. Information available to the surgery is incomplete. The fuzzy logic deals incomplete information with belief rather than likelihood (probability). In this paper, fuzzy conditional inference is discussed. The fuzzy logic with two membership functions will give more evidence than single membership function. Generalized fuzzy logic is discussed with two membership functions. Generalized fuzzy certainty factor is discussed to eliminate conflict between two membership functions. The medical diagnosis is studied as an example. The fuzzy decision set is studied for decision making. The surgery intelligence is studied as an application.
Let [Formula: see text] be a simple, undirected and connected graph. A vertex [Formula: see text] of a simple, undirected graph [Formula: see text]-dominates all edges incident to at least one vertex in its closed neighborhood [Formula: see text]. A set [Formula: see text] of vertices is a vertex-edge dominating set of [Formula: see text], if every edge of graph [Formula: see text] is [Formula: see text]-dominated by some vertex of [Formula: see text]. A vertex-edge dominating set [Formula: see text] of [Formula: see text] is called a total vertex-edge dominating set if the induced subgraph [Formula: see text] has no isolated vertices. The total vertex-edge domination number [Formula: see text] is the minimum cardinality of a total vertex-edge dominating set of [Formula: see text]. In this paper, we prove that the decision problem corresponding to [Formula: see text] is NP-complete for chordal graphs, star convex bipartite graphs, comb convex bipartite graphs and planar graphs. The problem of determining [Formula: see text] of a graph [Formula: see text] is called the minimum total vertex-edge domination problem (MTVEDP). We prove that MTVEDP is linear time solvable for chain graphs and threshold graphs. We also show that MTVEDP can be approximated within approximation ratio of [Formula: see text]. It is shown that the domination and total vertex-edge domination problems are not equivalent in computational complexity aspects. Finally, an integer linear programming formulation for MTVEDP is presented.
Indian languages have long history. Brahmini language, the Indian fist script. Sanskrit is the fist Indian language Panini’s was the first to propose Grammar for Sanskrit language with about 4000 rules in sixth century BC. The Natural Languages are possible to processes with the English character set. It is possible to process Sanskrit languages by translating in to English character set the fundamental aspect of Natural language processing is Knowledge representation. In this paper Sanskrit language is represented in First Order Predicate Logic using English character set by using Om Transliteration. Sanskrit language is processed for Bhagavad Gita with the Logic Programming.
The information available to the system is incomplete in many applications like Decision Support Systems, Control Systems and Medical Expert Systems. Sometimes decision has to be taken under risk with incomplete information. Fuzzy logic deals with incomplete information with belief rather than likelihood (probability). The fuzzy set is defined with single membership function. The fuzzy set with two membership functions will give more information than single membership function. In this paper, the Fuzzy Certainty Factor (FCF) is studied as difference between fuzzy membership functions "true" and "false" for decision making. The fuzzy certainty factor is studied for fuzzy risk set. The fuzzy inference is studied. Business application is given as an application to fuzzy risk set.
Indian languages have long history in World Natural languages. Panini was the first to define Grammar for Sanskrit language with about 4000 rules in fifth century. These rules contain uncertainty information. It is not possible to Computer processing of Sanskrit language with uncertain information. In this paper, fuzzy logic and fuzzy reasoning are proposed to deal to eliminate uncertain information for reasoning with Sanskrit grammar. The Sanskrit language processing is also discussed in this paper.
Sometimes AI has to deal with incomplete problems. Knowledge Representation is the main component to solve the problems in AI. Various Knowledge representation techniques are available to deal with complete information in Artificial Intelligence. The Knowledge Representation is necessary to deal with incomplete information. Many theories deal with incomplete information is based on Probable (Likelihood) where as fuzzy logic is based on the commonsense and belief. In this paper Fuzzy Knowledge Representation is proposed to deal with the incomplete information. The fuzzy propositions are transformed in to fuzzy modulations and transformed in to Fuzzy Predicate Logic (FPL). The Fuzzy Automated Reasoning is studied using Fuzzy Predicate Logic. The programming in Prolog is given for FPL.
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